Properties

Label 1638.2.j.j.1171.1
Level $1638$
Weight $2$
Character 1638.1171
Analytic conductor $13.079$
Analytic rank $0$
Dimension $2$
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1638,2,Mod(235,1638)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1638, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 4, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1638.235");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1638.j (of order \(3\), degree \(2\), 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: \(13.0794958511\)
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 546)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 1171.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1638.1171
Dual form 1638.2.j.j.235.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(1.50000 - 2.59808i) q^{5} +(-0.500000 + 2.59808i) q^{7} -1.00000 q^{8} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(1.50000 - 2.59808i) q^{5} +(-0.500000 + 2.59808i) q^{7} -1.00000 q^{8} +(-1.50000 - 2.59808i) q^{10} +(1.50000 + 2.59808i) q^{11} +1.00000 q^{13} +(2.00000 + 1.73205i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(3.00000 + 5.19615i) q^{17} +(2.00000 - 3.46410i) q^{19} -3.00000 q^{20} +3.00000 q^{22} +(3.00000 - 5.19615i) q^{23} +(-2.00000 - 3.46410i) q^{25} +(0.500000 - 0.866025i) q^{26} +(2.50000 - 0.866025i) q^{28} +9.00000 q^{29} +(-2.50000 - 4.33013i) q^{31} +(0.500000 + 0.866025i) q^{32} +6.00000 q^{34} +(6.00000 + 5.19615i) q^{35} +(2.00000 - 3.46410i) q^{37} +(-2.00000 - 3.46410i) q^{38} +(-1.50000 + 2.59808i) q^{40} +12.0000 q^{41} -4.00000 q^{43} +(1.50000 - 2.59808i) q^{44} +(-3.00000 - 5.19615i) q^{46} +(-6.00000 + 10.3923i) q^{47} +(-6.50000 - 2.59808i) q^{49} -4.00000 q^{50} +(-0.500000 - 0.866025i) q^{52} +(-4.50000 - 7.79423i) q^{53} +9.00000 q^{55} +(0.500000 - 2.59808i) q^{56} +(4.50000 - 7.79423i) q^{58} +(-4.50000 - 7.79423i) q^{59} +(-4.00000 + 6.92820i) q^{61} -5.00000 q^{62} +1.00000 q^{64} +(1.50000 - 2.59808i) q^{65} +(2.00000 + 3.46410i) q^{67} +(3.00000 - 5.19615i) q^{68} +(7.50000 - 2.59808i) q^{70} -6.00000 q^{71} +(-7.00000 - 12.1244i) q^{73} +(-2.00000 - 3.46410i) q^{74} -4.00000 q^{76} +(-7.50000 + 2.59808i) q^{77} +(0.500000 - 0.866025i) q^{79} +(1.50000 + 2.59808i) q^{80} +(6.00000 - 10.3923i) q^{82} -3.00000 q^{83} +18.0000 q^{85} +(-2.00000 + 3.46410i) q^{86} +(-1.50000 - 2.59808i) q^{88} +(-0.500000 + 2.59808i) q^{91} -6.00000 q^{92} +(6.00000 + 10.3923i) q^{94} +(-6.00000 - 10.3923i) q^{95} +5.00000 q^{97} +(-5.50000 + 4.33013i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + q^{2} - q^{4} + 3 q^{5} - q^{7} - 2 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + q^{2} - q^{4} + 3 q^{5} - q^{7} - 2 q^{8} - 3 q^{10} + 3 q^{11} + 2 q^{13} + 4 q^{14} - q^{16} + 6 q^{17} + 4 q^{19} - 6 q^{20} + 6 q^{22} + 6 q^{23} - 4 q^{25} + q^{26} + 5 q^{28} + 18 q^{29} - 5 q^{31} + q^{32} + 12 q^{34} + 12 q^{35} + 4 q^{37} - 4 q^{38} - 3 q^{40} + 24 q^{41} - 8 q^{43} + 3 q^{44} - 6 q^{46} - 12 q^{47} - 13 q^{49} - 8 q^{50} - q^{52} - 9 q^{53} + 18 q^{55} + q^{56} + 9 q^{58} - 9 q^{59} - 8 q^{61} - 10 q^{62} + 2 q^{64} + 3 q^{65} + 4 q^{67} + 6 q^{68} + 15 q^{70} - 12 q^{71} - 14 q^{73} - 4 q^{74} - 8 q^{76} - 15 q^{77} + q^{79} + 3 q^{80} + 12 q^{82} - 6 q^{83} + 36 q^{85} - 4 q^{86} - 3 q^{88} - q^{91} - 12 q^{92} + 12 q^{94} - 12 q^{95} + 10 q^{97} - 11 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1638\mathbb{Z}\right)^\times\).

\(n\) \(379\) \(703\) \(911\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 0.866025i 0.353553 0.612372i
\(3\) 0 0
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 1.50000 2.59808i 0.670820 1.16190i −0.306851 0.951757i \(-0.599275\pi\)
0.977672 0.210138i \(-0.0673912\pi\)
\(6\) 0 0
\(7\) −0.500000 + 2.59808i −0.188982 + 0.981981i
\(8\) −1.00000 −0.353553
\(9\) 0 0
\(10\) −1.50000 2.59808i −0.474342 0.821584i
\(11\) 1.50000 + 2.59808i 0.452267 + 0.783349i 0.998526 0.0542666i \(-0.0172821\pi\)
−0.546259 + 0.837616i \(0.683949\pi\)
\(12\) 0 0
\(13\) 1.00000 0.277350
\(14\) 2.00000 + 1.73205i 0.534522 + 0.462910i
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 3.00000 + 5.19615i 0.727607 + 1.26025i 0.957892 + 0.287129i \(0.0927008\pi\)
−0.230285 + 0.973123i \(0.573966\pi\)
\(18\) 0 0
\(19\) 2.00000 3.46410i 0.458831 0.794719i −0.540068 0.841621i \(-0.681602\pi\)
0.998899 + 0.0469020i \(0.0149348\pi\)
\(20\) −3.00000 −0.670820
\(21\) 0 0
\(22\) 3.00000 0.639602
\(23\) 3.00000 5.19615i 0.625543 1.08347i −0.362892 0.931831i \(-0.618211\pi\)
0.988436 0.151642i \(-0.0484560\pi\)
\(24\) 0 0
\(25\) −2.00000 3.46410i −0.400000 0.692820i
\(26\) 0.500000 0.866025i 0.0980581 0.169842i
\(27\) 0 0
\(28\) 2.50000 0.866025i 0.472456 0.163663i
\(29\) 9.00000 1.67126 0.835629 0.549294i \(-0.185103\pi\)
0.835629 + 0.549294i \(0.185103\pi\)
\(30\) 0 0
\(31\) −2.50000 4.33013i −0.449013 0.777714i 0.549309 0.835619i \(-0.314891\pi\)
−0.998322 + 0.0579057i \(0.981558\pi\)
\(32\) 0.500000 + 0.866025i 0.0883883 + 0.153093i
\(33\) 0 0
\(34\) 6.00000 1.02899
\(35\) 6.00000 + 5.19615i 1.01419 + 0.878310i
\(36\) 0 0
\(37\) 2.00000 3.46410i 0.328798 0.569495i −0.653476 0.756948i \(-0.726690\pi\)
0.982274 + 0.187453i \(0.0600231\pi\)
\(38\) −2.00000 3.46410i −0.324443 0.561951i
\(39\) 0 0
\(40\) −1.50000 + 2.59808i −0.237171 + 0.410792i
\(41\) 12.0000 1.87409 0.937043 0.349215i \(-0.113552\pi\)
0.937043 + 0.349215i \(0.113552\pi\)
\(42\) 0 0
\(43\) −4.00000 −0.609994 −0.304997 0.952353i \(-0.598656\pi\)
−0.304997 + 0.952353i \(0.598656\pi\)
\(44\) 1.50000 2.59808i 0.226134 0.391675i
\(45\) 0 0
\(46\) −3.00000 5.19615i −0.442326 0.766131i
\(47\) −6.00000 + 10.3923i −0.875190 + 1.51587i −0.0186297 + 0.999826i \(0.505930\pi\)
−0.856560 + 0.516047i \(0.827403\pi\)
\(48\) 0 0
\(49\) −6.50000 2.59808i −0.928571 0.371154i
\(50\) −4.00000 −0.565685
\(51\) 0 0
\(52\) −0.500000 0.866025i −0.0693375 0.120096i
\(53\) −4.50000 7.79423i −0.618123 1.07062i −0.989828 0.142269i \(-0.954560\pi\)
0.371706 0.928351i \(-0.378773\pi\)
\(54\) 0 0
\(55\) 9.00000 1.21356
\(56\) 0.500000 2.59808i 0.0668153 0.347183i
\(57\) 0 0
\(58\) 4.50000 7.79423i 0.590879 1.02343i
\(59\) −4.50000 7.79423i −0.585850 1.01472i −0.994769 0.102151i \(-0.967427\pi\)
0.408919 0.912571i \(-0.365906\pi\)
\(60\) 0 0
\(61\) −4.00000 + 6.92820i −0.512148 + 0.887066i 0.487753 + 0.872982i \(0.337817\pi\)
−0.999901 + 0.0140840i \(0.995517\pi\)
\(62\) −5.00000 −0.635001
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 1.50000 2.59808i 0.186052 0.322252i
\(66\) 0 0
\(67\) 2.00000 + 3.46410i 0.244339 + 0.423207i 0.961946 0.273241i \(-0.0880957\pi\)
−0.717607 + 0.696449i \(0.754762\pi\)
\(68\) 3.00000 5.19615i 0.363803 0.630126i
\(69\) 0 0
\(70\) 7.50000 2.59808i 0.896421 0.310530i
\(71\) −6.00000 −0.712069 −0.356034 0.934473i \(-0.615871\pi\)
−0.356034 + 0.934473i \(0.615871\pi\)
\(72\) 0 0
\(73\) −7.00000 12.1244i −0.819288 1.41905i −0.906208 0.422833i \(-0.861036\pi\)
0.0869195 0.996215i \(-0.472298\pi\)
\(74\) −2.00000 3.46410i −0.232495 0.402694i
\(75\) 0 0
\(76\) −4.00000 −0.458831
\(77\) −7.50000 + 2.59808i −0.854704 + 0.296078i
\(78\) 0 0
\(79\) 0.500000 0.866025i 0.0562544 0.0974355i −0.836527 0.547926i \(-0.815418\pi\)
0.892781 + 0.450490i \(0.148751\pi\)
\(80\) 1.50000 + 2.59808i 0.167705 + 0.290474i
\(81\) 0 0
\(82\) 6.00000 10.3923i 0.662589 1.14764i
\(83\) −3.00000 −0.329293 −0.164646 0.986353i \(-0.552648\pi\)
−0.164646 + 0.986353i \(0.552648\pi\)
\(84\) 0 0
\(85\) 18.0000 1.95237
\(86\) −2.00000 + 3.46410i −0.215666 + 0.373544i
\(87\) 0 0
\(88\) −1.50000 2.59808i −0.159901 0.276956i
\(89\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(90\) 0 0
\(91\) −0.500000 + 2.59808i −0.0524142 + 0.272352i
\(92\) −6.00000 −0.625543
\(93\) 0 0
\(94\) 6.00000 + 10.3923i 0.618853 + 1.07188i
\(95\) −6.00000 10.3923i −0.615587 1.06623i
\(96\) 0 0
\(97\) 5.00000 0.507673 0.253837 0.967247i \(-0.418307\pi\)
0.253837 + 0.967247i \(0.418307\pi\)
\(98\) −5.50000 + 4.33013i −0.555584 + 0.437409i
\(99\) 0 0
\(100\) −2.00000 + 3.46410i −0.200000 + 0.346410i
\(101\) 9.00000 + 15.5885i 0.895533 + 1.55111i 0.833143 + 0.553058i \(0.186539\pi\)
0.0623905 + 0.998052i \(0.480128\pi\)
\(102\) 0 0
\(103\) −4.00000 + 6.92820i −0.394132 + 0.682656i −0.992990 0.118199i \(-0.962288\pi\)
0.598858 + 0.800855i \(0.295621\pi\)
\(104\) −1.00000 −0.0980581
\(105\) 0 0
\(106\) −9.00000 −0.874157
\(107\) 1.50000 2.59808i 0.145010 0.251166i −0.784366 0.620298i \(-0.787012\pi\)
0.929377 + 0.369132i \(0.120345\pi\)
\(108\) 0 0
\(109\) 8.00000 + 13.8564i 0.766261 + 1.32720i 0.939577 + 0.342337i \(0.111218\pi\)
−0.173316 + 0.984866i \(0.555448\pi\)
\(110\) 4.50000 7.79423i 0.429058 0.743151i
\(111\) 0 0
\(112\) −2.00000 1.73205i −0.188982 0.163663i
\(113\) 12.0000 1.12887 0.564433 0.825479i \(-0.309095\pi\)
0.564433 + 0.825479i \(0.309095\pi\)
\(114\) 0 0
\(115\) −9.00000 15.5885i −0.839254 1.45363i
\(116\) −4.50000 7.79423i −0.417815 0.723676i
\(117\) 0 0
\(118\) −9.00000 −0.828517
\(119\) −15.0000 + 5.19615i −1.37505 + 0.476331i
\(120\) 0 0
\(121\) 1.00000 1.73205i 0.0909091 0.157459i
\(122\) 4.00000 + 6.92820i 0.362143 + 0.627250i
\(123\) 0 0
\(124\) −2.50000 + 4.33013i −0.224507 + 0.388857i
\(125\) 3.00000 0.268328
\(126\) 0 0
\(127\) −7.00000 −0.621150 −0.310575 0.950549i \(-0.600522\pi\)
−0.310575 + 0.950549i \(0.600522\pi\)
\(128\) 0.500000 0.866025i 0.0441942 0.0765466i
\(129\) 0 0
\(130\) −1.50000 2.59808i −0.131559 0.227866i
\(131\) 10.5000 18.1865i 0.917389 1.58896i 0.114024 0.993478i \(-0.463626\pi\)
0.803365 0.595487i \(-0.203041\pi\)
\(132\) 0 0
\(133\) 8.00000 + 6.92820i 0.693688 + 0.600751i
\(134\) 4.00000 0.345547
\(135\) 0 0
\(136\) −3.00000 5.19615i −0.257248 0.445566i
\(137\) −6.00000 10.3923i −0.512615 0.887875i −0.999893 0.0146279i \(-0.995344\pi\)
0.487278 0.873247i \(-0.337990\pi\)
\(138\) 0 0
\(139\) −4.00000 −0.339276 −0.169638 0.985506i \(-0.554260\pi\)
−0.169638 + 0.985506i \(0.554260\pi\)
\(140\) 1.50000 7.79423i 0.126773 0.658733i
\(141\) 0 0
\(142\) −3.00000 + 5.19615i −0.251754 + 0.436051i
\(143\) 1.50000 + 2.59808i 0.125436 + 0.217262i
\(144\) 0 0
\(145\) 13.5000 23.3827i 1.12111 1.94183i
\(146\) −14.0000 −1.15865
\(147\) 0 0
\(148\) −4.00000 −0.328798
\(149\) 3.00000 5.19615i 0.245770 0.425685i −0.716578 0.697507i \(-0.754293\pi\)
0.962348 + 0.271821i \(0.0876260\pi\)
\(150\) 0 0
\(151\) 9.50000 + 16.4545i 0.773099 + 1.33905i 0.935857 + 0.352381i \(0.114628\pi\)
−0.162758 + 0.986666i \(0.552039\pi\)
\(152\) −2.00000 + 3.46410i −0.162221 + 0.280976i
\(153\) 0 0
\(154\) −1.50000 + 7.79423i −0.120873 + 0.628077i
\(155\) −15.0000 −1.20483
\(156\) 0 0
\(157\) −1.00000 1.73205i −0.0798087 0.138233i 0.823359 0.567521i \(-0.192098\pi\)
−0.903167 + 0.429289i \(0.858764\pi\)
\(158\) −0.500000 0.866025i −0.0397779 0.0688973i
\(159\) 0 0
\(160\) 3.00000 0.237171
\(161\) 12.0000 + 10.3923i 0.945732 + 0.819028i
\(162\) 0 0
\(163\) −4.00000 + 6.92820i −0.313304 + 0.542659i −0.979076 0.203497i \(-0.934769\pi\)
0.665771 + 0.746156i \(0.268103\pi\)
\(164\) −6.00000 10.3923i −0.468521 0.811503i
\(165\) 0 0
\(166\) −1.50000 + 2.59808i −0.116423 + 0.201650i
\(167\) −12.0000 −0.928588 −0.464294 0.885681i \(-0.653692\pi\)
−0.464294 + 0.885681i \(0.653692\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 9.00000 15.5885i 0.690268 1.19558i
\(171\) 0 0
\(172\) 2.00000 + 3.46410i 0.152499 + 0.264135i
\(173\) 3.00000 5.19615i 0.228086 0.395056i −0.729155 0.684349i \(-0.760087\pi\)
0.957241 + 0.289292i \(0.0934200\pi\)
\(174\) 0 0
\(175\) 10.0000 3.46410i 0.755929 0.261861i
\(176\) −3.00000 −0.226134
\(177\) 0 0
\(178\) 0 0
\(179\) 6.00000 + 10.3923i 0.448461 + 0.776757i 0.998286 0.0585225i \(-0.0186389\pi\)
−0.549825 + 0.835280i \(0.685306\pi\)
\(180\) 0 0
\(181\) −16.0000 −1.18927 −0.594635 0.803996i \(-0.702704\pi\)
−0.594635 + 0.803996i \(0.702704\pi\)
\(182\) 2.00000 + 1.73205i 0.148250 + 0.128388i
\(183\) 0 0
\(184\) −3.00000 + 5.19615i −0.221163 + 0.383065i
\(185\) −6.00000 10.3923i −0.441129 0.764057i
\(186\) 0 0
\(187\) −9.00000 + 15.5885i −0.658145 + 1.13994i
\(188\) 12.0000 0.875190
\(189\) 0 0
\(190\) −12.0000 −0.870572
\(191\) 3.00000 5.19615i 0.217072 0.375980i −0.736839 0.676068i \(-0.763683\pi\)
0.953912 + 0.300088i \(0.0970159\pi\)
\(192\) 0 0
\(193\) 0.500000 + 0.866025i 0.0359908 + 0.0623379i 0.883460 0.468507i \(-0.155208\pi\)
−0.847469 + 0.530845i \(0.821875\pi\)
\(194\) 2.50000 4.33013i 0.179490 0.310885i
\(195\) 0 0
\(196\) 1.00000 + 6.92820i 0.0714286 + 0.494872i
\(197\) 18.0000 1.28245 0.641223 0.767354i \(-0.278427\pi\)
0.641223 + 0.767354i \(0.278427\pi\)
\(198\) 0 0
\(199\) −4.00000 6.92820i −0.283552 0.491127i 0.688705 0.725042i \(-0.258180\pi\)
−0.972257 + 0.233915i \(0.924846\pi\)
\(200\) 2.00000 + 3.46410i 0.141421 + 0.244949i
\(201\) 0 0
\(202\) 18.0000 1.26648
\(203\) −4.50000 + 23.3827i −0.315838 + 1.64114i
\(204\) 0 0
\(205\) 18.0000 31.1769i 1.25717 2.17749i
\(206\) 4.00000 + 6.92820i 0.278693 + 0.482711i
\(207\) 0 0
\(208\) −0.500000 + 0.866025i −0.0346688 + 0.0600481i
\(209\) 12.0000 0.830057
\(210\) 0 0
\(211\) 8.00000 0.550743 0.275371 0.961338i \(-0.411199\pi\)
0.275371 + 0.961338i \(0.411199\pi\)
\(212\) −4.50000 + 7.79423i −0.309061 + 0.535310i
\(213\) 0 0
\(214\) −1.50000 2.59808i −0.102538 0.177601i
\(215\) −6.00000 + 10.3923i −0.409197 + 0.708749i
\(216\) 0 0
\(217\) 12.5000 4.33013i 0.848555 0.293948i
\(218\) 16.0000 1.08366
\(219\) 0 0
\(220\) −4.50000 7.79423i −0.303390 0.525487i
\(221\) 3.00000 + 5.19615i 0.201802 + 0.349531i
\(222\) 0 0
\(223\) −1.00000 −0.0669650 −0.0334825 0.999439i \(-0.510660\pi\)
−0.0334825 + 0.999439i \(0.510660\pi\)
\(224\) −2.50000 + 0.866025i −0.167038 + 0.0578638i
\(225\) 0 0
\(226\) 6.00000 10.3923i 0.399114 0.691286i
\(227\) −1.50000 2.59808i −0.0995585 0.172440i 0.811943 0.583736i \(-0.198410\pi\)
−0.911502 + 0.411296i \(0.865076\pi\)
\(228\) 0 0
\(229\) −13.0000 + 22.5167i −0.859064 + 1.48794i 0.0137585 + 0.999905i \(0.495620\pi\)
−0.872823 + 0.488037i \(0.837713\pi\)
\(230\) −18.0000 −1.18688
\(231\) 0 0
\(232\) −9.00000 −0.590879
\(233\) −3.00000 + 5.19615i −0.196537 + 0.340411i −0.947403 0.320043i \(-0.896303\pi\)
0.750867 + 0.660454i \(0.229636\pi\)
\(234\) 0 0
\(235\) 18.0000 + 31.1769i 1.17419 + 2.03376i
\(236\) −4.50000 + 7.79423i −0.292925 + 0.507361i
\(237\) 0 0
\(238\) −3.00000 + 15.5885i −0.194461 + 1.01045i
\(239\) −6.00000 −0.388108 −0.194054 0.980991i \(-0.562164\pi\)
−0.194054 + 0.980991i \(0.562164\pi\)
\(240\) 0 0
\(241\) −8.50000 14.7224i −0.547533 0.948355i −0.998443 0.0557856i \(-0.982234\pi\)
0.450910 0.892570i \(-0.351100\pi\)
\(242\) −1.00000 1.73205i −0.0642824 0.111340i
\(243\) 0 0
\(244\) 8.00000 0.512148
\(245\) −16.5000 + 12.9904i −1.05415 + 0.829925i
\(246\) 0 0
\(247\) 2.00000 3.46410i 0.127257 0.220416i
\(248\) 2.50000 + 4.33013i 0.158750 + 0.274963i
\(249\) 0 0
\(250\) 1.50000 2.59808i 0.0948683 0.164317i
\(251\) 3.00000 0.189358 0.0946792 0.995508i \(-0.469817\pi\)
0.0946792 + 0.995508i \(0.469817\pi\)
\(252\) 0 0
\(253\) 18.0000 1.13165
\(254\) −3.50000 + 6.06218i −0.219610 + 0.380375i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −15.0000 + 25.9808i −0.935674 + 1.62064i −0.162247 + 0.986750i \(0.551874\pi\)
−0.773427 + 0.633885i \(0.781459\pi\)
\(258\) 0 0
\(259\) 8.00000 + 6.92820i 0.497096 + 0.430498i
\(260\) −3.00000 −0.186052
\(261\) 0 0
\(262\) −10.5000 18.1865i −0.648692 1.12357i
\(263\) 3.00000 + 5.19615i 0.184988 + 0.320408i 0.943572 0.331166i \(-0.107442\pi\)
−0.758585 + 0.651575i \(0.774109\pi\)
\(264\) 0 0
\(265\) −27.0000 −1.65860
\(266\) 10.0000 3.46410i 0.613139 0.212398i
\(267\) 0 0
\(268\) 2.00000 3.46410i 0.122169 0.211604i
\(269\) 1.50000 + 2.59808i 0.0914566 + 0.158408i 0.908124 0.418701i \(-0.137514\pi\)
−0.816668 + 0.577108i \(0.804181\pi\)
\(270\) 0 0
\(271\) 3.50000 6.06218i 0.212610 0.368251i −0.739921 0.672694i \(-0.765137\pi\)
0.952531 + 0.304443i \(0.0984703\pi\)
\(272\) −6.00000 −0.363803
\(273\) 0 0
\(274\) −12.0000 −0.724947
\(275\) 6.00000 10.3923i 0.361814 0.626680i
\(276\) 0 0
\(277\) −1.00000 1.73205i −0.0600842 0.104069i 0.834419 0.551131i \(-0.185804\pi\)
−0.894503 + 0.447062i \(0.852470\pi\)
\(278\) −2.00000 + 3.46410i −0.119952 + 0.207763i
\(279\) 0 0
\(280\) −6.00000 5.19615i −0.358569 0.310530i
\(281\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(282\) 0 0
\(283\) −1.00000 1.73205i −0.0594438 0.102960i 0.834772 0.550596i \(-0.185599\pi\)
−0.894216 + 0.447636i \(0.852266\pi\)
\(284\) 3.00000 + 5.19615i 0.178017 + 0.308335i
\(285\) 0 0
\(286\) 3.00000 0.177394
\(287\) −6.00000 + 31.1769i −0.354169 + 1.84032i
\(288\) 0 0
\(289\) −9.50000 + 16.4545i −0.558824 + 0.967911i
\(290\) −13.5000 23.3827i −0.792747 1.37308i
\(291\) 0 0
\(292\) −7.00000 + 12.1244i −0.409644 + 0.709524i
\(293\) −21.0000 −1.22683 −0.613417 0.789760i \(-0.710205\pi\)
−0.613417 + 0.789760i \(0.710205\pi\)
\(294\) 0 0
\(295\) −27.0000 −1.57200
\(296\) −2.00000 + 3.46410i −0.116248 + 0.201347i
\(297\) 0 0
\(298\) −3.00000 5.19615i −0.173785 0.301005i
\(299\) 3.00000 5.19615i 0.173494 0.300501i
\(300\) 0 0
\(301\) 2.00000 10.3923i 0.115278 0.599002i
\(302\) 19.0000 1.09333
\(303\) 0 0
\(304\) 2.00000 + 3.46410i 0.114708 + 0.198680i
\(305\) 12.0000 + 20.7846i 0.687118 + 1.19012i
\(306\) 0 0
\(307\) 2.00000 0.114146 0.0570730 0.998370i \(-0.481823\pi\)
0.0570730 + 0.998370i \(0.481823\pi\)
\(308\) 6.00000 + 5.19615i 0.341882 + 0.296078i
\(309\) 0 0
\(310\) −7.50000 + 12.9904i −0.425971 + 0.737804i
\(311\) −9.00000 15.5885i −0.510343 0.883940i −0.999928 0.0119847i \(-0.996185\pi\)
0.489585 0.871956i \(-0.337148\pi\)
\(312\) 0 0
\(313\) 9.50000 16.4545i 0.536972 0.930062i −0.462093 0.886831i \(-0.652902\pi\)
0.999065 0.0432311i \(-0.0137652\pi\)
\(314\) −2.00000 −0.112867
\(315\) 0 0
\(316\) −1.00000 −0.0562544
\(317\) −7.50000 + 12.9904i −0.421242 + 0.729612i −0.996061 0.0886679i \(-0.971739\pi\)
0.574819 + 0.818280i \(0.305072\pi\)
\(318\) 0 0
\(319\) 13.5000 + 23.3827i 0.755855 + 1.30918i
\(320\) 1.50000 2.59808i 0.0838525 0.145237i
\(321\) 0 0
\(322\) 15.0000 5.19615i 0.835917 0.289570i
\(323\) 24.0000 1.33540
\(324\) 0 0
\(325\) −2.00000 3.46410i −0.110940 0.192154i
\(326\) 4.00000 + 6.92820i 0.221540 + 0.383718i
\(327\) 0 0
\(328\) −12.0000 −0.662589
\(329\) −24.0000 20.7846i −1.32316 1.14589i
\(330\) 0 0
\(331\) −16.0000 + 27.7128i −0.879440 + 1.52323i −0.0274825 + 0.999622i \(0.508749\pi\)
−0.851957 + 0.523612i \(0.824584\pi\)
\(332\) 1.50000 + 2.59808i 0.0823232 + 0.142588i
\(333\) 0 0
\(334\) −6.00000 + 10.3923i −0.328305 + 0.568642i
\(335\) 12.0000 0.655630
\(336\) 0 0
\(337\) −31.0000 −1.68868 −0.844339 0.535810i \(-0.820006\pi\)
−0.844339 + 0.535810i \(0.820006\pi\)
\(338\) 0.500000 0.866025i 0.0271964 0.0471056i
\(339\) 0 0
\(340\) −9.00000 15.5885i −0.488094 0.845403i
\(341\) 7.50000 12.9904i 0.406148 0.703469i
\(342\) 0 0
\(343\) 10.0000 15.5885i 0.539949 0.841698i
\(344\) 4.00000 0.215666
\(345\) 0 0
\(346\) −3.00000 5.19615i −0.161281 0.279347i
\(347\) 6.00000 + 10.3923i 0.322097 + 0.557888i 0.980921 0.194409i \(-0.0622790\pi\)
−0.658824 + 0.752297i \(0.728946\pi\)
\(348\) 0 0
\(349\) −34.0000 −1.81998 −0.909989 0.414632i \(-0.863910\pi\)
−0.909989 + 0.414632i \(0.863910\pi\)
\(350\) 2.00000 10.3923i 0.106904 0.555492i
\(351\) 0 0
\(352\) −1.50000 + 2.59808i −0.0799503 + 0.138478i
\(353\) −15.0000 25.9808i −0.798369 1.38282i −0.920677 0.390324i \(-0.872363\pi\)
0.122308 0.992492i \(-0.460970\pi\)
\(354\) 0 0
\(355\) −9.00000 + 15.5885i −0.477670 + 0.827349i
\(356\) 0 0
\(357\) 0 0
\(358\) 12.0000 0.634220
\(359\) −3.00000 + 5.19615i −0.158334 + 0.274242i −0.934268 0.356572i \(-0.883946\pi\)
0.775934 + 0.630814i \(0.217279\pi\)
\(360\) 0 0
\(361\) 1.50000 + 2.59808i 0.0789474 + 0.136741i
\(362\) −8.00000 + 13.8564i −0.420471 + 0.728277i
\(363\) 0 0
\(364\) 2.50000 0.866025i 0.131036 0.0453921i
\(365\) −42.0000 −2.19838
\(366\) 0 0
\(367\) 3.50000 + 6.06218i 0.182699 + 0.316443i 0.942799 0.333363i \(-0.108183\pi\)
−0.760100 + 0.649806i \(0.774850\pi\)
\(368\) 3.00000 + 5.19615i 0.156386 + 0.270868i
\(369\) 0 0
\(370\) −12.0000 −0.623850
\(371\) 22.5000 7.79423i 1.16814 0.404656i
\(372\) 0 0
\(373\) −7.00000 + 12.1244i −0.362446 + 0.627775i −0.988363 0.152115i \(-0.951392\pi\)
0.625917 + 0.779890i \(0.284725\pi\)
\(374\) 9.00000 + 15.5885i 0.465379 + 0.806060i
\(375\) 0 0
\(376\) 6.00000 10.3923i 0.309426 0.535942i
\(377\) 9.00000 0.463524
\(378\) 0 0
\(379\) −16.0000 −0.821865 −0.410932 0.911666i \(-0.634797\pi\)
−0.410932 + 0.911666i \(0.634797\pi\)
\(380\) −6.00000 + 10.3923i −0.307794 + 0.533114i
\(381\) 0 0
\(382\) −3.00000 5.19615i −0.153493 0.265858i
\(383\) −3.00000 + 5.19615i −0.153293 + 0.265511i −0.932436 0.361335i \(-0.882321\pi\)
0.779143 + 0.626846i \(0.215654\pi\)
\(384\) 0 0
\(385\) −4.50000 + 23.3827i −0.229341 + 1.19169i
\(386\) 1.00000 0.0508987
\(387\) 0 0
\(388\) −2.50000 4.33013i −0.126918 0.219829i
\(389\) 15.0000 + 25.9808i 0.760530 + 1.31728i 0.942578 + 0.333987i \(0.108394\pi\)
−0.182047 + 0.983290i \(0.558272\pi\)
\(390\) 0 0
\(391\) 36.0000 1.82060
\(392\) 6.50000 + 2.59808i 0.328300 + 0.131223i
\(393\) 0 0
\(394\) 9.00000 15.5885i 0.453413 0.785335i
\(395\) −1.50000 2.59808i −0.0754732 0.130723i
\(396\) 0 0
\(397\) −1.00000 + 1.73205i −0.0501886 + 0.0869291i −0.890028 0.455905i \(-0.849316\pi\)
0.839840 + 0.542834i \(0.182649\pi\)
\(398\) −8.00000 −0.401004
\(399\) 0 0
\(400\) 4.00000 0.200000
\(401\) 9.00000 15.5885i 0.449439 0.778450i −0.548911 0.835881i \(-0.684957\pi\)
0.998350 + 0.0574304i \(0.0182907\pi\)
\(402\) 0 0
\(403\) −2.50000 4.33013i −0.124534 0.215699i
\(404\) 9.00000 15.5885i 0.447767 0.775555i
\(405\) 0 0
\(406\) 18.0000 + 15.5885i 0.893325 + 0.773642i
\(407\) 12.0000 0.594818
\(408\) 0 0
\(409\) 3.50000 + 6.06218i 0.173064 + 0.299755i 0.939490 0.342578i \(-0.111300\pi\)
−0.766426 + 0.642333i \(0.777967\pi\)
\(410\) −18.0000 31.1769i −0.888957 1.53972i
\(411\) 0 0
\(412\) 8.00000 0.394132
\(413\) 22.5000 7.79423i 1.10715 0.383529i
\(414\) 0 0
\(415\) −4.50000 + 7.79423i −0.220896 + 0.382604i
\(416\) 0.500000 + 0.866025i 0.0245145 + 0.0424604i
\(417\) 0 0
\(418\) 6.00000 10.3923i 0.293470 0.508304i
\(419\) −24.0000 −1.17248 −0.586238 0.810139i \(-0.699392\pi\)
−0.586238 + 0.810139i \(0.699392\pi\)
\(420\) 0 0
\(421\) 8.00000 0.389896 0.194948 0.980814i \(-0.437546\pi\)
0.194948 + 0.980814i \(0.437546\pi\)
\(422\) 4.00000 6.92820i 0.194717 0.337260i
\(423\) 0 0
\(424\) 4.50000 + 7.79423i 0.218539 + 0.378521i
\(425\) 12.0000 20.7846i 0.582086 1.00820i
\(426\) 0 0
\(427\) −16.0000 13.8564i −0.774294 0.670559i
\(428\) −3.00000 −0.145010
\(429\) 0 0
\(430\) 6.00000 + 10.3923i 0.289346 + 0.501161i
\(431\) 15.0000 + 25.9808i 0.722525 + 1.25145i 0.959985 + 0.280052i \(0.0903517\pi\)
−0.237460 + 0.971397i \(0.576315\pi\)
\(432\) 0 0
\(433\) 2.00000 0.0961139 0.0480569 0.998845i \(-0.484697\pi\)
0.0480569 + 0.998845i \(0.484697\pi\)
\(434\) 2.50000 12.9904i 0.120004 0.623558i
\(435\) 0 0
\(436\) 8.00000 13.8564i 0.383131 0.663602i
\(437\) −12.0000 20.7846i −0.574038 0.994263i
\(438\) 0 0
\(439\) 0.500000 0.866025i 0.0238637 0.0413331i −0.853847 0.520524i \(-0.825737\pi\)
0.877711 + 0.479191i \(0.159070\pi\)
\(440\) −9.00000 −0.429058
\(441\) 0 0
\(442\) 6.00000 0.285391
\(443\) −1.50000 + 2.59808i −0.0712672 + 0.123438i −0.899457 0.437009i \(-0.856038\pi\)
0.828190 + 0.560448i \(0.189371\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) −0.500000 + 0.866025i −0.0236757 + 0.0410075i
\(447\) 0 0
\(448\) −0.500000 + 2.59808i −0.0236228 + 0.122748i
\(449\) 12.0000 0.566315 0.283158 0.959073i \(-0.408618\pi\)
0.283158 + 0.959073i \(0.408618\pi\)
\(450\) 0 0
\(451\) 18.0000 + 31.1769i 0.847587 + 1.46806i
\(452\) −6.00000 10.3923i −0.282216 0.488813i
\(453\) 0 0
\(454\) −3.00000 −0.140797
\(455\) 6.00000 + 5.19615i 0.281284 + 0.243599i
\(456\) 0 0
\(457\) 9.50000 16.4545i 0.444391 0.769708i −0.553618 0.832771i \(-0.686753\pi\)
0.998010 + 0.0630623i \(0.0200867\pi\)
\(458\) 13.0000 + 22.5167i 0.607450 + 1.05213i
\(459\) 0 0
\(460\) −9.00000 + 15.5885i −0.419627 + 0.726816i
\(461\) −18.0000 −0.838344 −0.419172 0.907907i \(-0.637680\pi\)
−0.419172 + 0.907907i \(0.637680\pi\)
\(462\) 0 0
\(463\) −16.0000 −0.743583 −0.371792 0.928316i \(-0.621256\pi\)
−0.371792 + 0.928316i \(0.621256\pi\)
\(464\) −4.50000 + 7.79423i −0.208907 + 0.361838i
\(465\) 0 0
\(466\) 3.00000 + 5.19615i 0.138972 + 0.240707i
\(467\) −18.0000 + 31.1769i −0.832941 + 1.44270i 0.0627555 + 0.998029i \(0.480011\pi\)
−0.895696 + 0.444667i \(0.853322\pi\)
\(468\) 0 0
\(469\) −10.0000 + 3.46410i −0.461757 + 0.159957i
\(470\) 36.0000 1.66056
\(471\) 0 0
\(472\) 4.50000 + 7.79423i 0.207129 + 0.358758i
\(473\) −6.00000 10.3923i −0.275880 0.477839i
\(474\) 0 0
\(475\) −16.0000 −0.734130
\(476\) 12.0000 + 10.3923i 0.550019 + 0.476331i
\(477\) 0 0
\(478\) −3.00000 + 5.19615i −0.137217 + 0.237666i
\(479\) 3.00000 + 5.19615i 0.137073 + 0.237418i 0.926388 0.376571i \(-0.122897\pi\)
−0.789314 + 0.613990i \(0.789564\pi\)
\(480\) 0 0
\(481\) 2.00000 3.46410i 0.0911922 0.157949i
\(482\) −17.0000 −0.774329
\(483\) 0 0
\(484\) −2.00000 −0.0909091
\(485\) 7.50000 12.9904i 0.340557 0.589863i
\(486\) 0 0
\(487\) −11.5000 19.9186i −0.521115 0.902597i −0.999698 0.0245553i \(-0.992183\pi\)
0.478584 0.878042i \(-0.341150\pi\)
\(488\) 4.00000 6.92820i 0.181071 0.313625i
\(489\) 0 0
\(490\) 3.00000 + 20.7846i 0.135526 + 0.938953i
\(491\) 15.0000 0.676941 0.338470 0.940977i \(-0.390091\pi\)
0.338470 + 0.940977i \(0.390091\pi\)
\(492\) 0 0
\(493\) 27.0000 + 46.7654i 1.21602 + 2.10621i
\(494\) −2.00000 3.46410i −0.0899843 0.155857i
\(495\) 0 0
\(496\) 5.00000 0.224507
\(497\) 3.00000 15.5885i 0.134568 0.699238i
\(498\) 0 0
\(499\) 8.00000 13.8564i 0.358129 0.620298i −0.629519 0.776985i \(-0.716748\pi\)
0.987648 + 0.156687i \(0.0500814\pi\)
\(500\) −1.50000 2.59808i −0.0670820 0.116190i
\(501\) 0 0
\(502\) 1.50000 2.59808i 0.0669483 0.115958i
\(503\) −30.0000 −1.33763 −0.668817 0.743427i \(-0.733199\pi\)
−0.668817 + 0.743427i \(0.733199\pi\)
\(504\) 0 0
\(505\) 54.0000 2.40297
\(506\) 9.00000 15.5885i 0.400099 0.692991i
\(507\) 0 0
\(508\) 3.50000 + 6.06218i 0.155287 + 0.268966i
\(509\) 4.50000 7.79423i 0.199459 0.345473i −0.748894 0.662690i \(-0.769415\pi\)
0.948353 + 0.317217i \(0.102748\pi\)
\(510\) 0 0
\(511\) 35.0000 12.1244i 1.54831 0.536350i
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) 15.0000 + 25.9808i 0.661622 + 1.14596i
\(515\) 12.0000 + 20.7846i 0.528783 + 0.915879i
\(516\) 0 0
\(517\) −36.0000 −1.58328
\(518\) 10.0000 3.46410i 0.439375 0.152204i
\(519\) 0 0
\(520\) −1.50000 + 2.59808i −0.0657794 + 0.113933i
\(521\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(522\) 0 0
\(523\) −4.00000 + 6.92820i −0.174908 + 0.302949i −0.940129 0.340818i \(-0.889296\pi\)
0.765222 + 0.643767i \(0.222629\pi\)
\(524\) −21.0000 −0.917389
\(525\) 0 0
\(526\) 6.00000 0.261612
\(527\) 15.0000 25.9808i 0.653410 1.13174i
\(528\) 0 0
\(529\) −6.50000 11.2583i −0.282609 0.489493i
\(530\) −13.5000 + 23.3827i −0.586403 + 1.01568i
\(531\) 0 0
\(532\) 2.00000 10.3923i 0.0867110 0.450564i
\(533\) 12.0000 0.519778
\(534\) 0 0
\(535\) −4.50000 7.79423i −0.194552 0.336974i
\(536\) −2.00000 3.46410i −0.0863868 0.149626i
\(537\) 0 0
\(538\) 3.00000 0.129339
\(539\) −3.00000 20.7846i −0.129219 0.895257i
\(540\) 0 0
\(541\) −10.0000 + 17.3205i −0.429934 + 0.744667i −0.996867 0.0790969i \(-0.974796\pi\)
0.566933 + 0.823764i \(0.308130\pi\)
\(542\) −3.50000 6.06218i −0.150338 0.260393i
\(543\) 0 0
\(544\) −3.00000 + 5.19615i −0.128624 + 0.222783i
\(545\) 48.0000 2.05609
\(546\) 0 0
\(547\) 44.0000 1.88130 0.940652 0.339372i \(-0.110215\pi\)
0.940652 + 0.339372i \(0.110215\pi\)
\(548\) −6.00000 + 10.3923i −0.256307 + 0.443937i
\(549\) 0 0
\(550\) −6.00000 10.3923i −0.255841 0.443129i
\(551\) 18.0000 31.1769i 0.766826 1.32818i
\(552\) 0 0
\(553\) 2.00000 + 1.73205i 0.0850487 + 0.0736543i
\(554\) −2.00000 −0.0849719
\(555\) 0 0
\(556\) 2.00000 + 3.46410i 0.0848189 + 0.146911i
\(557\) −10.5000 18.1865i −0.444899 0.770588i 0.553146 0.833084i \(-0.313427\pi\)
−0.998045 + 0.0624962i \(0.980094\pi\)
\(558\) 0 0
\(559\) −4.00000 −0.169182
\(560\) −7.50000 + 2.59808i −0.316933 + 0.109789i
\(561\) 0 0
\(562\) 0 0
\(563\) 16.5000 + 28.5788i 0.695392 + 1.20445i 0.970048 + 0.242912i \(0.0781026\pi\)
−0.274656 + 0.961542i \(0.588564\pi\)
\(564\) 0 0
\(565\) 18.0000 31.1769i 0.757266 1.31162i
\(566\) −2.00000 −0.0840663
\(567\) 0 0
\(568\) 6.00000 0.251754
\(569\) 6.00000 10.3923i 0.251533 0.435668i −0.712415 0.701758i \(-0.752399\pi\)
0.963948 + 0.266090i \(0.0857319\pi\)
\(570\) 0 0
\(571\) 20.0000 + 34.6410i 0.836974 + 1.44968i 0.892413 + 0.451219i \(0.149011\pi\)
−0.0554391 + 0.998462i \(0.517656\pi\)
\(572\) 1.50000 2.59808i 0.0627182 0.108631i
\(573\) 0 0
\(574\) 24.0000 + 20.7846i 1.00174 + 0.867533i
\(575\) −24.0000 −1.00087
\(576\) 0 0
\(577\) −8.50000 14.7224i −0.353860 0.612903i 0.633062 0.774101i \(-0.281798\pi\)
−0.986922 + 0.161198i \(0.948464\pi\)
\(578\) 9.50000 + 16.4545i 0.395148 + 0.684416i
\(579\) 0 0
\(580\) −27.0000 −1.12111
\(581\) 1.50000 7.79423i 0.0622305 0.323359i
\(582\) 0 0
\(583\) 13.5000 23.3827i 0.559113 0.968412i
\(584\) 7.00000 + 12.1244i 0.289662 + 0.501709i
\(585\) 0 0
\(586\) −10.5000 + 18.1865i −0.433751 + 0.751279i
\(587\) −33.0000 −1.36206 −0.681028 0.732257i \(-0.738467\pi\)
−0.681028 + 0.732257i \(0.738467\pi\)
\(588\) 0 0
\(589\) −20.0000 −0.824086
\(590\) −13.5000 + 23.3827i −0.555786 + 0.962650i
\(591\) 0 0
\(592\) 2.00000 + 3.46410i 0.0821995 + 0.142374i
\(593\) −6.00000 + 10.3923i −0.246390 + 0.426761i −0.962522 0.271205i \(-0.912578\pi\)
0.716131 + 0.697966i \(0.245911\pi\)
\(594\) 0 0
\(595\) −9.00000 + 46.7654i −0.368964 + 1.91719i
\(596\) −6.00000 −0.245770
\(597\) 0 0
\(598\) −3.00000 5.19615i −0.122679 0.212486i
\(599\) 3.00000 + 5.19615i 0.122577 + 0.212309i 0.920783 0.390075i \(-0.127551\pi\)
−0.798206 + 0.602384i \(0.794218\pi\)
\(600\) 0 0
\(601\) −37.0000 −1.50926 −0.754631 0.656150i \(-0.772184\pi\)
−0.754631 + 0.656150i \(0.772184\pi\)
\(602\) −8.00000 6.92820i −0.326056 0.282372i
\(603\) 0 0
\(604\) 9.50000 16.4545i 0.386550 0.669523i
\(605\) −3.00000 5.19615i −0.121967 0.211254i
\(606\) 0 0
\(607\) −2.50000 + 4.33013i −0.101472 + 0.175754i −0.912291 0.409542i \(-0.865689\pi\)
0.810819 + 0.585296i \(0.199022\pi\)
\(608\) 4.00000 0.162221
\(609\) 0 0
\(610\) 24.0000 0.971732
\(611\) −6.00000 + 10.3923i −0.242734 + 0.420428i
\(612\) 0 0
\(613\) 8.00000 + 13.8564i 0.323117 + 0.559655i 0.981129 0.193352i \(-0.0619359\pi\)
−0.658012 + 0.753007i \(0.728603\pi\)
\(614\) 1.00000 1.73205i 0.0403567 0.0698999i
\(615\) 0 0
\(616\) 7.50000 2.59808i 0.302184 0.104679i
\(617\) −48.0000 −1.93241 −0.966204 0.257780i \(-0.917009\pi\)
−0.966204 + 0.257780i \(0.917009\pi\)
\(618\) 0 0
\(619\) −10.0000 17.3205i −0.401934 0.696170i 0.592025 0.805919i \(-0.298329\pi\)
−0.993959 + 0.109749i \(0.964995\pi\)
\(620\) 7.50000 + 12.9904i 0.301207 + 0.521706i
\(621\) 0 0
\(622\) −18.0000 −0.721734
\(623\) 0 0
\(624\) 0 0
\(625\) 14.5000 25.1147i 0.580000 1.00459i
\(626\) −9.50000 16.4545i −0.379696 0.657653i
\(627\) 0 0
\(628\) −1.00000 + 1.73205i −0.0399043 + 0.0691164i
\(629\) 24.0000 0.956943
\(630\) 0 0
\(631\) −13.0000 −0.517522 −0.258761 0.965941i \(-0.583314\pi\)
−0.258761 + 0.965941i \(0.583314\pi\)
\(632\) −0.500000 + 0.866025i −0.0198889 + 0.0344486i
\(633\) 0 0
\(634\) 7.50000 + 12.9904i 0.297863 + 0.515914i
\(635\) −10.5000 + 18.1865i −0.416680 + 0.721711i
\(636\) 0 0
\(637\) −6.50000 2.59808i −0.257539 0.102940i
\(638\) 27.0000 1.06894
\(639\) 0 0
\(640\) −1.50000 2.59808i −0.0592927 0.102698i
\(641\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(642\) 0 0
\(643\) 8.00000 0.315489 0.157745 0.987480i \(-0.449578\pi\)
0.157745 + 0.987480i \(0.449578\pi\)
\(644\) 3.00000 15.5885i 0.118217 0.614271i
\(645\) 0 0
\(646\) 12.0000 20.7846i 0.472134 0.817760i
\(647\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(648\) 0 0
\(649\) 13.5000 23.3827i 0.529921 0.917851i
\(650\) −4.00000 −0.156893
\(651\) 0 0
\(652\) 8.00000 0.313304
\(653\) 4.50000 7.79423i 0.176099 0.305012i −0.764442 0.644692i \(-0.776986\pi\)
0.940541 + 0.339680i \(0.110319\pi\)
\(654\) 0 0
\(655\) −31.5000 54.5596i −1.23081 2.13182i
\(656\) −6.00000 + 10.3923i −0.234261 + 0.405751i
\(657\) 0 0
\(658\) −30.0000 + 10.3923i −1.16952 + 0.405134i
\(659\) −12.0000 −0.467454 −0.233727 0.972302i \(-0.575092\pi\)
−0.233727 + 0.972302i \(0.575092\pi\)
\(660\) 0 0
\(661\) −7.00000 12.1244i −0.272268 0.471583i 0.697174 0.716902i \(-0.254441\pi\)
−0.969442 + 0.245319i \(0.921107\pi\)
\(662\) 16.0000 + 27.7128i 0.621858 + 1.07709i
\(663\) 0 0
\(664\) 3.00000 0.116423
\(665\) 30.0000 10.3923i 1.16335 0.402996i
\(666\) 0 0
\(667\) 27.0000 46.7654i 1.04544 1.81076i
\(668\) 6.00000 + 10.3923i 0.232147 + 0.402090i
\(669\) 0 0
\(670\) 6.00000 10.3923i 0.231800 0.401490i
\(671\) −24.0000 −0.926510
\(672\) 0 0
\(673\) −31.0000 −1.19496 −0.597481 0.801883i \(-0.703832\pi\)
−0.597481 + 0.801883i \(0.703832\pi\)
\(674\) −15.5000 + 26.8468i −0.597038 + 1.03410i
\(675\) 0 0
\(676\) −0.500000 0.866025i −0.0192308 0.0333087i
\(677\) 4.50000 7.79423i 0.172949 0.299557i −0.766501 0.642244i \(-0.778004\pi\)
0.939450 + 0.342687i \(0.111337\pi\)
\(678\) 0 0
\(679\) −2.50000 + 12.9904i −0.0959412 + 0.498525i
\(680\) −18.0000 −0.690268
\(681\) 0 0
\(682\) −7.50000 12.9904i −0.287190 0.497427i
\(683\) −19.5000 33.7750i −0.746147 1.29236i −0.949657 0.313291i \(-0.898568\pi\)
0.203510 0.979073i \(-0.434765\pi\)
\(684\) 0 0
\(685\) −36.0000 −1.37549
\(686\) −8.50000 16.4545i −0.324532 0.628235i
\(687\) 0 0
\(688\) 2.00000 3.46410i 0.0762493 0.132068i
\(689\) −4.50000 7.79423i −0.171436 0.296936i
\(690\) 0 0
\(691\) 20.0000 34.6410i 0.760836 1.31781i −0.181584 0.983375i \(-0.558123\pi\)
0.942420 0.334431i \(-0.108544\pi\)
\(692\) −6.00000 −0.228086
\(693\) 0 0
\(694\) 12.0000 0.455514
\(695\) −6.00000 + 10.3923i −0.227593 + 0.394203i
\(696\) 0 0
\(697\) 36.0000 + 62.3538i 1.36360 + 2.36182i
\(698\) −17.0000 + 29.4449i −0.643459 + 1.11450i
\(699\) 0 0
\(700\) −8.00000 6.92820i −0.302372 0.261861i
\(701\) −15.0000 −0.566542 −0.283271 0.959040i \(-0.591420\pi\)
−0.283271 + 0.959040i \(0.591420\pi\)
\(702\) 0 0
\(703\) −8.00000 13.8564i −0.301726 0.522604i
\(704\) 1.50000 + 2.59808i 0.0565334 + 0.0979187i
\(705\) 0 0
\(706\) −30.0000 −1.12906
\(707\) −45.0000 + 15.5885i −1.69240 + 0.586264i
\(708\) 0 0
\(709\) 17.0000 29.4449i 0.638448 1.10583i −0.347325 0.937745i \(-0.612910\pi\)
0.985773 0.168080i \(-0.0537568\pi\)
\(710\) 9.00000 + 15.5885i 0.337764 + 0.585024i
\(711\) 0 0
\(712\) 0 0
\(713\) −30.0000 −1.12351
\(714\) 0 0
\(715\) 9.00000 0.336581
\(716\) 6.00000 10.3923i 0.224231 0.388379i
\(717\) 0 0
\(718\) 3.00000 + 5.19615i 0.111959 + 0.193919i
\(719\) −9.00000 + 15.5885i −0.335643 + 0.581351i −0.983608 0.180319i \(-0.942287\pi\)
0.647965 + 0.761670i \(0.275620\pi\)
\(720\) 0 0
\(721\) −16.0000 13.8564i −0.595871 0.516040i
\(722\) 3.00000 0.111648
\(723\) 0 0
\(724\) 8.00000 + 13.8564i 0.297318 + 0.514969i
\(725\) −18.0000 31.1769i −0.668503 1.15788i
\(726\) 0 0
\(727\) −37.0000 −1.37225 −0.686127 0.727482i \(-0.740691\pi\)
−0.686127 + 0.727482i \(0.740691\pi\)
\(728\) 0.500000 2.59808i 0.0185312 0.0962911i
\(729\) 0 0
\(730\) −21.0000 + 36.3731i −0.777245 + 1.34623i
\(731\) −12.0000 20.7846i −0.443836 0.768747i
\(732\) 0 0
\(733\) −25.0000 + 43.3013i −0.923396 + 1.59937i −0.129275 + 0.991609i \(0.541265\pi\)
−0.794121 + 0.607760i \(0.792068\pi\)
\(734\) 7.00000 0.258375
\(735\) 0 0
\(736\) 6.00000 0.221163
\(737\) −6.00000 + 10.3923i −0.221013 + 0.382805i
\(738\) 0 0
\(739\) −19.0000 32.9090i −0.698926 1.21058i −0.968839 0.247691i \(-0.920328\pi\)
0.269913 0.962885i \(-0.413005\pi\)
\(740\) −6.00000 + 10.3923i −0.220564 + 0.382029i
\(741\) 0 0
\(742\) 4.50000 23.3827i 0.165200 0.858405i
\(743\) 36.0000 1.32071 0.660356 0.750953i \(-0.270405\pi\)
0.660356 + 0.750953i \(0.270405\pi\)
\(744\) 0 0
\(745\) −9.00000 15.5885i −0.329734 0.571117i
\(746\) 7.00000 + 12.1244i 0.256288 + 0.443904i
\(747\) 0 0
\(748\) 18.0000 0.658145
\(749\) 6.00000 + 5.19615i 0.219235 + 0.189863i
\(750\) 0 0
\(751\) 15.5000 26.8468i 0.565603 0.979653i −0.431390 0.902165i \(-0.641977\pi\)
0.996993 0.0774878i \(-0.0246899\pi\)
\(752\) −6.00000 10.3923i −0.218797 0.378968i
\(753\) 0 0
\(754\) 4.50000 7.79423i 0.163880 0.283849i
\(755\) 57.0000 2.07444
\(756\) 0 0
\(757\) 2.00000 0.0726912 0.0363456 0.999339i \(-0.488428\pi\)
0.0363456 + 0.999339i \(0.488428\pi\)
\(758\) −8.00000 + 13.8564i −0.290573 + 0.503287i
\(759\) 0 0
\(760\) 6.00000 + 10.3923i 0.217643 + 0.376969i
\(761\) 18.0000 31.1769i 0.652499 1.13016i −0.330015 0.943976i \(-0.607054\pi\)
0.982514 0.186187i \(-0.0596129\pi\)
\(762\) 0 0
\(763\) −40.0000 + 13.8564i −1.44810 + 0.501636i
\(764\) −6.00000 −0.217072
\(765\) 0 0
\(766\) 3.00000 + 5.19615i 0.108394 + 0.187745i
\(767\) −4.50000 7.79423i −0.162486 0.281433i
\(768\) 0 0
\(769\) −1.00000 −0.0360609 −0.0180305 0.999837i \(-0.505740\pi\)
−0.0180305 + 0.999837i \(0.505740\pi\)
\(770\) 18.0000 + 15.5885i 0.648675 + 0.561769i
\(771\) 0 0
\(772\) 0.500000 0.866025i 0.0179954 0.0311689i
\(773\) −9.00000 15.5885i −0.323708 0.560678i 0.657542 0.753418i \(-0.271596\pi\)
−0.981250 + 0.192740i \(0.938263\pi\)
\(774\) 0 0
\(775\) −10.0000 + 17.3205i −0.359211 + 0.622171i
\(776\) −5.00000 −0.179490
\(777\) 0 0
\(778\) 30.0000 1.07555
\(779\) 24.0000 41.5692i 0.859889 1.48937i
\(780\) 0 0
\(781\) −9.00000 15.5885i −0.322045 0.557799i
\(782\) 18.0000 31.1769i 0.643679 1.11488i
\(783\) 0 0