Properties

Label 637.2.u.b.30.1
Level $637$
Weight $2$
Character 637.30
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 30.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 637.30
Dual form 637.2.u.b.361.1

$q$-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 \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.50000 0.866025i 1.06066 0.612372i 0.135045 0.990839i \(-0.456882\pi\)
0.925615 + 0.378467i \(0.123549\pi\)
\(3\) −2.00000 −1.15470 −0.577350 0.816497i \(-0.695913\pi\)
−0.577350 + 0.816497i \(0.695913\pi\)
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) −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
\(9\) 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 \(-0.951855\pi\)
0.624780 + 0.780801i \(0.285189\pi\)
\(18\) 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 0.988436 + 0.151642i \(0.0484560\pi\)
−0.362892 + 0.931831i \(0.618211\pi\)
\(24\) 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 −0.971023 0.238987i \(-0.923185\pi\)
0.692480 + 0.721437i \(0.256518\pi\)
\(30\) 6.00000 1.09545
\(31\) −3.00000 + 1.73205i −0.538816 + 0.311086i −0.744599 0.667512i \(-0.767359\pi\)
0.205783 + 0.978598i \(0.434026\pi\)
\(32\) 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 −0.967653 0.252286i \(-0.918817\pi\)
−0.265340 + 0.964155i \(0.585484\pi\)
\(38\) 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 \(-0.200343\pi\)
−0.105601 + 0.994409i \(0.533677\pi\)
\(42\) 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
\(45\) −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 \(-0.414634\pi\)
−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
\(52\) 3.50000 0.866025i 0.485363 0.120096i
\(53\) 1.50000 + 2.59808i 0.206041 + 0.356873i 0.950464 0.310835i \(-0.100609\pi\)
−0.744423 + 0.667708i \(0.767275\pi\)
\(54\) 6.00000 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 \(-0.184405\pi\)
−0.0556984 + 0.998448i \(0.517739\pi\)
\(60\) 3.00000 1.73205i 0.387298 0.223607i
\(61\) −1.00000 −0.128037 −0.0640184 0.997949i \(-0.520392\pi\)
−0.0640184 + 0.997949i \(0.520392\pi\)
\(62\) −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 \(-0.932131\pi\)
0.977356 0.211604i \(-0.0678686\pi\)
\(68\) 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 −0.311305 0.950310i \(-0.600766\pi\)
0.667340 + 0.744753i \(0.267433\pi\)
\(72\) 1.73205i 0.204124i
\(73\) −1.50000 + 0.866025i −0.175562 + 0.101361i −0.585206 0.810885i \(-0.698986\pi\)
0.409644 + 0.912245i \(0.365653\pi\)
\(74\) −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 −0.956325 0.292306i \(-0.905577\pi\)
0.731307 + 0.682048i \(0.238911\pi\)
\(80\) 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 \(-0.786348\pi\)
0.147073 + 0.989126i \(0.453015\pi\)
\(90\) −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 \(-0.781072\pi\)
0.163448 + 0.986552i \(0.447739\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −2.00000 −0.200000
\(101\) 3.00000 0.298511 0.149256 0.988799i \(-0.452312\pi\)
0.149256 + 0.988799i \(0.452312\pi\)
\(102\) 10.3923i 1.02899i
\(103\) −5.00000 + 8.66025i −0.492665 + 0.853320i −0.999964 0.00844953i \(-0.997310\pi\)
0.507300 + 0.861770i \(0.330644\pi\)
\(104\) −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 0.683793 0.729676i \(-0.260329\pi\)
−0.973814 + 0.227345i \(0.926996\pi\)
\(108\) 2.00000 3.46410i 0.192450 0.333333i
\(109\) −12.0000 + 6.92820i −1.14939 + 0.663602i −0.948739 0.316061i \(-0.897640\pi\)
−0.200653 + 0.979662i \(0.564306\pi\)
\(110\) 0 0
\(111\) 15.0000 8.66025i 1.42374 0.821995i
\(112\) 0 0
\(113\) 7.50000 + 12.9904i 0.705541 + 1.22203i 0.966496 + 0.256681i \(0.0826291\pi\)
−0.260955 + 0.965351i \(0.584038\pi\)
\(114\) −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 −0.818241 0.574875i \(-0.805051\pi\)
0.906977 + 0.421180i \(0.138384\pi\)
\(128\) −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 −0.141865 0.989886i \(-0.545310\pi\)
0.928199 0.372084i \(-0.121357\pi\)
\(132\) 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 0.949709 0.313133i \(-0.101379\pi\)
0.203674 + 0.979039i \(0.434712\pi\)
\(138\) −18.0000 10.3923i −1.53226 0.884652i
\(139\) −2.00000 3.46410i −0.169638 0.293821i 0.768655 0.639664i \(-0.220926\pi\)
−0.938293 + 0.345843i \(0.887593\pi\)
\(140\) 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 \(-0.715004\pi\)
0.625252 0.780423i \(-0.284996\pi\)
\(150\) 6.00000 + 3.46410i 0.489898 + 0.282843i
\(151\) 15.0000 8.66025i 1.22068 0.704761i 0.255619 0.966778i \(-0.417721\pi\)
0.965064 + 0.262016i \(0.0843873\pi\)
\(152\) −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 −0.999762 0.0217953i \(-0.993062\pi\)
0.481006 0.876717i \(-0.340272\pi\)
\(158\) 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 \(0.302708\pi\)
−0.580881 + 0.813988i \(0.697292\pi\)
\(164\) 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 \(-0.153223\pi\)
0.0422232 + 0.999108i \(0.486556\pi\)
\(168\) 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 \(-0.573247\pi\)
−0.228086 + 0.973641i \(0.573247\pi\)
\(174\) 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 \(-0.634057\pi\)
−0.408812 + 0.912619i \(0.634057\pi\)
\(182\) 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 \(0.0598809\pi\)
−0.982357 + 0.187014i \(0.940119\pi\)
\(194\) −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 0.862323 0.506359i \(-0.169009\pi\)
−0.00735824 + 0.999973i \(0.502342\pi\)
\(198\) 0 0
\(199\) −1.00000 + 1.73205i −0.0708881 + 0.122782i −0.899291 0.437351i \(-0.855917\pi\)
0.828403 + 0.560133i \(0.189250\pi\)
\(200\) 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 −0.985211 0.171347i \(-0.945188\pi\)
0.640996 + 0.767544i \(0.278521\pi\)
\(212\) 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 \(-0.220208\pi\)
−0.167412 + 0.985887i \(0.553541\pi\)
\(224\) 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 \(-0.0356478\pi\)
0.400083 + 0.916479i \(0.368981\pi\)
\(228\) −6.00000 3.46410i −0.397360 0.229416i
\(229\) 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 \(0.229636\pi\)
\(234\) 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 \(-0.765340\pi\)
0.740349 0.672222i \(-0.234660\pi\)
\(240\) 17.3205i 1.11803i
\(241\) −1.50000 0.866025i −0.0966235 0.0557856i 0.450910 0.892570i \(-0.351100\pi\)
−0.547533 + 0.836784i \(0.684433\pi\)
\(242\) 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 −0.996756 0.0804789i \(-0.974355\pi\)
0.428681 0.903456i \(-0.358978\pi\)
\(252\) 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 \(-0.136840\pi\)
−0.815442 + 0.578838i \(0.803506\pi\)
\(258\) 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 \(-0.891886\pi\)
0.759958 + 0.649972i \(0.225219\pi\)
\(270\) −12.0000 −0.730297
\(271\) 18.0000 10.3923i 1.09342 0.631288i 0.158937 0.987289i \(-0.449193\pi\)
0.934485 + 0.356001i \(0.115860\pi\)
\(272\) −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 −0.741512 0.670940i \(-0.765891\pi\)
0.951807 + 0.306699i \(0.0992243\pi\)
\(278\) −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 \(-0.765601\pi\)
0.740900 0.671616i \(-0.234399\pi\)
\(282\) 12.0000 0.714590
\(283\) −4.00000 −0.237775 −0.118888 0.992908i \(-0.537933\pi\)
−0.118888 + 0.992908i \(0.537933\pi\)
\(284\) 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 \(-0.715168\pi\)
0.362761 + 0.931882i \(0.381834\pi\)
\(294\) 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 −0.880693 0.473688i \(-0.842923\pi\)
0.0301210 0.999546i \(-0.490411\pi\)
\(312\) 9.00000 8.66025i 0.509525 0.490290i
\(313\) 5.00000 8.66025i 0.282617 0.489506i −0.689412 0.724370i \(-0.742131\pi\)
0.972028 + 0.234863i \(0.0754642\pi\)
\(314\) −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 0.621021 0.783794i \(-0.286718\pi\)
−0.368275 + 0.929717i \(0.620052\pi\)
\(318\) −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 \(-0.724406\pi\)
0.648027 0.761617i \(-0.275594\pi\)
\(332\) −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 −0.110885 0.993833i \(-0.535369\pi\)
0.916127 0.400887i \(-0.131298\pi\)
\(348\) −3.00000 5.19615i −0.160817 0.278543i
\(349\) −12.0000 6.92820i −0.642345 0.370858i 0.143172 0.989698i \(-0.454270\pi\)
−0.785517 + 0.618840i \(0.787603\pi\)
\(350\) 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 0.649906 0.760014i \(-0.274808\pi\)
−0.333238 + 0.942843i \(0.608141\pi\)
\(360\) 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 \(-0.305315\pi\)
0.574195 + 0.818718i \(0.305315\pi\)
\(368\) −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 −0.148153 0.988964i \(-0.547333\pi\)
−0.930545 + 0.366178i \(0.880666\pi\)
\(380\) −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 0.957263 0.289220i \(-0.0933960\pi\)
−0.729103 + 0.684403i \(0.760063\pi\)
\(390\) 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 −0.462079 0.886839i \(-0.652896\pi\)
0.536985 + 0.843592i \(0.319563\pi\)
\(402\) 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 \(-0.207397\pi\)
−0.127609 + 0.991825i \(0.540730\pi\)
\(410\) −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 \(-0.688426\pi\)
0.997665 + 0.0683046i \(0.0217590\pi\)
\(420\) 0 0
\(421\) 15.5885i 0.759735i 0.925041 + 0.379867i \(0.124030\pi\)
−0.925041 + 0.379867i \(0.875970\pi\)
\(422\) 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 \(0.0533628\pi\)
−0.985981 + 0.166860i \(0.946637\pi\)
\(432\) 10.0000 + 17.3205i 0.481125 + 0.833333i
\(433\) −8.50000 14.7224i −0.408484 0.707515i 0.586236 0.810140i \(-0.300609\pi\)
−0.994720 + 0.102625i \(0.967276\pi\)
\(434\) 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 −0.978412 0.206666i \(-0.933739\pi\)
0.310228 0.950662i \(-0.399595\pi\)
\(440\) 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 \(0.0746503\pi\)
\(444\) 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 −0.634852 0.772634i \(-0.718939\pi\)
0.351694 + 0.936115i \(0.385606\pi\)
\(450\) −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 −0.534673 0.845059i \(-0.679565\pi\)
0.464506 + 0.885570i \(0.346232\pi\)
\(458\) 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 \(-0.842359\pi\)
−0.0283522 + 0.999598i \(0.509026\pi\)
\(462\) 0 0
\(463\) 13.8564i 0.643962i 0.946746 + 0.321981i \(0.104349\pi\)
−0.946746 + 0.321981i \(0.895651\pi\)
\(464\) −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 \(-0.743779\pi\)
0.970799 + 0.239892i \(0.0771121\pi\)
\(468\) 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 0.629744 0.776802i \(-0.283160\pi\)
−0.357858 + 0.933776i \(0.616493\pi\)
\(488\) 1.73205i 0.0784063i
\(489\) 41.5692i 1.87983i
\(490\) 0 0
\(491\) −6.00000 + 10.3923i −0.270776 + 0.468998i −0.969061 0.246822i \(-0.920614\pi\)
0.698285 + 0.715820i \(0.253947\pi\)
\(492\) −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 −0.246214 0.969216i \(-0.579187\pi\)
−0.962472 + 0.271380i \(0.912520\pi\)
\(500\) 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 0.917912 + 0.396783i \(0.129873\pi\)
−0.115332 + 0.993327i \(0.536793\pi\)
\(504\) 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 \(-0.527909\pi\)
0.818916 + 0.573914i \(0.194576\pi\)
\(510\) −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 \(-0.103499\pi\)
−0.750454 + 0.660922i \(0.770165\pi\)
\(522\) 5.19615i 0.227429i
\(523\) −8.00000 13.8564i −0.349816 0.605898i 0.636401 0.771358i \(-0.280422\pi\)
−0.986216 + 0.165460i \(0.947089\pi\)
\(524\) −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 −0.161076 0.986942i \(-0.551496\pi\)
−0.935255 + 0.353975i \(0.884830\pi\)
\(542\) 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 \(0.107134\pi\)
−0.943893 + 0.330252i \(0.892866\pi\)
\(558\) −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 \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(564\) 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 0.850935 + 0.525271i \(0.176036\pi\)
0.0294311 + 0.999567i \(0.490630\pi\)
\(570\) 20.7846i 0.870572i
\(571\) −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
\(576\) −1.00000 −0.0416667
\(577\) 16.5000 9.52628i 0.686904 0.396584i −0.115547 0.993302i \(-0.536862\pi\)
0.802451 + 0.596718i \(0.203529\pi\)
\(578\) 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 \(-0.192222\pi\)
−0.0801976 + 0.996779i \(0.525555\pi\)
\(588\) 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 \(-0.512438\pi\)
−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
\(598\) 9.00000 + 36.3731i 0.368037 + 1.48741i
\(599\) −15.0000 25.9808i −0.612883 1.06155i −0.990752 0.135686i \(-0.956676\pi\)
0.377869 0.925859i \(-0.376657\pi\)
\(600\) −6.00000 + 3.46410i −0.244949 + 0.141421i
\(601\) 12.5000 21.6506i 0.509886 0.883148i −0.490049 0.871695i \(-0.663021\pi\)
0.999934 0.0114528i \(-0.00364562\pi\)
\(602\) 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 \(-0.257607\pi\)
0.690009 + 0.723801i \(0.257607\pi\)
\(608\) −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 \(0.0787384\pi\)
−0.969561 + 0.244849i \(0.921262\pi\)
\(614\) 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 −0.838214 0.545342i \(-0.816400\pi\)
0.0531732 + 0.998585i \(0.483066\pi\)
\(618\) 34.6410i 1.39347i
\(619\) 18.0000 10.3923i 0.723481 0.417702i −0.0925515 0.995708i \(-0.529502\pi\)
0.816033 + 0.578006i \(0.196169\pi\)
\(620\) 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 −0.705473 + 0.708737i \(0.749265\pi\)
−0.966521 + 0.256589i \(0.917401\pi\)
\(632\) −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 0.330997 + 0.943632i \(0.392615\pi\)
−0.982708 + 0.185164i \(0.940718\pi\)
\(642\) 18.0000 + 10.3923i 0.710403 + 0.410152i
\(643\) −12.0000 + 6.92820i −0.473234 + 0.273222i −0.717592 0.696463i \(-0.754756\pi\)
0.244359 + 0.969685i \(0.421423\pi\)
\(644\) 0 0
\(645\) 27.7128i 1.09119i
\(646\) −18.0000 −0.708201
\(647\) −18.0000 −0.707653 −0.353827 0.935311i \(-0.615120\pi\)
−0.353827 + 0.935311i \(0.615120\pi\)
\(648\) 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 0.994623 + 0.103558i \(0.0330227\pi\)
−0.407628 + 0.913148i \(0.633644\pi\)
\(654\) 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 0.958902 0.283738i \(-0.0915745\pi\)
−0.725175 + 0.688565i \(0.758241\pi\)
\(660\) 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 −0.622770 0.782405i \(-0.713993\pi\)
0.988968 + 0.148132i \(0.0473259\pi\)
\(674\) −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 \(-0.870116\pi\)
0.802600 + 0.596518i \(0.203449\pi\)
\(678\) −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 0.0411658 0.999152i \(-0.486893\pi\)
−0.844708 + 0.535227i \(0.820226\pi\)
\(684\) 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 \(-0.581770\pi\)
0.710572 + 0.703624i \(0.248436\pi\)
\(692\) −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 \(-0.968892\pi\)
0.995228 0.0975728i \(-0.0311079\pi\)
\(710\) −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 \(-0.147140\pi\)
0.895049 + 0.445968i \(0.147140\pi\)
\(720\) 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 \(-0.297782\pi\)
0.593407 + 0.804902i \(0.297782\pi\)
\(728\) 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 \(-0.261451\pi\)
−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
\(738\) 9.00000 0.331295
\(739\) 20.7846i 0.764574i 0.924044 + 0.382287i \(0.124863\pi\)
−0.924044 + 0.382287i \(0.875137\pi\)
\(740\) 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 −0.164216 0.986424i \(-0.552510\pi\)
−0.936377 + 0.350997i \(0.885843\pi\)
\(744\) 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 0.974265 0.225407i \(-0.0723712\pi\)
−0.682341 + 0.731034i \(0.739038\pi\)
\(752\) 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 −0.527011 0.849858i \(-0.676688\pi\)
0.999505 + 0.0314762i \(0.0100208\pi\)
\(758\) −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 \(-0.373200\pi\)
−0.604266 + 0.796782i \(0.706534\pi\)
\(770\) 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 \(-0.547410\pi\)
−0.930633 + 0.365953i \(0.880743\pi\)
\(774\) −12.0000 6.92820i −0.431331 0.249029i
\(775\) 6.00000 + 3.46410i 0.215526 + 0.124434i
\(776\)