Properties

Label 637.2.u.c.361.1
Level $637$
Weight $2$
Character 637.361
Analytic conductor $5.086$
Analytic rank $0$
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(30,637)]
 
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([2, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("637.30");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 637 = 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 637.u (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: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 13)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 361.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 637.361
Dual form 637.2.u.c.30.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.50000 + 0.866025i) q^{2} +2.00000 q^{3} +(0.500000 + 0.866025i) q^{4} +(1.50000 - 0.866025i) q^{5} +(3.00000 + 1.73205i) q^{6} -1.73205i q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+(1.50000 + 0.866025i) q^{2} +2.00000 q^{3} +(0.500000 + 0.866025i) q^{4} +(1.50000 - 0.866025i) q^{5} +(3.00000 + 1.73205i) q^{6} -1.73205i q^{8} +1.00000 q^{9} +3.00000 q^{10} +(1.00000 + 1.73205i) q^{12} +(-2.50000 + 2.59808i) q^{13} +(3.00000 - 1.73205i) q^{15} +(2.50000 - 4.33013i) q^{16} +(1.50000 + 2.59808i) q^{17} +(1.50000 + 0.866025i) q^{18} +3.46410i q^{19} +(1.50000 + 0.866025i) q^{20} +(3.00000 - 5.19615i) q^{23} -3.46410i q^{24} +(-1.00000 + 1.73205i) q^{25} +(-6.00000 + 1.73205i) q^{26} -4.00000 q^{27} +(-1.50000 - 2.59808i) q^{29} +6.00000 q^{30} +(3.00000 + 1.73205i) q^{31} +(4.50000 - 2.59808i) q^{32} +5.19615i q^{34} +(0.500000 + 0.866025i) q^{36} +(-7.50000 - 4.33013i) q^{37} +(-3.00000 + 5.19615i) q^{38} +(-5.00000 + 5.19615i) q^{39} +(-1.50000 - 2.59808i) q^{40} +(-4.50000 + 2.59808i) q^{41} +(-4.00000 + 6.92820i) q^{43} +(1.50000 - 0.866025i) q^{45} +(9.00000 - 5.19615i) q^{46} +(3.00000 - 1.73205i) q^{47} +(5.00000 - 8.66025i) q^{48} +(-3.00000 + 1.73205i) q^{50} +(3.00000 + 5.19615i) q^{51} +(-3.50000 - 0.866025i) q^{52} +(1.50000 - 2.59808i) q^{53} +(-6.00000 - 3.46410i) q^{54} +6.92820i q^{57} -5.19615i q^{58} +(-6.00000 + 3.46410i) q^{59} +(3.00000 + 1.73205i) q^{60} +1.00000 q^{61} +(3.00000 + 5.19615i) q^{62} -1.00000 q^{64} +(-1.50000 + 6.06218i) q^{65} +3.46410i q^{67} +(-1.50000 + 2.59808i) q^{68} +(6.00000 - 10.3923i) q^{69} +(3.00000 + 1.73205i) q^{71} -1.73205i q^{72} +(1.50000 + 0.866025i) q^{73} +(-7.50000 - 12.9904i) q^{74} +(-2.00000 + 3.46410i) q^{75} +(-3.00000 + 1.73205i) q^{76} +(-12.0000 + 3.46410i) q^{78} +(-2.00000 - 3.46410i) q^{79} -8.66025i q^{80} -11.0000 q^{81} -9.00000 q^{82} -13.8564i q^{83} +(4.50000 + 2.59808i) q^{85} +(-12.0000 + 6.92820i) q^{86} +(-3.00000 - 5.19615i) q^{87} +(6.00000 + 3.46410i) q^{89} +3.00000 q^{90} +6.00000 q^{92} +(6.00000 + 3.46410i) q^{93} +6.00000 q^{94} +(3.00000 + 5.19615i) q^{95} +(9.00000 - 5.19615i) q^{96} +(6.00000 + 3.46410i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 3 q^{2} + 4 q^{3} + q^{4} + 3 q^{5} + 6 q^{6} + 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 3 q^{2} + 4 q^{3} + q^{4} + 3 q^{5} + 6 q^{6} + 2 q^{9} + 6 q^{10} + 2 q^{12} - 5 q^{13} + 6 q^{15} + 5 q^{16} + 3 q^{17} + 3 q^{18} + 3 q^{20} + 6 q^{23} - 2 q^{25} - 12 q^{26} - 8 q^{27} - 3 q^{29} + 12 q^{30} + 6 q^{31} + 9 q^{32} + q^{36} - 15 q^{37} - 6 q^{38} - 10 q^{39} - 3 q^{40} - 9 q^{41} - 8 q^{43} + 3 q^{45} + 18 q^{46} + 6 q^{47} + 10 q^{48} - 6 q^{50} + 6 q^{51} - 7 q^{52} + 3 q^{53} - 12 q^{54} - 12 q^{59} + 6 q^{60} + 2 q^{61} + 6 q^{62} - 2 q^{64} - 3 q^{65} - 3 q^{68} + 12 q^{69} + 6 q^{71} + 3 q^{73} - 15 q^{74} - 4 q^{75} - 6 q^{76} - 24 q^{78} - 4 q^{79} - 22 q^{81} - 18 q^{82} + 9 q^{85} - 24 q^{86} - 6 q^{87} + 12 q^{89} + 6 q^{90} + 12 q^{92} + 12 q^{93} + 12 q^{94} + 6 q^{95} + 18 q^{96} + 12 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(197\) \(248\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.50000 + 0.866025i 1.06066 + 0.612372i 0.925615 0.378467i \(-0.123549\pi\)
0.135045 + 0.990839i \(0.456882\pi\)
\(3\) 2.00000 1.15470 0.577350 0.816497i \(-0.304087\pi\)
0.577350 + 0.816497i \(0.304087\pi\)
\(4\) 0.500000 + 0.866025i 0.250000 + 0.433013i
\(5\) 1.50000 0.866025i 0.670820 0.387298i −0.125567 0.992085i \(-0.540075\pi\)
0.796387 + 0.604787i \(0.206742\pi\)
\(6\) 3.00000 + 1.73205i 1.22474 + 0.707107i
\(7\) 0 0
\(8\) 1.73205i 0.612372i
\(9\) 1.00000 0.333333
\(10\) 3.00000 0.948683
\(11\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(12\) 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
\(16\) 2.50000 4.33013i 0.625000 1.08253i
\(17\) 1.50000 + 2.59808i 0.363803 + 0.630126i 0.988583 0.150675i \(-0.0481447\pi\)
−0.624780 + 0.780801i \(0.714811\pi\)
\(18\) 1.50000 + 0.866025i 0.353553 + 0.204124i
\(19\) 3.46410i 0.794719i 0.917663 + 0.397360i \(0.130073\pi\)
−0.917663 + 0.397360i \(0.869927\pi\)
\(20\) 1.50000 + 0.866025i 0.335410 + 0.193649i
\(21\) 0 0
\(22\) 0 0
\(23\) 3.00000 5.19615i 0.625543 1.08347i −0.362892 0.931831i \(-0.618211\pi\)
0.988436 0.151642i \(-0.0484560\pi\)
\(24\) 3.46410i 0.707107i
\(25\) −1.00000 + 1.73205i −0.200000 + 0.346410i
\(26\) −6.00000 + 1.73205i −1.17670 + 0.339683i
\(27\) −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 \(0.923185\pi\)
\(30\) 6.00000 1.09545
\(31\) 3.00000 + 1.73205i 0.538816 + 0.311086i 0.744599 0.667512i \(-0.232641\pi\)
−0.205783 + 0.978598i \(0.565974\pi\)
\(32\) 4.50000 2.59808i 0.795495 0.459279i
\(33\) 0 0
\(34\) 5.19615i 0.891133i
\(35\) 0 0
\(36\) 0.500000 + 0.866025i 0.0833333 + 0.144338i
\(37\) −7.50000 4.33013i −1.23299 0.711868i −0.265340 0.964155i \(-0.585484\pi\)
−0.967653 + 0.252286i \(0.918817\pi\)
\(38\) −3.00000 + 5.19615i −0.486664 + 0.842927i
\(39\) −5.00000 + 5.19615i −0.800641 + 0.832050i
\(40\) −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
\(45\) 1.50000 0.866025i 0.223607 0.129099i
\(46\) 9.00000 5.19615i 1.32698 0.766131i
\(47\) 3.00000 1.73205i 0.437595 0.252646i −0.264982 0.964253i \(-0.585366\pi\)
0.702577 + 0.711608i \(0.252033\pi\)
\(48\) 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
\(52\) −3.50000 0.866025i −0.485363 0.120096i
\(53\) 1.50000 2.59808i 0.206041 0.356873i −0.744423 0.667708i \(-0.767275\pi\)
0.950464 + 0.310835i \(0.100609\pi\)
\(54\) −6.00000 3.46410i −0.816497 0.471405i
\(55\) 0 0
\(56\) 0 0
\(57\) 6.92820i 0.917663i
\(58\) 5.19615i 0.682288i
\(59\) −6.00000 + 3.46410i −0.781133 + 0.450988i −0.836832 0.547460i \(-0.815595\pi\)
0.0556984 + 0.998448i \(0.482261\pi\)
\(60\) 3.00000 + 1.73205i 0.387298 + 0.223607i
\(61\) 1.00000 0.128037 0.0640184 0.997949i \(-0.479608\pi\)
0.0640184 + 0.997949i \(0.479608\pi\)
\(62\) 3.00000 + 5.19615i 0.381000 + 0.659912i
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) −1.50000 + 6.06218i −0.186052 + 0.751921i
\(66\) 0 0
\(67\) 3.46410i 0.423207i 0.977356 + 0.211604i \(0.0678686\pi\)
−0.977356 + 0.211604i \(0.932131\pi\)
\(68\) −1.50000 + 2.59808i −0.181902 + 0.315063i
\(69\) 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 \(0.600766\pi\)
\(72\) 1.73205i 0.204124i
\(73\) 1.50000 + 0.866025i 0.175562 + 0.101361i 0.585206 0.810885i \(-0.301014\pi\)
−0.409644 + 0.912245i \(0.634347\pi\)
\(74\) −7.50000 12.9904i −0.871857 1.51010i
\(75\) −2.00000 + 3.46410i −0.230940 + 0.400000i
\(76\) −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 0.731307 0.682048i \(-0.238911\pi\)
−0.956325 + 0.292306i \(0.905577\pi\)
\(80\) 8.66025i 0.968246i
\(81\) −11.0000 −1.22222
\(82\) −9.00000 −0.993884
\(83\) 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
\(87\) −3.00000 5.19615i −0.321634 0.557086i
\(88\) 0 0
\(89\) 6.00000 + 3.46410i 0.635999 + 0.367194i 0.783072 0.621932i \(-0.213652\pi\)
−0.147073 + 0.989126i \(0.546985\pi\)
\(90\) 3.00000 0.316228
\(91\) 0 0
\(92\) 6.00000 0.625543
\(93\) 6.00000 + 3.46410i 0.622171 + 0.359211i
\(94\) 6.00000 0.618853
\(95\) 3.00000 + 5.19615i 0.307794 + 0.533114i
\(96\) 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
\(100\) −2.00000 −0.200000
\(101\) −3.00000 −0.298511 −0.149256 0.988799i \(-0.547688\pi\)
−0.149256 + 0.988799i \(0.547688\pi\)
\(102\) 10.3923i 1.02899i
\(103\) 5.00000 + 8.66025i 0.492665 + 0.853320i 0.999964 0.00844953i \(-0.00268960\pi\)
−0.507300 + 0.861770i \(0.669356\pi\)
\(104\) 4.50000 + 4.33013i 0.441261 + 0.424604i
\(105\) 0 0
\(106\) 4.50000 2.59808i 0.437079 0.252347i
\(107\) −3.00000 + 5.19615i −0.290021 + 0.502331i −0.973814 0.227345i \(-0.926996\pi\)
0.683793 + 0.729676i \(0.260329\pi\)
\(108\) −2.00000 3.46410i −0.192450 0.333333i
\(109\) −12.0000 6.92820i −1.14939 0.663602i −0.200653 0.979662i \(-0.564306\pi\)
−0.948739 + 0.316061i \(0.897640\pi\)
\(110\) 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 \(-0.0826291\pi\)
\(114\) −6.00000 + 10.3923i −0.561951 + 0.973329i
\(115\) 10.3923i 0.969087i
\(116\) 1.50000 2.59808i 0.139272 0.241225i
\(117\) −2.50000 + 2.59808i −0.231125 + 0.240192i
\(118\) −12.0000 −1.10469
\(119\) 0 0
\(120\) −3.00000 5.19615i −0.273861 0.474342i
\(121\) 11.0000 1.00000
\(122\) 1.50000 + 0.866025i 0.135804 + 0.0784063i
\(123\) −9.00000 + 5.19615i −0.811503 + 0.468521i
\(124\) 3.46410i 0.311086i
\(125\) 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 \(0.805051\pi\)
\(128\) −10.5000 6.06218i −0.928078 0.535826i
\(129\) −8.00000 + 13.8564i −0.704361 + 1.21999i
\(130\) −7.50000 + 7.79423i −0.657794 + 0.683599i
\(131\) −9.00000 15.5885i −0.786334 1.36197i −0.928199 0.372084i \(-0.878643\pi\)
0.141865 0.989886i \(-0.454690\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −3.00000 + 5.19615i −0.259161 + 0.448879i
\(135\) −6.00000 + 3.46410i −0.516398 + 0.298142i
\(136\) 4.50000 2.59808i 0.385872 0.222783i
\(137\) 13.5000 7.79423i 1.15338 0.665906i 0.203674 0.979039i \(-0.434712\pi\)
0.949709 + 0.313133i \(0.101379\pi\)
\(138\) 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
\(145\) −4.50000 2.59808i −0.373705 0.215758i
\(146\) 1.50000 + 2.59808i 0.124141 + 0.215018i
\(147\) 0 0
\(148\) 8.66025i 0.711868i
\(149\) 19.0526i 1.56085i 0.625252 + 0.780423i \(0.284996\pi\)
−0.625252 + 0.780423i \(0.715004\pi\)
\(150\) −6.00000 + 3.46410i −0.489898 + 0.282843i
\(151\) 15.0000 + 8.66025i 1.22068 + 0.704761i 0.965064 0.262016i \(-0.0843873\pi\)
0.255619 + 0.966778i \(0.417721\pi\)
\(152\) 6.00000 0.486664
\(153\) 1.50000 + 2.59808i 0.121268 + 0.210042i
\(154\) 0 0
\(155\) 6.00000 0.481932
\(156\) −7.00000 1.73205i −0.560449 0.138675i
\(157\) 6.50000 11.2583i 0.518756 0.898513i −0.481006 0.876717i \(-0.659728\pi\)
0.999762 0.0217953i \(-0.00693820\pi\)
\(158\) 6.92820i 0.551178i
\(159\) 3.00000 5.19615i 0.237915 0.412082i
\(160\) 4.50000 7.79423i 0.355756 0.616188i
\(161\) 0 0
\(162\) −16.5000 9.52628i −1.29636 0.748455i
\(163\) 20.7846i 1.62798i −0.580881 0.813988i \(-0.697292\pi\)
0.580881 0.813988i \(-0.302708\pi\)
\(164\) −4.50000 2.59808i −0.351391 0.202876i
\(165\) 0 0
\(166\) 12.0000 20.7846i 0.931381 1.61320i
\(167\) −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
\(171\) 3.46410i 0.264906i
\(172\) −8.00000 −0.609994
\(173\) 6.00000 0.456172 0.228086 0.973641i \(-0.426753\pi\)
0.228086 + 0.973641i \(0.426753\pi\)
\(174\) 10.3923i 0.787839i
\(175\) 0 0
\(176\) 0 0
\(177\) −12.0000 + 6.92820i −0.901975 + 0.520756i
\(178\) 6.00000 + 10.3923i 0.449719 + 0.778936i
\(179\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(180\) 1.50000 + 0.866025i 0.111803 + 0.0645497i
\(181\) 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
\(184\) −9.00000 5.19615i −0.663489 0.383065i
\(185\) −15.0000 −1.10282
\(186\) 6.00000 + 10.3923i 0.439941 + 0.762001i
\(187\) 0 0
\(188\) 3.00000 + 1.73205i 0.218797 + 0.126323i
\(189\) 0 0
\(190\) 10.3923i 0.753937i
\(191\) 18.0000 1.30243 0.651217 0.758891i \(-0.274259\pi\)
0.651217 + 0.758891i \(0.274259\pi\)
\(192\) −2.00000 −0.144338
\(193\) 5.19615i 0.374027i −0.982357 0.187014i \(-0.940119\pi\)
0.982357 0.187014i \(-0.0598809\pi\)
\(194\) 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
\(199\) 1.00000 + 1.73205i 0.0708881 + 0.122782i 0.899291 0.437351i \(-0.144083\pi\)
−0.828403 + 0.560133i \(0.810750\pi\)
\(200\) 3.00000 + 1.73205i 0.212132 + 0.122474i
\(201\) 6.92820i 0.488678i
\(202\) −4.50000 2.59808i −0.316619 0.182800i
\(203\) 0 0
\(204\) −3.00000 + 5.19615i −0.210042 + 0.363803i
\(205\) −4.50000 + 7.79423i −0.314294 + 0.544373i
\(206\) 17.3205i 1.20678i
\(207\) 3.00000 5.19615i 0.208514 0.361158i
\(208\) 5.00000 + 17.3205i 0.346688 + 1.20096i
\(209\) 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 \(0.945188\pi\)
\(212\) 3.00000 0.206041
\(213\) 6.00000 + 3.46410i 0.411113 + 0.237356i
\(214\) −9.00000 + 5.19615i −0.615227 + 0.355202i
\(215\) 13.8564i 0.944999i
\(216\) 6.92820i 0.471405i
\(217\) 0 0
\(218\) −12.0000 20.7846i −0.812743 1.40771i
\(219\) 3.00000 + 1.73205i 0.202721 + 0.117041i
\(220\) 0 0
\(221\) −10.5000 2.59808i −0.706306 0.174766i
\(222\) −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
\(227\) −21.0000 + 12.1244i −1.39382 + 0.804722i −0.993736 0.111757i \(-0.964352\pi\)
−0.400083 + 0.916479i \(0.631019\pi\)
\(228\) −6.00000 + 3.46410i −0.397360 + 0.229416i
\(229\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(230\) 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 0.750867 0.660454i \(-0.229636\pi\)
−0.947403 + 0.320043i \(0.896303\pi\)
\(234\) −6.00000 + 1.73205i −0.392232 + 0.113228i
\(235\) 3.00000 5.19615i 0.195698 0.338960i
\(236\) −6.00000 3.46410i −0.390567 0.225494i
\(237\) −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 \(0.765340\pi\)
\(240\) 17.3205i 1.11803i
\(241\) 1.50000 0.866025i 0.0966235 0.0557856i −0.450910 0.892570i \(-0.648900\pi\)
0.547533 + 0.836784i \(0.315567\pi\)
\(242\) 16.5000 + 9.52628i 1.06066 + 0.612372i
\(243\) −10.0000 −0.641500
\(244\) 0.500000 + 0.866025i 0.0320092 + 0.0554416i
\(245\) 0 0
\(246\) −18.0000 −1.14764
\(247\) −9.00000 8.66025i −0.572656 0.551039i
\(248\) 3.00000 5.19615i 0.190500 0.329956i
\(249\) 27.7128i 1.75623i
\(250\) −10.5000 + 18.1865i −0.664078 + 1.15022i
\(251\) 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
\(254\) 3.46410i 0.217357i
\(255\) 9.00000 + 5.19615i 0.563602 + 0.325396i
\(256\) −9.50000 16.4545i −0.593750 1.02841i
\(257\) −1.50000 + 2.59808i −0.0935674 + 0.162064i −0.909010 0.416775i \(-0.863160\pi\)
0.815442 + 0.578838i \(0.196494\pi\)
\(258\) −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
\(262\) 31.1769i 1.92612i
\(263\) 12.0000 0.739952 0.369976 0.929041i \(-0.379366\pi\)
0.369976 + 0.929041i \(0.379366\pi\)
\(264\) 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
\(269\) 3.00000 + 5.19615i 0.182913 + 0.316815i 0.942871 0.333157i \(-0.108114\pi\)
−0.759958 + 0.649972i \(0.774781\pi\)
\(270\) −12.0000 −0.730297
\(271\) −18.0000 10.3923i −1.09342 0.631288i −0.158937 0.987289i \(-0.550807\pi\)
−0.934485 + 0.356001i \(0.884140\pi\)
\(272\) 15.0000 0.909509
\(273\) 0 0
\(274\) 27.0000 1.63113
\(275\) 0 0
\(276\) 12.0000 0.722315
\(277\) 3.50000 + 6.06218i 0.210295 + 0.364241i 0.951807 0.306699i \(-0.0992243\pi\)
−0.741512 + 0.670940i \(0.765891\pi\)
\(278\) 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 \(0.765601\pi\)
\(282\) 12.0000 0.714590
\(283\) 4.00000 0.237775 0.118888 0.992908i \(-0.462067\pi\)
0.118888 + 0.992908i \(0.462067\pi\)
\(284\) 3.46410i 0.205557i
\(285\) 6.00000 + 10.3923i 0.355409 + 0.615587i
\(286\) 0 0
\(287\) 0 0
\(288\) 4.50000 2.59808i 0.265165 0.153093i
\(289\) 4.00000 6.92820i 0.235294 0.407541i
\(290\) −4.50000 7.79423i −0.264249 0.457693i
\(291\) 12.0000 + 6.92820i 0.703452 + 0.406138i
\(292\) 1.73205i 0.101361i
\(293\) 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
\(296\) −7.50000 + 12.9904i −0.435929 + 0.755051i
\(297\) 0 0
\(298\) −16.5000 + 28.5788i −0.955819 + 1.65553i
\(299\) 6.00000 + 20.7846i 0.346989 + 1.20201i
\(300\) −4.00000 −0.230940
\(301\) 0 0
\(302\) 15.0000 + 25.9808i 0.863153 + 1.49502i
\(303\) −6.00000 −0.344691
\(304\) 15.0000 + 8.66025i 0.860309 + 0.496700i
\(305\) 1.50000 0.866025i 0.0858898 0.0495885i
\(306\) 5.19615i 0.297044i
\(307\) 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
\(310\) 9.00000 + 5.19615i 0.511166 + 0.295122i
\(311\) 15.0000 25.9808i 0.850572 1.47323i −0.0301210 0.999546i \(-0.509589\pi\)
0.880693 0.473688i \(-0.157077\pi\)
\(312\) 9.00000 + 8.66025i 0.509525 + 0.490290i
\(313\) −5.00000 8.66025i −0.282617 0.489506i 0.689412 0.724370i \(-0.257869\pi\)
−0.972028 + 0.234863i \(0.924536\pi\)
\(314\) 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 \(-0.620052\pi\)
0.621021 + 0.783794i \(0.286718\pi\)
\(318\) 9.00000 5.19615i 0.504695 0.291386i
\(319\) 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
\(325\) −2.00000 6.92820i −0.110940 0.384308i
\(326\) 18.0000 31.1769i 0.996928 1.72673i
\(327\) −24.0000 13.8564i −1.32720 0.766261i
\(328\) 4.50000 + 7.79423i 0.248471 + 0.430364i
\(329\) 0 0
\(330\) 0 0
\(331\) 27.7128i 1.52323i 0.648027 + 0.761617i \(0.275594\pi\)
−0.648027 + 0.761617i \(0.724406\pi\)
\(332\) 12.0000 6.92820i 0.658586 0.380235i
\(333\) −7.50000 4.33013i −0.410997 0.237289i
\(334\) −24.0000 −1.31322
\(335\) 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 \(0.715491\pi\)
\(338\) 10.5000 19.9186i 0.571125 1.08343i
\(339\) 15.0000 25.9808i 0.814688 1.41108i
\(340\) 5.19615i 0.281801i
\(341\) 0 0
\(342\) −3.00000 + 5.19615i −0.162221 + 0.280976i
\(343\) 0 0
\(344\) 12.0000 + 6.92820i 0.646997 + 0.373544i
\(345\) 20.7846i 1.11901i
\(346\) 9.00000 + 5.19615i 0.483843 + 0.279347i
\(347\) 15.0000 + 25.9808i 0.805242 + 1.39472i 0.916127 + 0.400887i \(0.131298\pi\)
−0.110885 + 0.993833i \(0.535369\pi\)
\(348\) 3.00000 5.19615i 0.160817 0.278543i
\(349\) 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
\(353\) 32.9090i 1.75157i 0.482704 + 0.875784i \(0.339655\pi\)
−0.482704 + 0.875784i \(0.660345\pi\)
\(354\) −24.0000 −1.27559
\(355\) 6.00000 0.318447
\(356\) 6.92820i 0.367194i
\(357\) 0 0
\(358\) 0 0
\(359\) 6.00000 3.46410i 0.316668 0.182828i −0.333238 0.942843i \(-0.608141\pi\)
0.649906 + 0.760014i \(0.274808\pi\)
\(360\) −1.50000 2.59808i −0.0790569 0.136931i
\(361\) 7.00000 0.368421
\(362\) 16.5000 + 9.52628i 0.867221 + 0.500690i
\(363\) 22.0000 1.15470
\(364\) 0 0
\(365\) 3.00000 0.157027
\(366\) 3.00000 + 1.73205i 0.156813 + 0.0905357i
\(367\) −22.0000 −1.14839 −0.574195 0.818718i \(-0.694685\pi\)
−0.574195 + 0.818718i \(0.694685\pi\)
\(368\) −15.0000 25.9808i −0.781929 1.35434i
\(369\) −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
\(373\) 19.0000 0.983783 0.491891 0.870657i \(-0.336306\pi\)
0.491891 + 0.870657i \(0.336306\pi\)
\(374\) 0 0
\(375\) 24.2487i 1.25220i
\(376\) −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 \(0.547333\pi\)
\(380\) −3.00000 + 5.19615i −0.153897 + 0.266557i
\(381\) 2.00000 + 3.46410i 0.102463 + 0.177471i
\(382\) 27.0000 + 15.5885i 1.38144 + 0.797575i
\(383\) 20.7846i 1.06204i 0.847358 + 0.531022i \(0.178192\pi\)
−0.847358 + 0.531022i \(0.821808\pi\)
\(384\) −21.0000 12.1244i −1.07165 0.618718i
\(385\) 0 0
\(386\) 4.50000 7.79423i 0.229044 0.396716i
\(387\) −4.00000 + 6.92820i −0.203331 + 0.352180i
\(388\) 6.92820i 0.351726i
\(389\) 4.50000 7.79423i 0.228159 0.395183i −0.729103 0.684403i \(-0.760063\pi\)
0.957263 + 0.289220i \(0.0933960\pi\)
\(390\) −15.0000 + 15.5885i −0.759555 + 0.789352i
\(391\) 18.0000 0.910299
\(392\) 0 0
\(393\) −18.0000 31.1769i −0.907980 1.57267i
\(394\) 24.0000 1.20910
\(395\) −6.00000 3.46410i −0.301893 0.174298i
\(396\) 0 0
\(397\) 13.8564i 0.695433i 0.937600 + 0.347717i \(0.113043\pi\)
−0.937600 + 0.347717i \(0.886957\pi\)
\(398\) 3.46410i 0.173640i
\(399\) 0 0
\(400\) 5.00000 + 8.66025i 0.250000 + 0.433013i
\(401\) 1.50000 + 0.866025i 0.0749064 + 0.0432472i 0.536985 0.843592i \(-0.319563\pi\)
−0.462079 + 0.886839i \(0.652896\pi\)
\(402\) −6.00000 + 10.3923i −0.299253 + 0.518321i
\(403\) −12.0000 + 3.46410i −0.597763 + 0.172559i
\(404\) −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
\(409\) −13.5000 + 7.79423i −0.667532 + 0.385400i −0.795141 0.606425i \(-0.792603\pi\)
0.127609 + 0.991825i \(0.459270\pi\)
\(410\) −13.5000 + 7.79423i −0.666717 + 0.384930i
\(411\) 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
\(416\) −4.50000 + 18.1865i −0.220631 + 0.891668i
\(417\) 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 \(-0.124030\pi\)
\(422\) 17.3205i 0.843149i
\(423\) 3.00000 1.73205i 0.145865 0.0842152i
\(424\) −4.50000 2.59808i −0.218539 0.126174i
\(425\) −6.00000 −0.291043
\(426\) 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
\(431\) 6.92820i 0.333720i −0.985981 0.166860i \(-0.946637\pi\)
0.985981 0.166860i \(-0.0533628\pi\)
\(432\) −10.0000 + 17.3205i −0.481125 + 0.833333i
\(433\) 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
\(436\) 13.8564i 0.663602i
\(437\) 18.0000 + 10.3923i 0.861057 + 0.497131i
\(438\) 3.00000 + 5.19615i 0.143346 + 0.248282i
\(439\) 14.0000 24.2487i 0.668184 1.15733i −0.310228 0.950662i \(-0.600405\pi\)
0.978412 0.206666i \(-0.0662612\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) −13.5000 12.9904i −0.642130 0.617889i
\(443\) 6.00000 + 10.3923i 0.285069 + 0.493753i 0.972626 0.232377i \(-0.0746503\pi\)
−0.687557 + 0.726130i \(0.741317\pi\)
\(444\) 17.3205i 0.821995i
\(445\) 12.0000 0.568855
\(446\) −18.0000 −0.852325
\(447\) 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
\(452\) 15.0000 0.705541
\(453\) 30.0000 + 17.3205i 1.40952 + 0.813788i
\(454\) −42.0000 −1.97116
\(455\) 0 0
\(456\) 12.0000 0.561951
\(457\) −1.50000 0.866025i −0.0701670 0.0405110i 0.464506 0.885570i \(-0.346232\pi\)
−0.534673 + 0.845059i \(0.679565\pi\)
\(458\) 0 0
\(459\) −6.00000 10.3923i −0.280056 0.485071i
\(460\) 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 \(-0.104349\pi\)
\(464\) −15.0000 −0.696358
\(465\) 12.0000 0.556487
\(466\) 10.3923i 0.481414i
\(467\) −6.00000 10.3923i −0.277647 0.480899i 0.693153 0.720791i \(-0.256221\pi\)
−0.970799 + 0.239892i \(0.922888\pi\)
\(468\) −3.50000 0.866025i −0.161788 0.0400320i
\(469\) 0 0
\(470\) 9.00000 5.19615i 0.415139 0.239681i
\(471\) 13.0000 22.5167i 0.599008 1.03751i
\(472\) 6.00000 + 10.3923i 0.276172 + 0.478345i
\(473\) 0 0
\(474\) 13.8564i 0.636446i
\(475\) −6.00000 3.46410i −0.275299 0.158944i
\(476\) 0 0
\(477\) 1.50000 2.59808i 0.0686803 0.118958i
\(478\) −18.0000 + 31.1769i −0.823301 + 1.42600i
\(479\) 24.2487i 1.10795i 0.832533 + 0.553976i \(0.186890\pi\)
−0.832533 + 0.553976i \(0.813110\pi\)
\(480\) 9.00000 15.5885i 0.410792 0.711512i
\(481\) 30.0000 8.66025i 1.36788 0.394874i
\(482\) 3.00000 0.136646
\(483\) 0 0
\(484\) 5.50000 + 9.52628i 0.250000 + 0.433013i
\(485\) 12.0000 0.544892
\(486\) −15.0000 8.66025i −0.680414 0.392837i
\(487\) 6.00000 3.46410i 0.271886 0.156973i −0.357858 0.933776i \(-0.616493\pi\)
0.629744 + 0.776802i \(0.283160\pi\)
\(488\) 1.73205i 0.0784063i
\(489\) 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 \(0.920614\pi\)
\(492\) −9.00000 5.19615i −0.405751 0.234261i
\(493\) 4.50000 7.79423i 0.202670 0.351034i
\(494\) −6.00000 20.7846i −0.269953 0.935144i
\(495\) 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 \(-0.912520\pi\)
−0.246214 + 0.969216i \(0.579187\pi\)
\(500\) −10.5000 + 6.06218i −0.469574 + 0.271109i
\(501\) −24.0000 + 13.8564i −1.07224 + 0.619059i
\(502\) 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
\(507\) −1.00000 25.9808i −0.0444116 1.15385i
\(508\) −1.00000 + 1.73205i −0.0443678 + 0.0768473i
\(509\) −16.5000 9.52628i −0.731350 0.422245i 0.0875661 0.996159i \(-0.472091\pi\)
−0.818916 + 0.573914i \(0.805424\pi\)
\(510\) 9.00000 + 15.5885i 0.398527 + 0.690268i
\(511\) 0 0
\(512\) 8.66025i 0.382733i
\(513\) 13.8564i 0.611775i
\(514\) −4.50000 + 2.59808i −0.198486 + 0.114596i
\(515\) 15.0000 + 8.66025i 0.660979 + 0.381616i
\(516\) −16.0000 −0.704361
\(517\) 0 0
\(518\) 0 0
\(519\) 12.0000 0.526742
\(520\) 10.5000 + 2.59808i 0.460455 + 0.113933i
\(521\) −4.50000 + 7.79423i −0.197149 + 0.341471i −0.947603 0.319451i \(-0.896501\pi\)
0.750454 + 0.660922i \(0.229835\pi\)
\(522\) 5.19615i 0.227429i
\(523\) 8.00000 13.8564i 0.349816 0.605898i −0.636401 0.771358i \(-0.719578\pi\)
0.986216 + 0.165460i \(0.0529109\pi\)
\(524\) 9.00000 15.5885i 0.393167 0.680985i
\(525\) 0 0
\(526\) 18.0000 + 10.3923i 0.784837 + 0.453126i
\(527\) 10.3923i 0.452696i
\(528\) 0 0
\(529\) −6.50000 11.2583i −0.282609 0.489493i
\(530\) 4.50000 7.79423i 0.195468 0.338560i
\(531\) −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
\(535\) 10.3923i 0.449299i
\(536\) 6.00000 0.259161
\(537\) 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 \(-0.884830\pi\)
−0.161076 + 0.986942i \(0.551496\pi\)
\(542\) −18.0000 31.1769i −0.773166 1.33916i
\(543\) 22.0000 0.944110
\(544\) 13.5000 + 7.79423i 0.578808 + 0.334175i
\(545\) −24.0000 −1.02805
\(546\) 0 0
\(547\) −22.0000 −0.940652 −0.470326 0.882493i \(-0.655864\pi\)
−0.470326 + 0.882493i \(0.655864\pi\)
\(548\) 13.5000 + 7.79423i 0.576691 + 0.332953i
\(549\) 1.00000 0.0426790
\(550\) 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
\(555\) −30.0000 −1.27343
\(556\) 4.00000 0.169638
\(557\) 15.5885i 0.660504i −0.943893 0.330252i \(-0.892866\pi\)
0.943893 0.330252i \(-0.107134\pi\)
\(558\) 3.00000 + 5.19615i 0.127000 + 0.219971i
\(559\) −8.00000 27.7128i −0.338364 1.17213i
\(560\) 0 0
\(561\) 0 0
\(562\) −19.5000 + 33.7750i −0.822558 + 1.42471i
\(563\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(564\) 6.00000 + 3.46410i 0.252646 + 0.145865i
\(565\) 25.9808i 1.09302i
\(566\) 6.00000 + 3.46410i 0.252199 + 0.145607i
\(567\) 0 0
\(568\) 3.00000 5.19615i 0.125877 0.218026i
\(569\) 21.0000 36.3731i 0.880366 1.52484i 0.0294311 0.999567i \(-0.490630\pi\)
0.850935 0.525271i \(-0.176036\pi\)
\(570\) 20.7846i 0.870572i
\(571\) −20.0000 + 34.6410i −0.836974 + 1.44968i 0.0554391 + 0.998462i \(0.482344\pi\)
−0.892413 + 0.451219i \(0.850989\pi\)
\(572\) 0 0
\(573\) 36.0000 1.50392
\(574\) 0 0
\(575\) 6.00000 + 10.3923i 0.250217 + 0.433389i
\(576\) −1.00000 −0.0416667
\(577\) −16.5000 9.52628i −0.686904 0.396584i 0.115547 0.993302i \(-0.463138\pi\)
−0.802451 + 0.596718i \(0.796471\pi\)
\(578\) 12.0000 6.92820i 0.499134 0.288175i
\(579\) 10.3923i 0.431889i
\(580\) 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
\(585\) −1.50000 + 6.06218i −0.0620174 + 0.250640i
\(586\) 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
\(591\) 24.0000 13.8564i 0.987228 0.569976i
\(592\) −37.5000 + 21.6506i −1.54124 + 0.889836i
\(593\) 22.5000 12.9904i 0.923964 0.533451i 0.0390666 0.999237i \(-0.487562\pi\)
0.884898 + 0.465786i \(0.154228\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −16.5000 + 9.52628i −0.675866 + 0.390212i
\(597\) 2.00000 + 3.46410i 0.0818546 + 0.141776i
\(598\) −9.00000 + 36.3731i −0.368037 + 1.48741i
\(599\) −15.0000 + 25.9808i −0.612883 + 1.06155i 0.377869 + 0.925859i \(0.376657\pi\)
−0.990752 + 0.135686i \(0.956676\pi\)
\(600\) 6.00000 + 3.46410i 0.244949 + 0.141421i
\(601\) −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
\(604\) 17.3205i 0.704761i
\(605\) 16.5000 9.52628i 0.670820 0.387298i
\(606\) −9.00000 5.19615i −0.365600 0.211079i
\(607\) −34.0000 −1.38002 −0.690009 0.723801i \(-0.742393\pi\)
−0.690009 + 0.723801i \(0.742393\pi\)
\(608\) 9.00000 + 15.5885i 0.364998 + 0.632195i
\(609\) 0 0
\(610\) 3.00000 0.121466
\(611\) −3.00000 + 12.1244i −0.121367 + 0.490499i
\(612\) −1.50000 + 2.59808i −0.0606339 + 0.105021i
\(613\) 12.1244i 0.489698i −0.969561 0.244849i \(-0.921262\pi\)
0.969561 0.244849i \(-0.0787384\pi\)
\(614\) −15.0000 + 25.9808i −0.605351 + 1.04850i
\(615\) −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 \(0.816400\pi\)
\(618\) 34.6410i 1.39347i
\(619\) −18.0000 10.3923i −0.723481 0.417702i 0.0925515 0.995708i \(-0.470498\pi\)
−0.816033 + 0.578006i \(0.803831\pi\)
\(620\) 3.00000 + 5.19615i 0.120483 + 0.208683i
\(621\) −12.0000 + 20.7846i −0.481543 + 0.834058i
\(622\) 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
\(626\) 17.3205i 0.692267i
\(627\) 0 0
\(628\) 13.0000 0.518756
\(629\) 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
\(633\) −10.0000 17.3205i −0.397464 0.688428i
\(634\) 9.00000 0.357436
\(635\) 3.00000 + 1.73205i 0.119051 + 0.0687343i
\(636\) 6.00000 0.237915
\(637\) 0 0
\(638\) 0 0
\(639\) 3.00000 + 1.73205i 0.118678 + 0.0685189i
\(640\) −21.0000 −0.830098
\(641\) −16.5000 28.5788i −0.651711 1.12880i −0.982708 0.185164i \(-0.940718\pi\)
0.330997 0.943632i \(-0.392615\pi\)
\(642\) −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
\(646\) −18.0000 −0.708201
\(647\) 18.0000 0.707653 0.353827 0.935311i \(-0.384880\pi\)
0.353827 + 0.935311i \(0.384880\pi\)
\(648\) 19.0526i 0.748455i
\(649\) 0 0
\(650\) 3.00000 12.1244i 0.117670 0.475556i
\(651\) 0 0
\(652\) 18.0000 10.3923i 0.704934 0.406994i
\(653\) 15.0000 25.9808i 0.586995 1.01671i −0.407628 0.913148i \(-0.633644\pi\)
0.994623 0.103558i \(-0.0330227\pi\)
\(654\) −24.0000 41.5692i −0.938474 1.62549i
\(655\) −27.0000 15.5885i −1.05498 0.609091i
\(656\) 25.9808i 1.01438i
\(657\) 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
\(661\) 46.7654i 1.81896i −0.415745 0.909481i \(-0.636479\pi\)
0.415745 0.909481i \(-0.363521\pi\)
\(662\) −24.0000 + 41.5692i −0.932786 + 1.61563i
\(663\) −21.0000 5.19615i −0.815572 0.201802i
\(664\) −24.0000 −0.931381
\(665\) 0 0
\(666\) −7.50000 12.9904i −0.290619 0.503367i
\(667\) −18.0000 −0.696963
\(668\) −12.0000 6.92820i −0.464294 0.268060i
\(669\) −18.0000 + 10.3923i −0.695920 + 0.401790i
\(670\) 10.3923i 0.401490i
\(671\) 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 \(0.713993\pi\)
\(674\) −34.5000 19.9186i −1.32889 0.767235i
\(675\) 4.00000 6.92820i 0.153960 0.266667i
\(676\) 11.0000 6.92820i 0.423077 0.266469i
\(677\) 3.00000 + 5.19615i 0.115299 + 0.199704i 0.917899 0.396813i \(-0.129884\pi\)
−0.802600 + 0.596518i \(0.796551\pi\)
\(678\) 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
\(683\) −21.0000 + 12.1244i −0.803543 + 0.463926i −0.844708 0.535227i \(-0.820226\pi\)
0.0411658 + 0.999152i \(0.486893\pi\)
\(684\) −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
\(689\) 3.00000 + 10.3923i 0.114291 + 0.395915i
\(690\) 18.0000 31.1769i 0.685248 1.18688i
\(691\) −12.0000 6.92820i −0.456502 0.263561i 0.254071 0.967186i \(-0.418230\pi\)
−0.710572 + 0.703624i \(0.751564\pi\)
\(692\) 3.00000 + 5.19615i 0.114043 + 0.197528i
\(693\) 0 0
\(694\) 51.9615i 1.97243i
\(695\) 6.92820i 0.262802i
\(696\) −9.00000 + 5.19615i −0.341144 + 0.196960i
\(697\) −13.5000 7.79423i −0.511349 0.295227i
\(698\) 24.0000 0.908413
\(699\) −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 \(0.389598\pi\)
\(702\) 24.0000 6.92820i 0.905822 0.261488i
\(703\) 15.0000 25.9808i 0.565736 0.979883i
\(704\) 0 0
\(705\) 6.00000 10.3923i 0.225973 0.391397i
\(706\) −28.5000 + 49.3634i −1.07261 + 1.85782i
\(707\) 0 0
\(708\) −12.0000 6.92820i −0.450988 0.260378i
\(709\) 5.19615i 0.195146i 0.995228 + 0.0975728i \(0.0311079\pi\)
−0.995228 + 0.0975728i \(0.968892\pi\)
\(710\) 9.00000 + 5.19615i 0.337764 + 0.195008i
\(711\) −2.00000 3.46410i −0.0750059 0.129914i
\(712\) 6.00000 10.3923i 0.224860 0.389468i
\(713\) 18.0000 10.3923i 0.674105 0.389195i
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 41.5692i 1.55243i
\(718\) 12.0000 0.447836
\(719\) −48.0000 −1.79010 −0.895049 0.445968i \(-0.852860\pi\)
−0.895049 + 0.445968i \(0.852860\pi\)
\(720\) 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
\(724\) 5.50000 + 9.52628i 0.204406 + 0.354041i
\(725\) 6.00000 0.222834
\(726\) 33.0000 + 19.0526i 1.22474 + 0.707107i
\(727\) −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
\(730\) 4.50000 + 2.59808i 0.166552 + 0.0961591i
\(731\) −24.0000 −0.887672
\(732\) 1.00000 + 1.73205i 0.0369611 + 0.0640184i
\(733\) −10.5000 + 6.06218i −0.387826 + 0.223912i −0.681218 0.732081i \(-0.738549\pi\)
0.293392 + 0.955992i \(0.405216\pi\)
\(734\) −33.0000 19.0526i −1.21805 0.703243i
\(735\) 0 0
\(736\) 31.1769i 1.14920i
\(737\) 0 0
\(738\) −9.00000 −0.331295
\(739\) 20.7846i 0.764574i −0.924044 0.382287i \(-0.875137\pi\)
0.924044 0.382287i \(-0.124863\pi\)
\(740\) −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 \(0.552510\pi\)
\(744\) 6.00000 10.3923i 0.219971 0.381000i
\(745\) 16.5000 + 28.5788i 0.604513 + 1.04705i
\(746\) 28.5000 + 16.4545i 1.04346 + 0.602441i
\(747\) 13.8564i 0.506979i
\(748\) 0 0
\(749\) 0 0
\(750\) −21.0000 + 36.3731i −0.766812 + 1.32816i
\(751\) 8.00000 13.8564i 0.291924 0.505627i −0.682341 0.731034i \(-0.739038\pi\)
0.974265 + 0.225407i \(0.0723712\pi\)
\(752\) 17.3205i 0.631614i
\(753\) 18.0000 31.1769i 0.655956 1.13615i
\(754\) 13.5000 + 12.9904i 0.491641 + 0.473082i
\(755\) 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 \(0.676688\pi\)
\(758\) −42.0000 −1.52551
\(759\) 0 0
\(760\) 9.00000 5.19615i 0.326464 0.188484i
\(761\) 34.6410i 1.25574i −0.778320 0.627868i \(-0.783928\pi\)
0.778320 0.627868i \(-0.216072\pi\)
\(762\) 6.92820i 0.250982i
\(763\) 0 0
\(764\) 9.00000 + 15.5885i 0.325609 + 0.563971i
\(765\) 4.50000 + 2.59808i 0.162698 + 0.0939336i
\(766\) −18.0000 + 31.1769i −0.650366 + 1.12647i
\(767\) 6.00000 24.2487i 0.216647 0.875570i
\(768\) −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
\(773\) 30.0000 17.3205i 1.07903 0.622975i 0.148392 0.988929i \(-0.452590\pi\)
0.930633 + 0.365953i \(0.119257\pi\)
\(774\) −12.0000 + 6.92820i −0.431331 + 0.249029i
\(775\) −6.00000 + 3.46410i −0.215526 + 0.124434i
\(776\) 6.00000 10.3923i 0.215387 0.373062i
\(777\)