Properties

Label 637.2.k.a.569.1
Level $637$
Weight $2$
Character 637.569
Analytic conductor $5.086$
Analytic rank $1$
Dimension $2$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [637,2,Mod(459,637)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(637, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([4, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("637.459");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 637 = 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 637.k (of order \(6\), 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: \(5.08647060876\)
Analytic rank: \(1\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 13)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 569.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 637.569
Dual form 637.2.k.a.459.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.73205i q^{2} +(-1.00000 + 1.73205i) q^{3} -1.00000 q^{4} +(-1.50000 - 0.866025i) q^{5} +(3.00000 + 1.73205i) q^{6} -1.73205i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q-1.73205i q^{2} +(-1.00000 + 1.73205i) q^{3} -1.00000 q^{4} +(-1.50000 - 0.866025i) q^{5} +(3.00000 + 1.73205i) q^{6} -1.73205i q^{8} +(-0.500000 - 0.866025i) q^{9} +(-1.50000 + 2.59808i) q^{10} +(1.00000 - 1.73205i) q^{12} +(-2.50000 + 2.59808i) q^{13} +(3.00000 - 1.73205i) q^{15} -5.00000 q^{16} -3.00000 q^{17} +(-1.50000 + 0.866025i) q^{18} +(3.00000 - 1.73205i) q^{19} +(1.50000 + 0.866025i) q^{20} -6.00000 q^{23} +(3.00000 + 1.73205i) q^{24} +(-1.00000 - 1.73205i) q^{25} +(4.50000 + 4.33013i) q^{26} -4.00000 q^{27} +(-1.50000 - 2.59808i) q^{29} +(-3.00000 - 5.19615i) q^{30} +(-3.00000 + 1.73205i) q^{31} +5.19615i q^{32} +5.19615i q^{34} +(0.500000 + 0.866025i) q^{36} +8.66025i q^{37} +(-3.00000 - 5.19615i) q^{38} +(-2.00000 - 6.92820i) q^{39} +(-1.50000 + 2.59808i) q^{40} +(-4.50000 + 2.59808i) q^{41} +(-4.00000 + 6.92820i) q^{43} +1.73205i q^{45} +10.3923i q^{46} +(-3.00000 - 1.73205i) q^{47} +(5.00000 - 8.66025i) q^{48} +(-3.00000 + 1.73205i) q^{50} +(3.00000 - 5.19615i) q^{51} +(2.50000 - 2.59808i) q^{52} +(1.50000 + 2.59808i) q^{53} +6.92820i q^{54} +6.92820i q^{57} +(-4.50000 + 2.59808i) q^{58} -6.92820i q^{59} +(-3.00000 + 1.73205i) q^{60} +(-0.500000 - 0.866025i) q^{61} +(3.00000 + 5.19615i) q^{62} -1.00000 q^{64} +(6.00000 - 1.73205i) q^{65} +(-3.00000 - 1.73205i) q^{67} +3.00000 q^{68} +(6.00000 - 10.3923i) q^{69} +(3.00000 + 1.73205i) q^{71} +(-1.50000 + 0.866025i) q^{72} +(-1.50000 + 0.866025i) q^{73} +15.0000 q^{74} +4.00000 q^{75} +(-3.00000 + 1.73205i) q^{76} +(-12.0000 + 3.46410i) q^{78} +(-2.00000 + 3.46410i) q^{79} +(7.50000 + 4.33013i) q^{80} +(5.50000 - 9.52628i) q^{81} +(4.50000 + 7.79423i) q^{82} -13.8564i q^{83} +(4.50000 + 2.59808i) q^{85} +(12.0000 + 6.92820i) q^{86} +6.00000 q^{87} -6.92820i q^{89} +3.00000 q^{90} +6.00000 q^{92} -6.92820i q^{93} +(-3.00000 + 5.19615i) q^{94} -6.00000 q^{95} +(-9.00000 - 5.19615i) q^{96} +(6.00000 + 3.46410i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 2 q^{3} - 2 q^{4} - 3 q^{5} + 6 q^{6} - q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 2 q^{3} - 2 q^{4} - 3 q^{5} + 6 q^{6} - q^{9} - 3 q^{10} + 2 q^{12} - 5 q^{13} + 6 q^{15} - 10 q^{16} - 6 q^{17} - 3 q^{18} + 6 q^{19} + 3 q^{20} - 12 q^{23} + 6 q^{24} - 2 q^{25} + 9 q^{26} - 8 q^{27} - 3 q^{29} - 6 q^{30} - 6 q^{31} + q^{36} - 6 q^{38} - 4 q^{39} - 3 q^{40} - 9 q^{41} - 8 q^{43} - 6 q^{47} + 10 q^{48} - 6 q^{50} + 6 q^{51} + 5 q^{52} + 3 q^{53} - 9 q^{58} - 6 q^{60} - q^{61} + 6 q^{62} - 2 q^{64} + 12 q^{65} - 6 q^{67} + 6 q^{68} + 12 q^{69} + 6 q^{71} - 3 q^{72} - 3 q^{73} + 30 q^{74} + 8 q^{75} - 6 q^{76} - 24 q^{78} - 4 q^{79} + 15 q^{80} + 11 q^{81} + 9 q^{82} + 9 q^{85} + 24 q^{86} + 12 q^{87} + 6 q^{90} + 12 q^{92} - 6 q^{94} - 12 q^{95} - 18 q^{96} + 12 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(248\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.73205i 1.22474i −0.790569 0.612372i \(-0.790215\pi\)
0.790569 0.612372i \(-0.209785\pi\)
\(3\) −1.00000 + 1.73205i −0.577350 + 1.00000i 0.418432 + 0.908248i \(0.362580\pi\)
−0.995782 + 0.0917517i \(0.970753\pi\)
\(4\) −1.00000 −0.500000
\(5\) −1.50000 0.866025i −0.670820 0.387298i 0.125567 0.992085i \(-0.459925\pi\)
−0.796387 + 0.604787i \(0.793258\pi\)
\(6\) 3.00000 + 1.73205i 1.22474 + 0.707107i
\(7\) 0 0
\(8\) 1.73205i 0.612372i
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) −1.50000 + 2.59808i −0.474342 + 0.821584i
\(11\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(12\) 1.00000 1.73205i 0.288675 0.500000i
\(13\) −2.50000 + 2.59808i −0.693375 + 0.720577i
\(14\) 0 0
\(15\) 3.00000 1.73205i 0.774597 0.447214i
\(16\) −5.00000 −1.25000
\(17\) −3.00000 −0.727607 −0.363803 0.931476i \(-0.618522\pi\)
−0.363803 + 0.931476i \(0.618522\pi\)
\(18\) −1.50000 + 0.866025i −0.353553 + 0.204124i
\(19\) 3.00000 1.73205i 0.688247 0.397360i −0.114708 0.993399i \(-0.536593\pi\)
0.802955 + 0.596040i \(0.203260\pi\)
\(20\) 1.50000 + 0.866025i 0.335410 + 0.193649i
\(21\) 0 0
\(22\) 0 0
\(23\) −6.00000 −1.25109 −0.625543 0.780189i \(-0.715123\pi\)
−0.625543 + 0.780189i \(0.715123\pi\)
\(24\) 3.00000 + 1.73205i 0.612372 + 0.353553i
\(25\) −1.00000 1.73205i −0.200000 0.346410i
\(26\) 4.50000 + 4.33013i 0.882523 + 0.849208i
\(27\) −4.00000 −0.769800
\(28\) 0 0
\(29\) −1.50000 2.59808i −0.278543 0.482451i 0.692480 0.721437i \(-0.256518\pi\)
−0.971023 + 0.238987i \(0.923185\pi\)
\(30\) −3.00000 5.19615i −0.547723 0.948683i
\(31\) −3.00000 + 1.73205i −0.538816 + 0.311086i −0.744599 0.667512i \(-0.767359\pi\)
0.205783 + 0.978598i \(0.434026\pi\)
\(32\) 5.19615i 0.918559i
\(33\) 0 0
\(34\) 5.19615i 0.891133i
\(35\) 0 0
\(36\) 0.500000 + 0.866025i 0.0833333 + 0.144338i
\(37\) 8.66025i 1.42374i 0.702313 + 0.711868i \(0.252151\pi\)
−0.702313 + 0.711868i \(0.747849\pi\)
\(38\) −3.00000 5.19615i −0.486664 0.842927i
\(39\) −2.00000 6.92820i −0.320256 1.10940i
\(40\) −1.50000 + 2.59808i −0.237171 + 0.410792i
\(41\) −4.50000 + 2.59808i −0.702782 + 0.405751i −0.808383 0.588657i \(-0.799657\pi\)
0.105601 + 0.994409i \(0.466323\pi\)
\(42\) 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
\(45\) 1.73205i 0.258199i
\(46\) 10.3923i 1.53226i
\(47\) −3.00000 1.73205i −0.437595 0.252646i 0.264982 0.964253i \(-0.414634\pi\)
−0.702577 + 0.711608i \(0.747967\pi\)
\(48\) 5.00000 8.66025i 0.721688 1.25000i
\(49\) 0 0
\(50\) −3.00000 + 1.73205i −0.424264 + 0.244949i
\(51\) 3.00000 5.19615i 0.420084 0.727607i
\(52\) 2.50000 2.59808i 0.346688 0.360288i
\(53\) 1.50000 + 2.59808i 0.206041 + 0.356873i 0.950464 0.310835i \(-0.100609\pi\)
−0.744423 + 0.667708i \(0.767275\pi\)
\(54\) 6.92820i 0.942809i
\(55\) 0 0
\(56\) 0 0
\(57\) 6.92820i 0.917663i
\(58\) −4.50000 + 2.59808i −0.590879 + 0.341144i
\(59\) 6.92820i 0.901975i −0.892530 0.450988i \(-0.851072\pi\)
0.892530 0.450988i \(-0.148928\pi\)
\(60\) −3.00000 + 1.73205i −0.387298 + 0.223607i
\(61\) −0.500000 0.866025i −0.0640184 0.110883i 0.832240 0.554416i \(-0.187058\pi\)
−0.896258 + 0.443533i \(0.853725\pi\)
\(62\) 3.00000 + 5.19615i 0.381000 + 0.659912i
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 6.00000 1.73205i 0.744208 0.214834i
\(66\) 0 0
\(67\) −3.00000 1.73205i −0.366508 0.211604i 0.305424 0.952217i \(-0.401202\pi\)
−0.671932 + 0.740613i \(0.734535\pi\)
\(68\) 3.00000 0.363803
\(69\) 6.00000 10.3923i 0.722315 1.25109i
\(70\) 0 0
\(71\) 3.00000 + 1.73205i 0.356034 + 0.205557i 0.667340 0.744753i \(-0.267433\pi\)
−0.311305 + 0.950310i \(0.600766\pi\)
\(72\) −1.50000 + 0.866025i −0.176777 + 0.102062i
\(73\) −1.50000 + 0.866025i −0.175562 + 0.101361i −0.585206 0.810885i \(-0.698986\pi\)
0.409644 + 0.912245i \(0.365653\pi\)
\(74\) 15.0000 1.74371
\(75\) 4.00000 0.461880
\(76\) −3.00000 + 1.73205i −0.344124 + 0.198680i
\(77\) 0 0
\(78\) −12.0000 + 3.46410i −1.35873 + 0.392232i
\(79\) −2.00000 + 3.46410i −0.225018 + 0.389742i −0.956325 0.292306i \(-0.905577\pi\)
0.731307 + 0.682048i \(0.238911\pi\)
\(80\) 7.50000 + 4.33013i 0.838525 + 0.484123i
\(81\) 5.50000 9.52628i 0.611111 1.05848i
\(82\) 4.50000 + 7.79423i 0.496942 + 0.860729i
\(83\) 13.8564i 1.52094i −0.649374 0.760469i \(-0.724969\pi\)
0.649374 0.760469i \(-0.275031\pi\)
\(84\) 0 0
\(85\) 4.50000 + 2.59808i 0.488094 + 0.281801i
\(86\) 12.0000 + 6.92820i 1.29399 + 0.747087i
\(87\) 6.00000 0.643268
\(88\) 0 0
\(89\) 6.92820i 0.734388i −0.930144 0.367194i \(-0.880318\pi\)
0.930144 0.367194i \(-0.119682\pi\)
\(90\) 3.00000 0.316228
\(91\) 0 0
\(92\) 6.00000 0.625543
\(93\) 6.92820i 0.718421i
\(94\) −3.00000 + 5.19615i −0.309426 + 0.535942i
\(95\) −6.00000 −0.615587
\(96\) −9.00000 5.19615i −0.918559 0.530330i
\(97\) 6.00000 + 3.46410i 0.609208 + 0.351726i 0.772655 0.634826i \(-0.218928\pi\)
−0.163448 + 0.986552i \(0.552261\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 1.00000 + 1.73205i 0.100000 + 0.173205i
\(101\) 1.50000 2.59808i 0.149256 0.258518i −0.781697 0.623658i \(-0.785646\pi\)
0.930953 + 0.365140i \(0.118979\pi\)
\(102\) −9.00000 5.19615i −0.891133 0.514496i
\(103\) 5.00000 8.66025i 0.492665 0.853320i −0.507300 0.861770i \(-0.669356\pi\)
0.999964 + 0.00844953i \(0.00268960\pi\)
\(104\) 4.50000 + 4.33013i 0.441261 + 0.424604i
\(105\) 0 0
\(106\) 4.50000 2.59808i 0.437079 0.252347i
\(107\) 6.00000 0.580042 0.290021 0.957020i \(-0.406338\pi\)
0.290021 + 0.957020i \(0.406338\pi\)
\(108\) 4.00000 0.384900
\(109\) 12.0000 6.92820i 1.14939 0.663602i 0.200653 0.979662i \(-0.435694\pi\)
0.948739 + 0.316061i \(0.102360\pi\)
\(110\) 0 0
\(111\) −15.0000 8.66025i −1.42374 0.821995i
\(112\) 0 0
\(113\) 7.50000 12.9904i 0.705541 1.22203i −0.260955 0.965351i \(-0.584038\pi\)
0.966496 0.256681i \(-0.0826291\pi\)
\(114\) 12.0000 1.12390
\(115\) 9.00000 + 5.19615i 0.839254 + 0.484544i
\(116\) 1.50000 + 2.59808i 0.139272 + 0.241225i
\(117\) 3.50000 + 0.866025i 0.323575 + 0.0800641i
\(118\) −12.0000 −1.10469
\(119\) 0 0
\(120\) −3.00000 5.19615i −0.273861 0.474342i
\(121\) −5.50000 9.52628i −0.500000 0.866025i
\(122\) −1.50000 + 0.866025i −0.135804 + 0.0784063i
\(123\) 10.3923i 0.937043i
\(124\) 3.00000 1.73205i 0.269408 0.155543i
\(125\) 12.1244i 1.08444i
\(126\) 0 0
\(127\) 1.00000 + 1.73205i 0.0887357 + 0.153695i 0.906977 0.421180i \(-0.138384\pi\)
−0.818241 + 0.574875i \(0.805051\pi\)
\(128\) 12.1244i 1.07165i
\(129\) −8.00000 13.8564i −0.704361 1.21999i
\(130\) −3.00000 10.3923i −0.263117 0.911465i
\(131\) −9.00000 + 15.5885i −0.786334 + 1.36197i 0.141865 + 0.989886i \(0.454690\pi\)
−0.928199 + 0.372084i \(0.878643\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −3.00000 + 5.19615i −0.259161 + 0.448879i
\(135\) 6.00000 + 3.46410i 0.516398 + 0.298142i
\(136\) 5.19615i 0.445566i
\(137\) 15.5885i 1.33181i 0.746036 + 0.665906i \(0.231955\pi\)
−0.746036 + 0.665906i \(0.768045\pi\)
\(138\) −18.0000 10.3923i −1.53226 0.884652i
\(139\) 2.00000 3.46410i 0.169638 0.293821i −0.768655 0.639664i \(-0.779074\pi\)
0.938293 + 0.345843i \(0.112407\pi\)
\(140\) 0 0
\(141\) 6.00000 3.46410i 0.505291 0.291730i
\(142\) 3.00000 5.19615i 0.251754 0.436051i
\(143\) 0 0
\(144\) 2.50000 + 4.33013i 0.208333 + 0.360844i
\(145\) 5.19615i 0.431517i
\(146\) 1.50000 + 2.59808i 0.124141 + 0.215018i
\(147\) 0 0
\(148\) 8.66025i 0.711868i
\(149\) 16.5000 9.52628i 1.35173 0.780423i 0.363241 0.931695i \(-0.381670\pi\)
0.988492 + 0.151272i \(0.0483370\pi\)
\(150\) 6.92820i 0.565685i
\(151\) −15.0000 + 8.66025i −1.22068 + 0.704761i −0.965064 0.262016i \(-0.915613\pi\)
−0.255619 + 0.966778i \(0.582279\pi\)
\(152\) −3.00000 5.19615i −0.243332 0.421464i
\(153\) 1.50000 + 2.59808i 0.121268 + 0.210042i
\(154\) 0 0
\(155\) 6.00000 0.481932
\(156\) 2.00000 + 6.92820i 0.160128 + 0.554700i
\(157\) 6.50000 + 11.2583i 0.518756 + 0.898513i 0.999762 + 0.0217953i \(0.00693820\pi\)
−0.481006 + 0.876717i \(0.659728\pi\)
\(158\) 6.00000 + 3.46410i 0.477334 + 0.275589i
\(159\) −6.00000 −0.475831
\(160\) 4.50000 7.79423i 0.355756 0.616188i
\(161\) 0 0
\(162\) −16.5000 9.52628i −1.29636 0.748455i
\(163\) −18.0000 + 10.3923i −1.40987 + 0.813988i −0.995375 0.0960641i \(-0.969375\pi\)
−0.414494 + 0.910052i \(0.636041\pi\)
\(164\) 4.50000 2.59808i 0.351391 0.202876i
\(165\) 0 0
\(166\) −24.0000 −1.86276
\(167\) −12.0000 + 6.92820i −0.928588 + 0.536120i −0.886365 0.462988i \(-0.846777\pi\)
−0.0422232 + 0.999108i \(0.513444\pi\)
\(168\) 0 0
\(169\) −0.500000 12.9904i −0.0384615 0.999260i
\(170\) 4.50000 7.79423i 0.345134 0.597790i
\(171\) −3.00000 1.73205i −0.229416 0.132453i
\(172\) 4.00000 6.92820i 0.304997 0.528271i
\(173\) −3.00000 5.19615i −0.228086 0.395056i 0.729155 0.684349i \(-0.239913\pi\)
−0.957241 + 0.289292i \(0.906580\pi\)
\(174\) 10.3923i 0.787839i
\(175\) 0 0
\(176\) 0 0
\(177\) 12.0000 + 6.92820i 0.901975 + 0.520756i
\(178\) −12.0000 −0.899438
\(179\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(180\) 1.73205i 0.129099i
\(181\) 11.0000 0.817624 0.408812 0.912619i \(-0.365943\pi\)
0.408812 + 0.912619i \(0.365943\pi\)
\(182\) 0 0
\(183\) 2.00000 0.147844
\(184\) 10.3923i 0.766131i
\(185\) 7.50000 12.9904i 0.551411 0.955072i
\(186\) −12.0000 −0.879883
\(187\) 0 0
\(188\) 3.00000 + 1.73205i 0.218797 + 0.126323i
\(189\) 0 0
\(190\) 10.3923i 0.753937i
\(191\) −9.00000 15.5885i −0.651217 1.12794i −0.982828 0.184525i \(-0.940925\pi\)
0.331611 0.943416i \(-0.392408\pi\)
\(192\) 1.00000 1.73205i 0.0721688 0.125000i
\(193\) 4.50000 + 2.59808i 0.323917 + 0.187014i 0.653137 0.757240i \(-0.273452\pi\)
−0.329220 + 0.944253i \(0.606786\pi\)
\(194\) 6.00000 10.3923i 0.430775 0.746124i
\(195\) −3.00000 + 12.1244i −0.214834 + 0.868243i
\(196\) 0 0
\(197\) 12.0000 6.92820i 0.854965 0.493614i −0.00735824 0.999973i \(-0.502342\pi\)
0.862323 + 0.506359i \(0.169009\pi\)
\(198\) 0 0
\(199\) −2.00000 −0.141776 −0.0708881 0.997484i \(-0.522583\pi\)
−0.0708881 + 0.997484i \(0.522583\pi\)
\(200\) −3.00000 + 1.73205i −0.212132 + 0.122474i
\(201\) 6.00000 3.46410i 0.423207 0.244339i
\(202\) −4.50000 2.59808i −0.316619 0.182800i
\(203\) 0 0
\(204\) −3.00000 + 5.19615i −0.210042 + 0.363803i
\(205\) 9.00000 0.628587
\(206\) −15.0000 8.66025i −1.04510 0.603388i
\(207\) 3.00000 + 5.19615i 0.208514 + 0.361158i
\(208\) 12.5000 12.9904i 0.866719 0.900721i
\(209\) 0 0
\(210\) 0 0
\(211\) −5.00000 8.66025i −0.344214 0.596196i 0.640996 0.767544i \(-0.278521\pi\)
−0.985211 + 0.171347i \(0.945188\pi\)
\(212\) −1.50000 2.59808i −0.103020 0.178437i
\(213\) −6.00000 + 3.46410i −0.411113 + 0.237356i
\(214\) 10.3923i 0.710403i
\(215\) 12.0000 6.92820i 0.818393 0.472500i
\(216\) 6.92820i 0.471405i
\(217\) 0 0
\(218\) −12.0000 20.7846i −0.812743 1.40771i
\(219\) 3.46410i 0.234082i
\(220\) 0 0
\(221\) 7.50000 7.79423i 0.504505 0.524297i
\(222\) −15.0000 + 25.9808i −1.00673 + 1.74371i
\(223\) −9.00000 + 5.19615i −0.602685 + 0.347960i −0.770097 0.637927i \(-0.779792\pi\)
0.167412 + 0.985887i \(0.446459\pi\)
\(224\) 0 0
\(225\) −1.00000 + 1.73205i −0.0666667 + 0.115470i
\(226\) −22.5000 12.9904i −1.49668 0.864107i
\(227\) 24.2487i 1.60944i −0.593652 0.804722i \(-0.702314\pi\)
0.593652 0.804722i \(-0.297686\pi\)
\(228\) 6.92820i 0.458831i
\(229\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(230\) 9.00000 15.5885i 0.593442 1.02787i
\(231\) 0 0
\(232\) −4.50000 + 2.59808i −0.295439 + 0.170572i
\(233\) −3.00000 + 5.19615i −0.196537 + 0.340411i −0.947403 0.320043i \(-0.896303\pi\)
0.750867 + 0.660454i \(0.229636\pi\)
\(234\) 1.50000 6.06218i 0.0980581 0.396297i
\(235\) 3.00000 + 5.19615i 0.195698 + 0.338960i
\(236\) 6.92820i 0.450988i
\(237\) −4.00000 6.92820i −0.259828 0.450035i
\(238\) 0 0
\(239\) 20.7846i 1.34444i 0.740349 + 0.672222i \(0.234660\pi\)
−0.740349 + 0.672222i \(0.765340\pi\)
\(240\) −15.0000 + 8.66025i −0.968246 + 0.559017i
\(241\) 1.73205i 0.111571i 0.998443 + 0.0557856i \(0.0177663\pi\)
−0.998443 + 0.0557856i \(0.982234\pi\)
\(242\) −16.5000 + 9.52628i −1.06066 + 0.612372i
\(243\) 5.00000 + 8.66025i 0.320750 + 0.555556i
\(244\) 0.500000 + 0.866025i 0.0320092 + 0.0554416i
\(245\) 0 0
\(246\) −18.0000 −1.14764
\(247\) −3.00000 + 12.1244i −0.190885 + 0.771454i
\(248\) 3.00000 + 5.19615i 0.190500 + 0.329956i
\(249\) 24.0000 + 13.8564i 1.52094 + 0.878114i
\(250\) 21.0000 1.32816
\(251\) 9.00000 15.5885i 0.568075 0.983935i −0.428681 0.903456i \(-0.641022\pi\)
0.996756 0.0804789i \(-0.0256450\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 3.00000 1.73205i 0.188237 0.108679i
\(255\) −9.00000 + 5.19615i −0.563602 + 0.325396i
\(256\) 19.0000 1.18750
\(257\) 3.00000 0.187135 0.0935674 0.995613i \(-0.470173\pi\)
0.0935674 + 0.995613i \(0.470173\pi\)
\(258\) −24.0000 + 13.8564i −1.49417 + 0.862662i
\(259\) 0 0
\(260\) −6.00000 + 1.73205i −0.372104 + 0.107417i
\(261\) −1.50000 + 2.59808i −0.0928477 + 0.160817i
\(262\) 27.0000 + 15.5885i 1.66807 + 0.963058i
\(263\) −6.00000 + 10.3923i −0.369976 + 0.640817i −0.989561 0.144112i \(-0.953967\pi\)
0.619586 + 0.784929i \(0.287301\pi\)
\(264\) 0 0
\(265\) 5.19615i 0.319197i
\(266\) 0 0
\(267\) 12.0000 + 6.92820i 0.734388 + 0.423999i
\(268\) 3.00000 + 1.73205i 0.183254 + 0.105802i
\(269\) −6.00000 −0.365826 −0.182913 0.983129i \(-0.558553\pi\)
−0.182913 + 0.983129i \(0.558553\pi\)
\(270\) 6.00000 10.3923i 0.365148 0.632456i
\(271\) 20.7846i 1.26258i 0.775549 + 0.631288i \(0.217473\pi\)
−0.775549 + 0.631288i \(0.782527\pi\)
\(272\) 15.0000 0.909509
\(273\) 0 0
\(274\) 27.0000 1.63113
\(275\) 0 0
\(276\) −6.00000 + 10.3923i −0.361158 + 0.625543i
\(277\) −7.00000 −0.420589 −0.210295 0.977638i \(-0.567442\pi\)
−0.210295 + 0.977638i \(0.567442\pi\)
\(278\) −6.00000 3.46410i −0.359856 0.207763i
\(279\) 3.00000 + 1.73205i 0.179605 + 0.103695i
\(280\) 0 0
\(281\) 22.5167i 1.34323i 0.740900 + 0.671616i \(0.234399\pi\)
−0.740900 + 0.671616i \(0.765601\pi\)
\(282\) −6.00000 10.3923i −0.357295 0.618853i
\(283\) −2.00000 + 3.46410i −0.118888 + 0.205919i −0.919327 0.393494i \(-0.871266\pi\)
0.800439 + 0.599414i \(0.204600\pi\)
\(284\) −3.00000 1.73205i −0.178017 0.102778i
\(285\) 6.00000 10.3923i 0.355409 0.615587i
\(286\) 0 0
\(287\) 0 0
\(288\) 4.50000 2.59808i 0.265165 0.153093i
\(289\) −8.00000 −0.470588
\(290\) 9.00000 0.528498
\(291\) −12.0000 + 6.92820i −0.703452 + 0.406138i
\(292\) 1.50000 0.866025i 0.0877809 0.0506803i
\(293\) 4.50000 + 2.59808i 0.262893 + 0.151781i 0.625653 0.780101i \(-0.284832\pi\)
−0.362761 + 0.931882i \(0.618166\pi\)
\(294\) 0 0
\(295\) −6.00000 + 10.3923i −0.349334 + 0.605063i
\(296\) 15.0000 0.871857
\(297\) 0 0
\(298\) −16.5000 28.5788i −0.955819 1.65553i
\(299\) 15.0000 15.5885i 0.867472 0.901504i
\(300\) −4.00000 −0.230940
\(301\) 0 0
\(302\) 15.0000 + 25.9808i 0.863153 + 1.49502i
\(303\) 3.00000 + 5.19615i 0.172345 + 0.298511i
\(304\) −15.0000 + 8.66025i −0.860309 + 0.496700i
\(305\) 1.73205i 0.0991769i
\(306\) 4.50000 2.59808i 0.257248 0.148522i
\(307\) 17.3205i 0.988534i 0.869310 + 0.494267i \(0.164563\pi\)
−0.869310 + 0.494267i \(0.835437\pi\)
\(308\) 0 0
\(309\) 10.0000 + 17.3205i 0.568880 + 0.985329i
\(310\) 10.3923i 0.590243i
\(311\) 15.0000 + 25.9808i 0.850572 + 1.47323i 0.880693 + 0.473688i \(0.157077\pi\)
−0.0301210 + 0.999546i \(0.509589\pi\)
\(312\) −12.0000 + 3.46410i −0.679366 + 0.196116i
\(313\) −5.00000 + 8.66025i −0.282617 + 0.489506i −0.972028 0.234863i \(-0.924536\pi\)
0.689412 + 0.724370i \(0.257869\pi\)
\(314\) 19.5000 11.2583i 1.10045 0.635344i
\(315\) 0 0
\(316\) 2.00000 3.46410i 0.112509 0.194871i
\(317\) −4.50000 2.59808i −0.252745 0.145922i 0.368275 0.929717i \(-0.379948\pi\)
−0.621021 + 0.783794i \(0.713282\pi\)
\(318\) 10.3923i 0.582772i
\(319\) 0 0
\(320\) 1.50000 + 0.866025i 0.0838525 + 0.0484123i
\(321\) −6.00000 + 10.3923i −0.334887 + 0.580042i
\(322\) 0 0
\(323\) −9.00000 + 5.19615i −0.500773 + 0.289122i
\(324\) −5.50000 + 9.52628i −0.305556 + 0.529238i
\(325\) 7.00000 + 1.73205i 0.388290 + 0.0960769i
\(326\) 18.0000 + 31.1769i 0.996928 + 1.72673i
\(327\) 27.7128i 1.53252i
\(328\) 4.50000 + 7.79423i 0.248471 + 0.430364i
\(329\) 0 0
\(330\) 0 0
\(331\) 24.0000 13.8564i 1.31916 0.761617i 0.335566 0.942017i \(-0.391072\pi\)
0.983593 + 0.180400i \(0.0577391\pi\)
\(332\) 13.8564i 0.760469i
\(333\) 7.50000 4.33013i 0.410997 0.237289i
\(334\) 12.0000 + 20.7846i 0.656611 + 1.13728i
\(335\) 3.00000 + 5.19615i 0.163908 + 0.283896i
\(336\) 0 0
\(337\) −23.0000 −1.25289 −0.626445 0.779466i \(-0.715491\pi\)
−0.626445 + 0.779466i \(0.715491\pi\)
\(338\) −22.5000 + 0.866025i −1.22384 + 0.0471056i
\(339\) 15.0000 + 25.9808i 0.814688 + 1.41108i
\(340\) −4.50000 2.59808i −0.244047 0.140900i
\(341\) 0 0
\(342\) −3.00000 + 5.19615i −0.162221 + 0.280976i
\(343\) 0 0
\(344\) 12.0000 + 6.92820i 0.646997 + 0.373544i
\(345\) −18.0000 + 10.3923i −0.969087 + 0.559503i
\(346\) −9.00000 + 5.19615i −0.483843 + 0.279347i
\(347\) −30.0000 −1.61048 −0.805242 0.592946i \(-0.797965\pi\)
−0.805242 + 0.592946i \(0.797965\pi\)
\(348\) −6.00000 −0.321634
\(349\) 12.0000 6.92820i 0.642345 0.370858i −0.143172 0.989698i \(-0.545730\pi\)
0.785517 + 0.618840i \(0.212397\pi\)
\(350\) 0 0
\(351\) 10.0000 10.3923i 0.533761 0.554700i
\(352\) 0 0
\(353\) −28.5000 16.4545i −1.51690 0.875784i −0.999803 0.0198582i \(-0.993679\pi\)
−0.517099 0.855926i \(-0.672988\pi\)
\(354\) 12.0000 20.7846i 0.637793 1.10469i
\(355\) −3.00000 5.19615i −0.159223 0.275783i
\(356\) 6.92820i 0.367194i
\(357\) 0 0
\(358\) 0 0
\(359\) −6.00000 3.46410i −0.316668 0.182828i 0.333238 0.942843i \(-0.391859\pi\)
−0.649906 + 0.760014i \(0.725192\pi\)
\(360\) 3.00000 0.158114
\(361\) −3.50000 + 6.06218i −0.184211 + 0.319062i
\(362\) 19.0526i 1.00138i
\(363\) 22.0000 1.15470
\(364\) 0 0
\(365\) 3.00000 0.157027
\(366\) 3.46410i 0.181071i
\(367\) 11.0000 19.0526i 0.574195 0.994535i −0.421933 0.906627i \(-0.638648\pi\)
0.996129 0.0879086i \(-0.0280183\pi\)
\(368\) 30.0000 1.56386
\(369\) 4.50000 + 2.59808i 0.234261 + 0.135250i
\(370\) −22.5000 12.9904i −1.16972 0.675338i
\(371\) 0 0
\(372\) 6.92820i 0.359211i
\(373\) −9.50000 16.4545i −0.491891 0.851981i 0.508065 0.861319i \(-0.330361\pi\)
−0.999956 + 0.00933789i \(0.997028\pi\)
\(374\) 0 0
\(375\) −21.0000 12.1244i −1.08444 0.626099i
\(376\) −3.00000 + 5.19615i −0.154713 + 0.267971i
\(377\) 10.5000 + 2.59808i 0.540778 + 0.133808i
\(378\) 0 0
\(379\) −21.0000 + 12.1244i −1.07870 + 0.622786i −0.930545 0.366178i \(-0.880666\pi\)
−0.148153 + 0.988964i \(0.547333\pi\)
\(380\) 6.00000 0.307794
\(381\) −4.00000 −0.204926
\(382\) −27.0000 + 15.5885i −1.38144 + 0.797575i
\(383\) 18.0000 10.3923i 0.919757 0.531022i 0.0361995 0.999345i \(-0.488475\pi\)
0.883558 + 0.468323i \(0.155141\pi\)
\(384\) −21.0000 12.1244i −1.07165 0.618718i
\(385\) 0 0
\(386\) 4.50000 7.79423i 0.229044 0.396716i
\(387\) 8.00000 0.406663
\(388\) −6.00000 3.46410i −0.304604 0.175863i
\(389\) 4.50000 + 7.79423i 0.228159 + 0.395183i 0.957263 0.289220i \(-0.0933960\pi\)
−0.729103 + 0.684403i \(0.760063\pi\)
\(390\) 21.0000 + 5.19615i 1.06338 + 0.263117i
\(391\) 18.0000 0.910299
\(392\) 0 0
\(393\) −18.0000 31.1769i −0.907980 1.57267i
\(394\) −12.0000 20.7846i −0.604551 1.04711i
\(395\) 6.00000 3.46410i 0.301893 0.174298i
\(396\) 0 0
\(397\) 12.0000 6.92820i 0.602263 0.347717i −0.167668 0.985843i \(-0.553624\pi\)
0.769931 + 0.638127i \(0.220290\pi\)
\(398\) 3.46410i 0.173640i
\(399\) 0 0
\(400\) 5.00000 + 8.66025i 0.250000 + 0.433013i
\(401\) 1.73205i 0.0864945i −0.999064 0.0432472i \(-0.986230\pi\)
0.999064 0.0432472i \(-0.0137703\pi\)
\(402\) −6.00000 10.3923i −0.299253 0.518321i
\(403\) 3.00000 12.1244i 0.149441 0.603957i
\(404\) −1.50000 + 2.59808i −0.0746278 + 0.129259i
\(405\) −16.5000 + 9.52628i −0.819892 + 0.473365i
\(406\) 0 0
\(407\) 0 0
\(408\) −9.00000 5.19615i −0.445566 0.257248i
\(409\) 15.5885i 0.770800i −0.922750 0.385400i \(-0.874064\pi\)
0.922750 0.385400i \(-0.125936\pi\)
\(410\) 15.5885i 0.769859i
\(411\) −27.0000 15.5885i −1.33181 0.768922i
\(412\) −5.00000 + 8.66025i −0.246332 + 0.426660i
\(413\) 0 0
\(414\) 9.00000 5.19615i 0.442326 0.255377i
\(415\) −12.0000 + 20.7846i −0.589057 + 1.02028i
\(416\) −13.5000 12.9904i −0.661892 0.636906i
\(417\) 4.00000 + 6.92820i 0.195881 + 0.339276i
\(418\) 0 0
\(419\) −9.00000 15.5885i −0.439679 0.761546i 0.557986 0.829851i \(-0.311574\pi\)
−0.997665 + 0.0683046i \(0.978241\pi\)
\(420\) 0 0
\(421\) 15.5885i 0.759735i −0.925041 0.379867i \(-0.875970\pi\)
0.925041 0.379867i \(-0.124030\pi\)
\(422\) −15.0000 + 8.66025i −0.730189 + 0.421575i
\(423\) 3.46410i 0.168430i
\(424\) 4.50000 2.59808i 0.218539 0.126174i
\(425\) 3.00000 + 5.19615i 0.145521 + 0.252050i
\(426\) 6.00000 + 10.3923i 0.290701 + 0.503509i
\(427\) 0 0
\(428\) −6.00000 −0.290021
\(429\) 0 0
\(430\) −12.0000 20.7846i −0.578691 1.00232i
\(431\) 6.00000 + 3.46410i 0.289010 + 0.166860i 0.637495 0.770454i \(-0.279971\pi\)
−0.348485 + 0.937314i \(0.613304\pi\)
\(432\) 20.0000 0.962250
\(433\) 8.50000 14.7224i 0.408484 0.707515i −0.586236 0.810140i \(-0.699391\pi\)
0.994720 + 0.102625i \(0.0327243\pi\)
\(434\) 0 0
\(435\) −9.00000 5.19615i −0.431517 0.249136i
\(436\) −12.0000 + 6.92820i −0.574696 + 0.331801i
\(437\) −18.0000 + 10.3923i −0.861057 + 0.497131i
\(438\) −6.00000 −0.286691
\(439\) −28.0000 −1.33637 −0.668184 0.743996i \(-0.732928\pi\)
−0.668184 + 0.743996i \(0.732928\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) −13.5000 12.9904i −0.642130 0.617889i
\(443\) 6.00000 10.3923i 0.285069 0.493753i −0.687557 0.726130i \(-0.741317\pi\)
0.972626 + 0.232377i \(0.0746503\pi\)
\(444\) 15.0000 + 8.66025i 0.711868 + 0.410997i
\(445\) −6.00000 + 10.3923i −0.284427 + 0.492642i
\(446\) 9.00000 + 15.5885i 0.426162 + 0.738135i
\(447\) 38.1051i 1.80231i
\(448\) 0 0
\(449\) −6.00000 3.46410i −0.283158 0.163481i 0.351694 0.936115i \(-0.385606\pi\)
−0.634852 + 0.772634i \(0.718939\pi\)
\(450\) 3.00000 + 1.73205i 0.141421 + 0.0816497i
\(451\) 0 0
\(452\) −7.50000 + 12.9904i −0.352770 + 0.611016i
\(453\) 34.6410i 1.62758i
\(454\) −42.0000 −1.97116
\(455\) 0 0
\(456\) 12.0000 0.561951
\(457\) 1.73205i 0.0810219i 0.999179 + 0.0405110i \(0.0128986\pi\)
−0.999179 + 0.0405110i \(0.987101\pi\)
\(458\) 0 0
\(459\) 12.0000 0.560112
\(460\) −9.00000 5.19615i −0.419627 0.242272i
\(461\) 19.5000 + 11.2583i 0.908206 + 0.524353i 0.879853 0.475245i \(-0.157641\pi\)
0.0283522 + 0.999598i \(0.490974\pi\)
\(462\) 0 0
\(463\) 13.8564i 0.643962i −0.946746 0.321981i \(-0.895651\pi\)
0.946746 0.321981i \(-0.104349\pi\)
\(464\) 7.50000 + 12.9904i 0.348179 + 0.603063i
\(465\) −6.00000 + 10.3923i −0.278243 + 0.481932i
\(466\) 9.00000 + 5.19615i 0.416917 + 0.240707i
\(467\) −6.00000 + 10.3923i −0.277647 + 0.480899i −0.970799 0.239892i \(-0.922888\pi\)
0.693153 + 0.720791i \(0.256221\pi\)
\(468\) −3.50000 0.866025i −0.161788 0.0400320i
\(469\) 0 0
\(470\) 9.00000 5.19615i 0.415139 0.239681i
\(471\) −26.0000 −1.19802
\(472\) −12.0000 −0.552345
\(473\) 0 0
\(474\) −12.0000 + 6.92820i −0.551178 + 0.318223i
\(475\) −6.00000 3.46410i −0.275299 0.158944i
\(476\) 0 0
\(477\) 1.50000 2.59808i 0.0686803 0.118958i
\(478\) 36.0000 1.64660
\(479\) −21.0000 12.1244i −0.959514 0.553976i −0.0634909 0.997982i \(-0.520223\pi\)
−0.896024 + 0.444006i \(0.853557\pi\)
\(480\) 9.00000 + 15.5885i 0.410792 + 0.711512i
\(481\) −22.5000 21.6506i −1.02591 0.987184i
\(482\) 3.00000 0.136646
\(483\) 0 0
\(484\) 5.50000 + 9.52628i 0.250000 + 0.433013i
\(485\) −6.00000 10.3923i −0.272446 0.471890i
\(486\) 15.0000 8.66025i 0.680414 0.392837i
\(487\) 6.92820i 0.313947i 0.987603 + 0.156973i \(0.0501737\pi\)
−0.987603 + 0.156973i \(0.949826\pi\)
\(488\) −1.50000 + 0.866025i −0.0679018 + 0.0392031i
\(489\) 41.5692i 1.87983i
\(490\) 0 0
\(491\) −6.00000 10.3923i −0.270776 0.468998i 0.698285 0.715820i \(-0.253947\pi\)
−0.969061 + 0.246822i \(0.920614\pi\)
\(492\) 10.3923i 0.468521i
\(493\) 4.50000 + 7.79423i 0.202670 + 0.351034i
\(494\) 21.0000 + 5.19615i 0.944835 + 0.233786i
\(495\) 0 0
\(496\) 15.0000 8.66025i 0.673520 0.388857i
\(497\) 0 0
\(498\) 24.0000 41.5692i 1.07547 1.86276i
\(499\) 27.0000 + 15.5885i 1.20869 + 0.697835i 0.962472 0.271380i \(-0.0874801\pi\)
0.246214 + 0.969216i \(0.420813\pi\)
\(500\) 12.1244i 0.542218i
\(501\) 27.7128i 1.23812i
\(502\) −27.0000 15.5885i −1.20507 0.695747i
\(503\) −18.0000 + 31.1769i −0.802580 + 1.39011i 0.115332 + 0.993327i \(0.463207\pi\)
−0.917912 + 0.396783i \(0.870127\pi\)
\(504\) 0 0
\(505\) −4.50000 + 2.59808i −0.200247 + 0.115613i
\(506\) 0 0
\(507\) 23.0000 + 12.1244i 1.02147 + 0.538462i
\(508\) −1.00000 1.73205i −0.0443678 0.0768473i
\(509\) 19.0526i 0.844490i 0.906482 + 0.422245i \(0.138758\pi\)
−0.906482 + 0.422245i \(0.861242\pi\)
\(510\) 9.00000 + 15.5885i 0.398527 + 0.690268i
\(511\) 0 0
\(512\) 8.66025i 0.382733i
\(513\) −12.0000 + 6.92820i −0.529813 + 0.305888i
\(514\) 5.19615i 0.229192i
\(515\) −15.0000 + 8.66025i −0.660979 + 0.381616i
\(516\) 8.00000 + 13.8564i 0.352180 + 0.609994i
\(517\) 0 0
\(518\) 0 0
\(519\) 12.0000 0.526742
\(520\) −3.00000 10.3923i −0.131559 0.455733i
\(521\) −4.50000 7.79423i −0.197149 0.341471i 0.750454 0.660922i \(-0.229835\pi\)
−0.947603 + 0.319451i \(0.896501\pi\)
\(522\) 4.50000 + 2.59808i 0.196960 + 0.113715i
\(523\) −16.0000 −0.699631 −0.349816 0.936819i \(-0.613756\pi\)
−0.349816 + 0.936819i \(0.613756\pi\)
\(524\) 9.00000 15.5885i 0.393167 0.680985i
\(525\) 0 0
\(526\) 18.0000 + 10.3923i 0.784837 + 0.453126i
\(527\) 9.00000 5.19615i 0.392046 0.226348i
\(528\) 0 0
\(529\) 13.0000 0.565217
\(530\) −9.00000 −0.390935
\(531\) −6.00000 + 3.46410i −0.260378 + 0.150329i
\(532\) 0 0
\(533\) 4.50000 18.1865i 0.194917 0.787746i
\(534\) 12.0000 20.7846i 0.519291 0.899438i
\(535\) −9.00000 5.19615i −0.389104 0.224649i
\(536\) −3.00000 + 5.19615i −0.129580 + 0.224440i
\(537\) 0 0
\(538\) 10.3923i 0.448044i
\(539\) 0 0
\(540\) −6.00000 3.46410i −0.258199 0.149071i
\(541\) 25.5000 + 14.7224i 1.09633 + 0.632967i 0.935255 0.353975i \(-0.115170\pi\)
0.161076 + 0.986942i \(0.448504\pi\)
\(542\) 36.0000 1.54633
\(543\) −11.0000 + 19.0526i −0.472055 + 0.817624i
\(544\) 15.5885i 0.668350i
\(545\) −24.0000 −1.02805
\(546\) 0 0
\(547\) −22.0000 −0.940652 −0.470326 0.882493i \(-0.655864\pi\)
−0.470326 + 0.882493i \(0.655864\pi\)
\(548\) 15.5885i 0.665906i
\(549\) −0.500000 + 0.866025i −0.0213395 + 0.0369611i
\(550\) 0 0
\(551\) −9.00000 5.19615i −0.383413 0.221364i
\(552\) −18.0000 10.3923i −0.766131 0.442326i
\(553\) 0 0
\(554\) 12.1244i 0.515115i
\(555\) 15.0000 + 25.9808i 0.636715 + 1.10282i
\(556\) −2.00000 + 3.46410i −0.0848189 + 0.146911i
\(557\) 13.5000 + 7.79423i 0.572013 + 0.330252i 0.757953 0.652309i \(-0.226200\pi\)
−0.185940 + 0.982561i \(0.559533\pi\)
\(558\) 3.00000 5.19615i 0.127000 0.219971i
\(559\) −8.00000 27.7128i −0.338364 1.17213i
\(560\) 0 0
\(561\) 0 0
\(562\) 39.0000 1.64512
\(563\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(564\) −6.00000 + 3.46410i −0.252646 + 0.145865i
\(565\) −22.5000 + 12.9904i −0.946582 + 0.546509i
\(566\) 6.00000 + 3.46410i 0.252199 + 0.145607i
\(567\) 0 0
\(568\) 3.00000 5.19615i 0.125877 0.218026i
\(569\) −42.0000 −1.76073 −0.880366 0.474295i \(-0.842703\pi\)
−0.880366 + 0.474295i \(0.842703\pi\)
\(570\) −18.0000 10.3923i −0.753937 0.435286i
\(571\) −20.0000 34.6410i −0.836974 1.44968i −0.892413 0.451219i \(-0.850989\pi\)
0.0554391 0.998462i \(-0.482344\pi\)
\(572\) 0 0
\(573\) 36.0000 1.50392
\(574\) 0 0
\(575\) 6.00000 + 10.3923i 0.250217 + 0.433389i
\(576\) 0.500000 + 0.866025i 0.0208333 + 0.0360844i
\(577\) 16.5000 9.52628i 0.686904 0.396584i −0.115547 0.993302i \(-0.536862\pi\)
0.802451 + 0.596718i \(0.203529\pi\)
\(578\) 13.8564i 0.576351i
\(579\) −9.00000 + 5.19615i −0.374027 + 0.215945i
\(580\) 5.19615i 0.215758i
\(581\) 0 0
\(582\) 12.0000 + 20.7846i 0.497416 + 0.861550i
\(583\) 0 0
\(584\) 1.50000 + 2.59808i 0.0620704 + 0.107509i
\(585\) −4.50000 4.33013i −0.186052 0.179029i
\(586\) 4.50000 7.79423i 0.185893 0.321977i
\(587\) −18.0000 + 10.3923i −0.742940 + 0.428936i −0.823137 0.567843i \(-0.807778\pi\)
0.0801976 + 0.996779i \(0.474445\pi\)
\(588\) 0 0
\(589\) −6.00000 + 10.3923i −0.247226 + 0.428207i
\(590\) 18.0000 + 10.3923i 0.741048 + 0.427844i
\(591\) 27.7128i 1.13995i
\(592\) 43.3013i 1.77967i
\(593\) −22.5000 12.9904i −0.923964 0.533451i −0.0390666 0.999237i \(-0.512438\pi\)
−0.884898 + 0.465786i \(0.845772\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −16.5000 + 9.52628i −0.675866 + 0.390212i
\(597\) 2.00000 3.46410i 0.0818546 0.141776i
\(598\) −27.0000 25.9808i −1.10411 1.06243i
\(599\) −15.0000 25.9808i −0.612883 1.06155i −0.990752 0.135686i \(-0.956676\pi\)
0.377869 0.925859i \(-0.376657\pi\)
\(600\) 6.92820i 0.282843i
\(601\) −12.5000 21.6506i −0.509886 0.883148i −0.999934 0.0114528i \(-0.996354\pi\)
0.490049 0.871695i \(-0.336979\pi\)
\(602\) 0 0
\(603\) 3.46410i 0.141069i
\(604\) 15.0000 8.66025i 0.610341 0.352381i
\(605\) 19.0526i 0.774597i
\(606\) 9.00000 5.19615i 0.365600 0.211079i
\(607\) 17.0000 + 29.4449i 0.690009 + 1.19513i 0.971834 + 0.235665i \(0.0757267\pi\)
−0.281826 + 0.959466i \(0.590940\pi\)
\(608\) 9.00000 + 15.5885i 0.364998 + 0.632195i
\(609\) 0 0
\(610\) 3.00000 0.121466
\(611\) 12.0000 3.46410i 0.485468 0.140143i
\(612\) −1.50000 2.59808i −0.0606339 0.105021i
\(613\) 10.5000 + 6.06218i 0.424091 + 0.244849i 0.696826 0.717240i \(-0.254595\pi\)
−0.272735 + 0.962089i \(0.587928\pi\)
\(614\) 30.0000 1.21070
\(615\) −9.00000 + 15.5885i −0.362915 + 0.628587i
\(616\) 0 0
\(617\) −19.5000 11.2583i −0.785040 0.453243i 0.0531732 0.998585i \(-0.483066\pi\)
−0.838214 + 0.545342i \(0.816400\pi\)
\(618\) 30.0000 17.3205i 1.20678 0.696733i
\(619\) 18.0000 10.3923i 0.723481 0.417702i −0.0925515 0.995708i \(-0.529502\pi\)
0.816033 + 0.578006i \(0.196169\pi\)
\(620\) −6.00000 −0.240966
\(621\) 24.0000 0.963087
\(622\) 45.0000 25.9808i 1.80434 1.04173i
\(623\) 0 0
\(624\) 10.0000 + 34.6410i 0.400320 + 1.38675i
\(625\) 5.50000 9.52628i 0.220000 0.381051i
\(626\) 15.0000 + 8.66025i 0.599521 + 0.346133i
\(627\) 0 0
\(628\) −6.50000 11.2583i −0.259378 0.449256i
\(629\) 25.9808i 1.03592i
\(630\) 0 0
\(631\) −42.0000 24.2487i −1.67199 0.965326i −0.966521 0.256589i \(-0.917401\pi\)
−0.705473 0.708737i \(-0.749265\pi\)
\(632\) 6.00000 + 3.46410i 0.238667 + 0.137795i
\(633\) 20.0000 0.794929
\(634\) −4.50000 + 7.79423i −0.178718 + 0.309548i
\(635\) 3.46410i 0.137469i
\(636\) 6.00000 0.237915
\(637\) 0 0
\(638\) 0 0
\(639\) 3.46410i 0.137038i
\(640\) 10.5000 18.1865i 0.415049 0.718886i
\(641\) 33.0000 1.30342 0.651711 0.758468i \(-0.274052\pi\)
0.651711 + 0.758468i \(0.274052\pi\)
\(642\) 18.0000 + 10.3923i 0.710403 + 0.410152i
\(643\) 12.0000 + 6.92820i 0.473234 + 0.273222i 0.717592 0.696463i \(-0.245244\pi\)
−0.244359 + 0.969685i \(0.578577\pi\)
\(644\) 0 0
\(645\) 27.7128i 1.09119i
\(646\) 9.00000 + 15.5885i 0.354100 + 0.613320i
\(647\) −9.00000 + 15.5885i −0.353827 + 0.612845i −0.986916 0.161233i \(-0.948453\pi\)
0.633090 + 0.774078i \(0.281786\pi\)
\(648\) −16.5000 9.52628i −0.648181 0.374228i
\(649\) 0 0
\(650\) 3.00000 12.1244i 0.117670 0.475556i
\(651\) 0 0
\(652\) 18.0000 10.3923i 0.704934 0.406994i
\(653\) −30.0000 −1.17399 −0.586995 0.809590i \(-0.699689\pi\)
−0.586995 + 0.809590i \(0.699689\pi\)
\(654\) 48.0000 1.87695
\(655\) 27.0000 15.5885i 1.05498 0.609091i
\(656\) 22.5000 12.9904i 0.878477 0.507189i
\(657\) 1.50000 + 0.866025i 0.0585206 + 0.0337869i
\(658\) 0 0
\(659\) 6.00000 10.3923i 0.233727 0.404827i −0.725175 0.688565i \(-0.758241\pi\)
0.958902 + 0.283738i \(0.0915745\pi\)
\(660\) 0 0
\(661\) 40.5000 + 23.3827i 1.57527 + 0.909481i 0.995506 + 0.0946945i \(0.0301874\pi\)
0.579761 + 0.814787i \(0.303146\pi\)
\(662\) −24.0000 41.5692i −0.932786 1.61563i
\(663\) 6.00000 + 20.7846i 0.233021 + 0.807207i
\(664\) −24.0000 −0.931381
\(665\) 0 0
\(666\) −7.50000 12.9904i −0.290619 0.503367i
\(667\) 9.00000 + 15.5885i 0.348481 + 0.603587i
\(668\) 12.0000 6.92820i 0.464294 0.268060i
\(669\) 20.7846i 0.803579i
\(670\) 9.00000 5.19615i 0.347700 0.200745i
\(671\) 0 0
\(672\) 0 0
\(673\) 9.50000 + 16.4545i 0.366198 + 0.634274i 0.988968 0.148132i \(-0.0473259\pi\)
−0.622770 + 0.782405i \(0.713993\pi\)
\(674\) 39.8372i 1.53447i
\(675\) 4.00000 + 6.92820i 0.153960 + 0.266667i
\(676\) 0.500000 + 12.9904i 0.0192308 + 0.499630i
\(677\) 3.00000 5.19615i 0.115299 0.199704i −0.802600 0.596518i \(-0.796551\pi\)
0.917899 + 0.396813i \(0.129884\pi\)
\(678\) 45.0000 25.9808i 1.72821 0.997785i
\(679\) 0 0
\(680\) 4.50000 7.79423i 0.172567 0.298895i
\(681\) 42.0000 + 24.2487i 1.60944 + 0.929213i
\(682\) 0 0
\(683\) 24.2487i 0.927851i −0.885874 0.463926i \(-0.846441\pi\)
0.885874 0.463926i \(-0.153559\pi\)
\(684\) 3.00000 + 1.73205i 0.114708 + 0.0662266i
\(685\) 13.5000 23.3827i 0.515808 0.893407i
\(686\) 0 0
\(687\) 0 0
\(688\) 20.0000 34.6410i 0.762493 1.32068i
\(689\) −10.5000 2.59808i −0.400018 0.0989788i
\(690\) 18.0000 + 31.1769i 0.685248 + 1.18688i
\(691\) 13.8564i 0.527123i 0.964643 + 0.263561i \(0.0848971\pi\)
−0.964643 + 0.263561i \(0.915103\pi\)
\(692\) 3.00000 + 5.19615i 0.114043 + 0.197528i
\(693\) 0 0
\(694\) 51.9615i 1.97243i
\(695\) −6.00000 + 3.46410i −0.227593 + 0.131401i
\(696\) 10.3923i 0.393919i
\(697\) 13.5000 7.79423i 0.511349 0.295227i
\(698\) −12.0000 20.7846i −0.454207 0.786709i
\(699\) −6.00000 10.3923i −0.226941 0.393073i
\(700\) 0 0
\(701\) 18.0000 0.679851 0.339925 0.940452i \(-0.389598\pi\)
0.339925 + 0.940452i \(0.389598\pi\)
\(702\) −18.0000 17.3205i −0.679366 0.653720i
\(703\) 15.0000 + 25.9808i 0.565736 + 0.979883i
\(704\) 0 0
\(705\) −12.0000 −0.451946
\(706\) −28.5000 + 49.3634i −1.07261 + 1.85782i
\(707\) 0 0
\(708\) −12.0000 6.92820i −0.450988 0.260378i
\(709\) 4.50000 2.59808i 0.169001 0.0975728i −0.413114 0.910679i \(-0.635559\pi\)
0.582115 + 0.813107i \(0.302225\pi\)
\(710\) −9.00000 + 5.19615i −0.337764 + 0.195008i
\(711\) 4.00000 0.150012
\(712\) −12.0000 −0.449719
\(713\) 18.0000 10.3923i 0.674105 0.389195i
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −36.0000 20.7846i −1.34444 0.776215i
\(718\) −6.00000 + 10.3923i −0.223918 + 0.387837i
\(719\) 24.0000 + 41.5692i 0.895049 + 1.55027i 0.833744 + 0.552151i \(0.186193\pi\)
0.0613050 + 0.998119i \(0.480474\pi\)
\(720\) 8.66025i 0.322749i
\(721\) 0 0
\(722\) 10.5000 + 6.06218i 0.390770 + 0.225611i
\(723\) −3.00000 1.73205i −0.111571 0.0644157i
\(724\) −11.0000 −0.408812
\(725\) −3.00000 + 5.19615i −0.111417 + 0.192980i
\(726\) 38.1051i 1.41421i
\(727\) −32.0000 −1.18681 −0.593407 0.804902i \(-0.702218\pi\)
−0.593407 + 0.804902i \(0.702218\pi\)
\(728\) 0 0
\(729\) 13.0000 0.481481
\(730\) 5.19615i 0.192318i
\(731\) 12.0000 20.7846i 0.443836 0.768747i
\(732\) −2.00000 −0.0739221
\(733\) 10.5000 + 6.06218i 0.387826 + 0.223912i 0.681218 0.732081i \(-0.261451\pi\)
−0.293392 + 0.955992i \(0.594784\pi\)
\(734\) −33.0000 19.0526i −1.21805 0.703243i
\(735\) 0 0
\(736\) 31.1769i 1.14920i
\(737\) 0 0
\(738\) 4.50000 7.79423i 0.165647 0.286910i
\(739\) 18.0000 + 10.3923i 0.662141 + 0.382287i 0.793092 0.609102i \(-0.208470\pi\)
−0.130951 + 0.991389i \(0.541803\pi\)
\(740\) −7.50000 + 12.9904i −0.275705 + 0.477536i
\(741\) −18.0000 17.3205i −0.661247 0.636285i
\(742\) 0 0
\(743\) −30.0000 + 17.3205i −1.10059 + 0.635428i −0.936377 0.350997i \(-0.885843\pi\)
−0.164216 + 0.986424i \(0.552510\pi\)
\(744\) −12.0000 −0.439941
\(745\) −33.0000 −1.20903
\(746\) −28.5000 + 16.4545i −1.04346 + 0.602441i
\(747\) −12.0000 + 6.92820i −0.439057 + 0.253490i
\(748\) 0 0
\(749\) 0 0
\(750\) −21.0000 + 36.3731i −0.766812 + 1.32816i
\(751\) −16.0000 −0.583848 −0.291924 0.956441i \(-0.594295\pi\)
−0.291924 + 0.956441i \(0.594295\pi\)
\(752\) 15.0000 + 8.66025i 0.546994 + 0.315807i
\(753\) 18.0000 + 31.1769i 0.655956 + 1.13615i
\(754\) 4.50000 18.1865i 0.163880 0.662314i
\(755\) 30.0000 1.09181
\(756\) 0 0
\(757\) 13.0000 + 22.5167i 0.472493 + 0.818382i 0.999505 0.0314762i \(-0.0100208\pi\)
−0.527011 + 0.849858i \(0.676688\pi\)
\(758\) 21.0000 + 36.3731i 0.762754 + 1.32113i
\(759\) 0 0
\(760\) 10.3923i 0.376969i
\(761\) −30.0000 + 17.3205i −1.08750 + 0.627868i −0.932910 0.360111i \(-0.882739\pi\)
−0.154590 + 0.987979i \(0.549406\pi\)
\(762\) 6.92820i 0.250982i
\(763\) 0 0
\(764\) 9.00000 + 15.5885i 0.325609 + 0.563971i
\(765\) 5.19615i 0.187867i
\(766\) −18.0000 31.1769i −0.650366 1.12647i
\(767\) 18.0000 + 17.3205i 0.649942 + 0.625407i
\(768\) −19.0000 + 32.9090i −0.685603 + 1.18750i
\(769\) 6.00000 3.46410i 0.216366 0.124919i −0.387901 0.921701i \(-0.626800\pi\)
0.604266 + 0.796782i \(0.293466\pi\)
\(770\) 0 0
\(771\) −3.00000 + 5.19615i −0.108042 + 0.187135i
\(772\) −4.50000 2.59808i −0.161959 0.0935068i
\(773\) 34.6410i 1.24595i 0.782241 + 0.622975i \(0.214076\pi\)
−0.782241 + 0.622975i \(0.785924\pi\)
\(774\) 13.8564i 0.498058i
\(775\) 6.00000 + 3.46410i 0.215526 + 0.124434i
\(776\) 6.00000 10.3923i 0.215387