Properties

Label 117.2.q.c.10.1
Level $117$
Weight $2$
Character 117.10
Analytic conductor $0.934$
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] = [117,2,Mod(10,117)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(117, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("117.10");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 117 = 3^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 117.q (of order \(6\), 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: \(0.934249703649\)
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 10.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 117.10
Dual form 117.2.q.c.82.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.50000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{4} -1.73205i q^{5} +1.73205i q^{8} +O(q^{10})\) \(q+(1.50000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{4} -1.73205i q^{5} +1.73205i q^{8} +(-1.50000 - 2.59808i) q^{10} +(-2.50000 + 2.59808i) q^{13} +(2.50000 + 4.33013i) q^{16} +(-1.50000 + 2.59808i) q^{17} +(-3.00000 - 1.73205i) q^{19} +(-1.50000 - 0.866025i) q^{20} +(-3.00000 - 5.19615i) q^{23} +2.00000 q^{25} +(-1.50000 + 6.06218i) q^{26} +(1.50000 + 2.59808i) q^{29} -3.46410i q^{31} +(4.50000 + 2.59808i) q^{32} +5.19615i q^{34} +(7.50000 - 4.33013i) q^{37} -6.00000 q^{38} +3.00000 q^{40} +(4.50000 - 2.59808i) q^{41} +(-4.00000 + 6.92820i) q^{43} +(-9.00000 - 5.19615i) q^{46} -3.46410i q^{47} +(-3.50000 - 6.06218i) q^{49} +(3.00000 - 1.73205i) q^{50} +(1.00000 + 3.46410i) q^{52} +3.00000 q^{53} +(4.50000 + 2.59808i) q^{58} +(-6.00000 - 3.46410i) q^{59} +(-0.500000 + 0.866025i) q^{61} +(-3.00000 - 5.19615i) q^{62} -1.00000 q^{64} +(4.50000 + 4.33013i) q^{65} +(3.00000 - 1.73205i) q^{67} +(1.50000 + 2.59808i) q^{68} +(-3.00000 - 1.73205i) q^{71} -1.73205i q^{73} +(7.50000 - 12.9904i) q^{74} +(-3.00000 + 1.73205i) q^{76} +4.00000 q^{79} +(7.50000 - 4.33013i) q^{80} +(4.50000 - 7.79423i) q^{82} +13.8564i q^{83} +(4.50000 + 2.59808i) q^{85} +13.8564i q^{86} +(6.00000 - 3.46410i) q^{89} -6.00000 q^{92} +(-3.00000 - 5.19615i) q^{94} +(-3.00000 + 5.19615i) q^{95} +(6.00000 + 3.46410i) q^{97} +(-10.5000 - 6.06218i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 3 q^{2} + q^{4}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 3 q^{2} + q^{4} - 3 q^{10} - 5 q^{13} + 5 q^{16} - 3 q^{17} - 6 q^{19} - 3 q^{20} - 6 q^{23} + 4 q^{25} - 3 q^{26} + 3 q^{29} + 9 q^{32} + 15 q^{37} - 12 q^{38} + 6 q^{40} + 9 q^{41} - 8 q^{43} - 18 q^{46} - 7 q^{49} + 6 q^{50} + 2 q^{52} + 6 q^{53} + 9 q^{58} - 12 q^{59} - q^{61} - 6 q^{62} - 2 q^{64} + 9 q^{65} + 6 q^{67} + 3 q^{68} - 6 q^{71} + 15 q^{74} - 6 q^{76} + 8 q^{79} + 15 q^{80} + 9 q^{82} + 9 q^{85} + 12 q^{89} - 12 q^{92} - 6 q^{94} - 6 q^{95} + 12 q^{97} - 21 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/117\mathbb{Z}\right)^\times\).

\(n\) \(28\) \(92\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.50000 0.866025i 1.06066 0.612372i 0.135045 0.990839i \(-0.456882\pi\)
0.925615 + 0.378467i \(0.123549\pi\)
\(3\) 0 0
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) 1.73205i 0.774597i −0.921954 0.387298i \(-0.873408\pi\)
0.921954 0.387298i \(-0.126592\pi\)
\(6\) 0 0
\(7\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(8\) 1.73205i 0.612372i
\(9\) 0 0
\(10\) −1.50000 2.59808i −0.474342 0.821584i
\(11\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(12\) 0 0
\(13\) −2.50000 + 2.59808i −0.693375 + 0.720577i
\(14\) 0 0
\(15\) 0 0
\(16\) 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 \(0.285189\pi\)
\(18\) 0 0
\(19\) −3.00000 1.73205i −0.688247 0.397360i 0.114708 0.993399i \(-0.463407\pi\)
−0.802955 + 0.596040i \(0.796740\pi\)
\(20\) −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 \(-0.951544\pi\)
0.362892 0.931831i \(-0.381789\pi\)
\(24\) 0 0
\(25\) 2.00000 0.400000
\(26\) −1.50000 + 6.06218i −0.294174 + 1.18889i
\(27\) 0 0
\(28\) 0 0
\(29\) 1.50000 + 2.59808i 0.278543 + 0.482451i 0.971023 0.238987i \(-0.0768152\pi\)
−0.692480 + 0.721437i \(0.743482\pi\)
\(30\) 0 0
\(31\) 3.46410i 0.622171i −0.950382 0.311086i \(-0.899307\pi\)
0.950382 0.311086i \(-0.100693\pi\)
\(32\) 4.50000 + 2.59808i 0.795495 + 0.459279i
\(33\) 0 0
\(34\) 5.19615i 0.891133i
\(35\) 0 0
\(36\) 0 0
\(37\) 7.50000 4.33013i 1.23299 0.711868i 0.265340 0.964155i \(-0.414516\pi\)
0.967653 + 0.252286i \(0.0811825\pi\)
\(38\) −6.00000 −0.973329
\(39\) 0 0
\(40\) 3.00000 0.474342
\(41\) 4.50000 2.59808i 0.702782 0.405751i −0.105601 0.994409i \(-0.533677\pi\)
0.808383 + 0.588657i \(0.200343\pi\)
\(42\) 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
\(45\) 0 0
\(46\) −9.00000 5.19615i −1.32698 0.766131i
\(47\) 3.46410i 0.505291i −0.967559 0.252646i \(-0.918699\pi\)
0.967559 0.252646i \(-0.0813007\pi\)
\(48\) 0 0
\(49\) −3.50000 6.06218i −0.500000 0.866025i
\(50\) 3.00000 1.73205i 0.424264 0.244949i
\(51\) 0 0
\(52\) 1.00000 + 3.46410i 0.138675 + 0.480384i
\(53\) 3.00000 0.412082 0.206041 0.978543i \(-0.433942\pi\)
0.206041 + 0.978543i \(0.433942\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 0 0
\(58\) 4.50000 + 2.59808i 0.590879 + 0.341144i
\(59\) −6.00000 3.46410i −0.781133 0.450988i 0.0556984 0.998448i \(-0.482261\pi\)
−0.836832 + 0.547460i \(0.815595\pi\)
\(60\) 0 0
\(61\) −0.500000 + 0.866025i −0.0640184 + 0.110883i −0.896258 0.443533i \(-0.853725\pi\)
0.832240 + 0.554416i \(0.187058\pi\)
\(62\) −3.00000 5.19615i −0.381000 0.659912i
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 4.50000 + 4.33013i 0.558156 + 0.537086i
\(66\) 0 0
\(67\) 3.00000 1.73205i 0.366508 0.211604i −0.305424 0.952217i \(-0.598798\pi\)
0.671932 + 0.740613i \(0.265465\pi\)
\(68\) 1.50000 + 2.59808i 0.181902 + 0.315063i
\(69\) 0 0
\(70\) 0 0
\(71\) −3.00000 1.73205i −0.356034 0.205557i 0.311305 0.950310i \(-0.399234\pi\)
−0.667340 + 0.744753i \(0.732567\pi\)
\(72\) 0 0
\(73\) 1.73205i 0.202721i −0.994850 0.101361i \(-0.967680\pi\)
0.994850 0.101361i \(-0.0323196\pi\)
\(74\) 7.50000 12.9904i 0.871857 1.51010i
\(75\) 0 0
\(76\) −3.00000 + 1.73205i −0.344124 + 0.198680i
\(77\) 0 0
\(78\) 0 0
\(79\) 4.00000 0.450035 0.225018 0.974355i \(-0.427756\pi\)
0.225018 + 0.974355i \(0.427756\pi\)
\(80\) 7.50000 4.33013i 0.838525 0.484123i
\(81\) 0 0
\(82\) 4.50000 7.79423i 0.496942 0.860729i
\(83\) 13.8564i 1.52094i 0.649374 + 0.760469i \(0.275031\pi\)
−0.649374 + 0.760469i \(0.724969\pi\)
\(84\) 0 0
\(85\) 4.50000 + 2.59808i 0.488094 + 0.281801i
\(86\) 13.8564i 1.49417i
\(87\) 0 0
\(88\) 0 0
\(89\) 6.00000 3.46410i 0.635999 0.367194i −0.147073 0.989126i \(-0.546985\pi\)
0.783072 + 0.621932i \(0.213652\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −6.00000 −0.625543
\(93\) 0 0
\(94\) −3.00000 5.19615i −0.309426 0.535942i
\(95\) −3.00000 + 5.19615i −0.307794 + 0.533114i
\(96\) 0 0
\(97\) 6.00000 + 3.46410i 0.609208 + 0.351726i 0.772655 0.634826i \(-0.218928\pi\)
−0.163448 + 0.986552i \(0.552261\pi\)
\(98\) −10.5000 6.06218i −1.06066 0.612372i
\(99\) 0 0
\(100\) 1.00000 1.73205i 0.100000 0.173205i
\(101\) −1.50000 2.59808i −0.149256 0.258518i 0.781697 0.623658i \(-0.214354\pi\)
−0.930953 + 0.365140i \(0.881021\pi\)
\(102\) 0 0
\(103\) −10.0000 −0.985329 −0.492665 0.870219i \(-0.663977\pi\)
−0.492665 + 0.870219i \(0.663977\pi\)
\(104\) −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 \(-0.0730044\pi\)
−0.683793 + 0.729676i \(0.739671\pi\)
\(108\) 0 0
\(109\) 13.8564i 1.32720i 0.748086 + 0.663602i \(0.230973\pi\)
−0.748086 + 0.663602i \(0.769027\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −7.50000 + 12.9904i −0.705541 + 1.22203i 0.260955 + 0.965351i \(0.415962\pi\)
−0.966496 + 0.256681i \(0.917371\pi\)
\(114\) 0 0
\(115\) −9.00000 + 5.19615i −0.839254 + 0.484544i
\(116\) 3.00000 0.278543
\(117\) 0 0
\(118\) −12.0000 −1.10469
\(119\) 0 0
\(120\) 0 0
\(121\) −5.50000 + 9.52628i −0.500000 + 0.866025i
\(122\) 1.73205i 0.156813i
\(123\) 0 0
\(124\) −3.00000 1.73205i −0.269408 0.155543i
\(125\) 12.1244i 1.08444i
\(126\) 0 0
\(127\) 1.00000 + 1.73205i 0.0887357 + 0.153695i 0.906977 0.421180i \(-0.138384\pi\)
−0.818241 + 0.574875i \(0.805051\pi\)
\(128\) −10.5000 + 6.06218i −0.928078 + 0.535826i
\(129\) 0 0
\(130\) 10.5000 + 2.59808i 0.920911 + 0.227866i
\(131\) −18.0000 −1.57267 −0.786334 0.617802i \(-0.788023\pi\)
−0.786334 + 0.617802i \(0.788023\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 3.00000 5.19615i 0.259161 0.448879i
\(135\) 0 0
\(136\) −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 \(0.434712\pi\)
\(138\) 0 0
\(139\) 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
\(141\) 0 0
\(142\) −6.00000 −0.503509
\(143\) 0 0
\(144\) 0 0
\(145\) 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
\(149\) 16.5000 + 9.52628i 1.35173 + 0.780423i 0.988492 0.151272i \(-0.0483370\pi\)
0.363241 + 0.931695i \(0.381670\pi\)
\(150\) 0 0
\(151\) 17.3205i 1.40952i −0.709444 0.704761i \(-0.751054\pi\)
0.709444 0.704761i \(-0.248946\pi\)
\(152\) 3.00000 5.19615i 0.243332 0.421464i
\(153\) 0 0
\(154\) 0 0
\(155\) −6.00000 −0.481932
\(156\) 0 0
\(157\) −13.0000 −1.03751 −0.518756 0.854922i \(-0.673605\pi\)
−0.518756 + 0.854922i \(0.673605\pi\)
\(158\) 6.00000 3.46410i 0.477334 0.275589i
\(159\) 0 0
\(160\) 4.50000 7.79423i 0.355756 0.616188i
\(161\) 0 0
\(162\) 0 0
\(163\) 18.0000 + 10.3923i 1.40987 + 0.813988i 0.995375 0.0960641i \(-0.0306254\pi\)
0.414494 + 0.910052i \(0.363959\pi\)
\(164\) 5.19615i 0.405751i
\(165\) 0 0
\(166\) 12.0000 + 20.7846i 0.931381 + 1.61320i
\(167\) 12.0000 6.92820i 0.928588 0.536120i 0.0422232 0.999108i \(-0.486556\pi\)
0.886365 + 0.462988i \(0.153223\pi\)
\(168\) 0 0
\(169\) −0.500000 12.9904i −0.0384615 0.999260i
\(170\) 9.00000 0.690268
\(171\) 0 0
\(172\) 4.00000 + 6.92820i 0.304997 + 0.528271i
\(173\) 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
\(175\) 0 0
\(176\) 0 0
\(177\) 0 0
\(178\) 6.00000 10.3923i 0.449719 0.778936i
\(179\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(180\) 0 0
\(181\) 11.0000 0.817624 0.408812 0.912619i \(-0.365943\pi\)
0.408812 + 0.912619i \(0.365943\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 9.00000 5.19615i 0.663489 0.383065i
\(185\) −7.50000 12.9904i −0.551411 0.955072i
\(186\) 0 0
\(187\) 0 0
\(188\) −3.00000 1.73205i −0.218797 0.126323i
\(189\) 0 0
\(190\) 10.3923i 0.753937i
\(191\) 9.00000 15.5885i 0.651217 1.12794i −0.331611 0.943416i \(-0.607592\pi\)
0.982828 0.184525i \(-0.0590746\pi\)
\(192\) 0 0
\(193\) −4.50000 + 2.59808i −0.323917 + 0.187014i −0.653137 0.757240i \(-0.726548\pi\)
0.329220 + 0.944253i \(0.393214\pi\)
\(194\) 12.0000 0.861550
\(195\) 0 0
\(196\) −7.00000 −0.500000
\(197\) −12.0000 + 6.92820i −0.854965 + 0.493614i −0.862323 0.506359i \(-0.830991\pi\)
0.00735824 + 0.999973i \(0.497658\pi\)
\(198\) 0 0
\(199\) 1.00000 1.73205i 0.0708881 0.122782i −0.828403 0.560133i \(-0.810750\pi\)
0.899291 + 0.437351i \(0.144083\pi\)
\(200\) 3.46410i 0.244949i
\(201\) 0 0
\(202\) −4.50000 2.59808i −0.316619 0.182800i
\(203\) 0 0
\(204\) 0 0
\(205\) −4.50000 7.79423i −0.314294 0.544373i
\(206\) −15.0000 + 8.66025i −1.04510 + 0.603388i
\(207\) 0 0
\(208\) −17.5000 4.33013i −1.21341 0.300240i
\(209\) 0 0
\(210\) 0 0
\(211\) −5.00000 8.66025i −0.344214 0.596196i 0.640996 0.767544i \(-0.278521\pi\)
−0.985211 + 0.171347i \(0.945188\pi\)
\(212\) 1.50000 2.59808i 0.103020 0.178437i
\(213\) 0 0
\(214\) 9.00000 + 5.19615i 0.615227 + 0.355202i
\(215\) 12.0000 + 6.92820i 0.818393 + 0.472500i
\(216\) 0 0
\(217\) 0 0
\(218\) 12.0000 + 20.7846i 0.812743 + 1.40771i
\(219\) 0 0
\(220\) 0 0
\(221\) −3.00000 10.3923i −0.201802 0.699062i
\(222\) 0 0
\(223\) −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
\(225\) 0 0
\(226\) 25.9808i 1.72821i
\(227\) −21.0000 12.1244i −1.39382 0.804722i −0.400083 0.916479i \(-0.631019\pi\)
−0.993736 + 0.111757i \(0.964352\pi\)
\(228\) 0 0
\(229\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(230\) −9.00000 + 15.5885i −0.593442 + 1.02787i
\(231\) 0 0
\(232\) −4.50000 + 2.59808i −0.295439 + 0.170572i
\(233\) −6.00000 −0.393073 −0.196537 0.980497i \(-0.562969\pi\)
−0.196537 + 0.980497i \(0.562969\pi\)
\(234\) 0 0
\(235\) −6.00000 −0.391397
\(236\) −6.00000 + 3.46410i −0.390567 + 0.225494i
\(237\) 0 0
\(238\) 0 0
\(239\) 20.7846i 1.34444i −0.740349 0.672222i \(-0.765340\pi\)
0.740349 0.672222i \(-0.234660\pi\)
\(240\) 0 0
\(241\) −1.50000 0.866025i −0.0966235 0.0557856i 0.450910 0.892570i \(-0.351100\pi\)
−0.547533 + 0.836784i \(0.684433\pi\)
\(242\) 19.0526i 1.22474i
\(243\) 0 0
\(244\) 0.500000 + 0.866025i 0.0320092 + 0.0554416i
\(245\) −10.5000 + 6.06218i −0.670820 + 0.387298i
\(246\) 0 0
\(247\) 12.0000 3.46410i 0.763542 0.220416i
\(248\) 6.00000 0.381000
\(249\) 0 0
\(250\) −10.5000 18.1865i −0.664078 1.15022i
\(251\) −9.00000 + 15.5885i −0.568075 + 0.983935i 0.428681 + 0.903456i \(0.358978\pi\)
−0.996756 + 0.0804789i \(0.974355\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 3.00000 + 1.73205i 0.188237 + 0.108679i
\(255\) 0 0
\(256\) −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 \(0.803506\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 6.00000 1.73205i 0.372104 0.107417i
\(261\) 0 0
\(262\) −27.0000 + 15.5885i −1.66807 + 0.963058i
\(263\) 6.00000 + 10.3923i 0.369976 + 0.640817i 0.989561 0.144112i \(-0.0460326\pi\)
−0.619586 + 0.784929i \(0.712699\pi\)
\(264\) 0 0
\(265\) 5.19615i 0.319197i
\(266\) 0 0
\(267\) 0 0
\(268\) 3.46410i 0.211604i
\(269\) −3.00000 + 5.19615i −0.182913 + 0.316815i −0.942871 0.333157i \(-0.891886\pi\)
0.759958 + 0.649972i \(0.225219\pi\)
\(270\) 0 0
\(271\) 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
\(276\) 0 0
\(277\) 3.50000 6.06218i 0.210295 0.364241i −0.741512 0.670940i \(-0.765891\pi\)
0.951807 + 0.306699i \(0.0992243\pi\)
\(278\) 6.92820i 0.415526i
\(279\) 0 0
\(280\) 0 0
\(281\) 22.5167i 1.34323i −0.740900 0.671616i \(-0.765601\pi\)
0.740900 0.671616i \(-0.234399\pi\)
\(282\) 0 0
\(283\) −2.00000 3.46410i −0.118888 0.205919i 0.800439 0.599414i \(-0.204600\pi\)
−0.919327 + 0.393494i \(0.871266\pi\)
\(284\) −3.00000 + 1.73205i −0.178017 + 0.102778i
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 4.00000 + 6.92820i 0.235294 + 0.407541i
\(290\) 4.50000 7.79423i 0.264249 0.457693i
\(291\) 0 0
\(292\) −1.50000 0.866025i −0.0877809 0.0506803i
\(293\) −4.50000 2.59808i −0.262893 0.151781i 0.362761 0.931882i \(-0.381834\pi\)
−0.625653 + 0.780101i \(0.715168\pi\)
\(294\) 0 0
\(295\) −6.00000 + 10.3923i −0.349334 + 0.605063i
\(296\) 7.50000 + 12.9904i 0.435929 + 0.755051i
\(297\) 0 0
\(298\) 33.0000 1.91164
\(299\) 21.0000 + 5.19615i 1.21446 + 0.300501i
\(300\) 0 0
\(301\) 0 0
\(302\) −15.0000 25.9808i −0.863153 1.49502i
\(303\) 0 0
\(304\) 17.3205i 0.993399i
\(305\) 1.50000 + 0.866025i 0.0858898 + 0.0495885i
\(306\) 0 0
\(307\) 17.3205i 0.988534i 0.869310 + 0.494267i \(0.164563\pi\)
−0.869310 + 0.494267i \(0.835437\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −9.00000 + 5.19615i −0.511166 + 0.295122i
\(311\) 30.0000 1.70114 0.850572 0.525859i \(-0.176256\pi\)
0.850572 + 0.525859i \(0.176256\pi\)
\(312\) 0 0
\(313\) 10.0000 0.565233 0.282617 0.959233i \(-0.408798\pi\)
0.282617 + 0.959233i \(0.408798\pi\)
\(314\) −19.5000 + 11.2583i −1.10045 + 0.635344i
\(315\) 0 0
\(316\) 2.00000 3.46410i 0.112509 0.194871i
\(317\) 5.19615i 0.291845i −0.989296 0.145922i \(-0.953385\pi\)
0.989296 0.145922i \(-0.0466150\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 1.73205i 0.0968246i
\(321\) 0 0
\(322\) 0 0
\(323\) 9.00000 5.19615i 0.500773 0.289122i
\(324\) 0 0
\(325\) −5.00000 + 5.19615i −0.277350 + 0.288231i
\(326\) 36.0000 1.99386
\(327\) 0 0
\(328\) 4.50000 + 7.79423i 0.248471 + 0.430364i
\(329\) 0 0
\(330\) 0 0
\(331\) −24.0000 13.8564i −1.31916 0.761617i −0.335566 0.942017i \(-0.608928\pi\)
−0.983593 + 0.180400i \(0.942261\pi\)
\(332\) 12.0000 + 6.92820i 0.658586 + 0.380235i
\(333\) 0 0
\(334\) 12.0000 20.7846i 0.656611 1.13728i
\(335\) −3.00000 5.19615i −0.163908 0.283896i
\(336\) 0 0
\(337\) −23.0000 −1.25289 −0.626445 0.779466i \(-0.715491\pi\)
−0.626445 + 0.779466i \(0.715491\pi\)
\(338\) −12.0000 19.0526i −0.652714 1.03632i
\(339\) 0 0
\(340\) 4.50000 2.59808i 0.244047 0.140900i
\(341\) 0 0
\(342\) 0 0
\(343\) 0 0
\(344\) −12.0000 6.92820i −0.646997 0.373544i
\(345\) 0 0
\(346\) 10.3923i 0.558694i
\(347\) −15.0000 + 25.9808i −0.805242 + 1.39472i 0.110885 + 0.993833i \(0.464631\pi\)
−0.916127 + 0.400887i \(0.868702\pi\)
\(348\) 0 0
\(349\) 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
\(351\) 0 0
\(352\) 0 0
\(353\) −28.5000 + 16.4545i −1.51690 + 0.875784i −0.517099 + 0.855926i \(0.672988\pi\)
−0.999803 + 0.0198582i \(0.993679\pi\)
\(354\) 0 0
\(355\) −3.00000 + 5.19615i −0.159223 + 0.275783i
\(356\) 6.92820i 0.367194i
\(357\) 0 0
\(358\) 0 0
\(359\) 6.92820i 0.365657i −0.983145 0.182828i \(-0.941475\pi\)
0.983145 0.182828i \(-0.0585252\pi\)
\(360\) 0 0
\(361\) −3.50000 6.06218i −0.184211 0.319062i
\(362\) 16.5000 9.52628i 0.867221 0.500690i
\(363\) 0 0
\(364\) 0 0
\(365\) −3.00000 −0.157027
\(366\) 0 0
\(367\) 11.0000 + 19.0526i 0.574195 + 0.994535i 0.996129 + 0.0879086i \(0.0280183\pi\)
−0.421933 + 0.906627i \(0.638648\pi\)
\(368\) 15.0000 25.9808i 0.781929 1.35434i
\(369\) 0 0
\(370\) −22.5000 12.9904i −1.16972 0.675338i
\(371\) 0 0
\(372\) 0 0
\(373\) −9.50000 + 16.4545i −0.491891 + 0.851981i −0.999956 0.00933789i \(-0.997028\pi\)
0.508065 + 0.861319i \(0.330361\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 6.00000 0.309426
\(377\) −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
\(381\) 0 0
\(382\) 31.1769i 1.59515i
\(383\) 18.0000 + 10.3923i 0.919757 + 0.531022i 0.883558 0.468323i \(-0.155141\pi\)
0.0361995 + 0.999345i \(0.488475\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −4.50000 + 7.79423i −0.229044 + 0.396716i
\(387\) 0 0
\(388\) 6.00000 3.46410i 0.304604 0.175863i
\(389\) 9.00000 0.456318 0.228159 0.973624i \(-0.426729\pi\)
0.228159 + 0.973624i \(0.426729\pi\)
\(390\) 0 0
\(391\) 18.0000 0.910299
\(392\) 10.5000 6.06218i 0.530330 0.306186i
\(393\) 0 0
\(394\) −12.0000 + 20.7846i −0.604551 + 1.04711i
\(395\) 6.92820i 0.348596i
\(396\) 0 0
\(397\) −12.0000 6.92820i −0.602263 0.347717i 0.167668 0.985843i \(-0.446376\pi\)
−0.769931 + 0.638127i \(0.779710\pi\)
\(398\) 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 \(0.319563\pi\)
\(402\) 0 0
\(403\) 9.00000 + 8.66025i 0.448322 + 0.431398i
\(404\) −3.00000 −0.149256
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 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
\(411\) 0 0
\(412\) −5.00000 + 8.66025i −0.246332 + 0.426660i
\(413\) 0 0
\(414\) 0 0
\(415\) 24.0000 1.17811
\(416\) −18.0000 + 5.19615i −0.882523 + 0.254762i
\(417\) 0 0
\(418\) 0 0
\(419\) 9.00000 + 15.5885i 0.439679 + 0.761546i 0.997665 0.0683046i \(-0.0217590\pi\)
−0.557986 + 0.829851i \(0.688426\pi\)
\(420\) 0 0
\(421\) 15.5885i 0.759735i −0.925041 0.379867i \(-0.875970\pi\)
0.925041 0.379867i \(-0.124030\pi\)
\(422\) −15.0000 8.66025i −0.730189 0.421575i
\(423\) 0 0
\(424\) 5.19615i 0.252347i
\(425\) −3.00000 + 5.19615i −0.145521 + 0.252050i
\(426\) 0 0
\(427\) 0 0
\(428\) 6.00000 0.290021
\(429\) 0 0
\(430\) 24.0000 1.15738
\(431\) 6.00000 3.46410i 0.289010 0.166860i −0.348485 0.937314i \(-0.613304\pi\)
0.637495 + 0.770454i \(0.279971\pi\)
\(432\) 0 0
\(433\) 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
\(435\) 0 0
\(436\) 12.0000 + 6.92820i 0.574696 + 0.331801i
\(437\) 20.7846i 0.994263i
\(438\) 0 0
\(439\) 14.0000 + 24.2487i 0.668184 + 1.15733i 0.978412 + 0.206666i \(0.0662612\pi\)
−0.310228 + 0.950662i \(0.600405\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) −13.5000 12.9904i −0.642130 0.617889i
\(443\) 12.0000 0.570137 0.285069 0.958507i \(-0.407984\pi\)
0.285069 + 0.958507i \(0.407984\pi\)
\(444\) 0 0
\(445\) −6.00000 10.3923i −0.284427 0.492642i
\(446\) −9.00000 + 15.5885i −0.426162 + 0.738135i
\(447\) 0 0
\(448\) 0 0
\(449\) 6.00000 + 3.46410i 0.283158 + 0.163481i 0.634852 0.772634i \(-0.281061\pi\)
−0.351694 + 0.936115i \(0.614394\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 7.50000 + 12.9904i 0.352770 + 0.611016i
\(453\) 0 0
\(454\) −42.0000 −1.97116
\(455\) 0 0
\(456\) 0 0
\(457\) 1.50000 0.866025i 0.0701670 0.0405110i −0.464506 0.885570i \(-0.653768\pi\)
0.534673 + 0.845059i \(0.320435\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 10.3923i 0.484544i
\(461\) −19.5000 11.2583i −0.908206 0.524353i −0.0283522 0.999598i \(-0.509026\pi\)
−0.879853 + 0.475245i \(0.842359\pi\)
\(462\) 0 0
\(463\) 13.8564i 0.643962i −0.946746 0.321981i \(-0.895651\pi\)
0.946746 0.321981i \(-0.104349\pi\)
\(464\) −7.50000 + 12.9904i −0.348179 + 0.603063i
\(465\) 0 0
\(466\) −9.00000 + 5.19615i −0.416917 + 0.240707i
\(467\) −12.0000 −0.555294 −0.277647 0.960683i \(-0.589555\pi\)
−0.277647 + 0.960683i \(0.589555\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) −9.00000 + 5.19615i −0.415139 + 0.239681i
\(471\) 0 0
\(472\) 6.00000 10.3923i 0.276172 0.478345i
\(473\) 0 0
\(474\) 0 0
\(475\) −6.00000 3.46410i −0.275299 0.158944i
\(476\) 0 0
\(477\) 0 0
\(478\) −18.0000 31.1769i −0.823301 1.42600i
\(479\) −21.0000 + 12.1244i −0.959514 + 0.553976i −0.896024 0.444006i \(-0.853557\pi\)
−0.0634909 + 0.997982i \(0.520223\pi\)
\(480\) 0 0
\(481\) −7.50000 + 30.3109i −0.341971 + 1.38206i
\(482\) −3.00000 −0.136646
\(483\) 0 0
\(484\) 5.50000 + 9.52628i 0.250000 + 0.433013i
\(485\) 6.00000 10.3923i 0.272446 0.471890i
\(486\) 0 0
\(487\) −6.00000 3.46410i −0.271886 0.156973i 0.357858 0.933776i \(-0.383507\pi\)
−0.629744 + 0.776802i \(0.716840\pi\)
\(488\) −1.50000 0.866025i −0.0679018 0.0392031i
\(489\) 0 0
\(490\) −10.5000 + 18.1865i −0.474342 + 0.821584i
\(491\) 6.00000 + 10.3923i 0.270776 + 0.468998i 0.969061 0.246822i \(-0.0793863\pi\)
−0.698285 + 0.715820i \(0.746053\pi\)
\(492\) 0 0
\(493\) −9.00000 −0.405340
\(494\) 15.0000 15.5885i 0.674882 0.701358i
\(495\) 0 0
\(496\) 15.0000 8.66025i 0.673520 0.388857i
\(497\) 0 0
\(498\) 0 0
\(499\) 31.1769i 1.39567i −0.716258 0.697835i \(-0.754147\pi\)
0.716258 0.697835i \(-0.245853\pi\)
\(500\) −10.5000 6.06218i −0.469574 0.271109i
\(501\) 0 0
\(502\) 31.1769i 1.39149i
\(503\) 18.0000 31.1769i 0.802580 1.39011i −0.115332 0.993327i \(-0.536793\pi\)
0.917912 0.396783i \(-0.129873\pi\)
\(504\) 0 0
\(505\) −4.50000 + 2.59808i −0.200247 + 0.115613i
\(506\) 0 0
\(507\) 0 0
\(508\) 2.00000 0.0887357
\(509\) −16.5000 + 9.52628i −0.731350 + 0.422245i −0.818916 0.573914i \(-0.805424\pi\)
0.0875661 + 0.996159i \(0.472091\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 8.66025i 0.382733i
\(513\) 0 0
\(514\) 4.50000 + 2.59808i 0.198486 + 0.114596i
\(515\) 17.3205i 0.763233i
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) −7.50000 + 7.79423i −0.328897 + 0.341800i
\(521\) −9.00000 −0.394297 −0.197149 0.980374i \(-0.563168\pi\)
−0.197149 + 0.980374i \(0.563168\pi\)
\(522\) 0 0
\(523\) 8.00000 + 13.8564i 0.349816 + 0.605898i 0.986216 0.165460i \(-0.0529109\pi\)
−0.636401 + 0.771358i \(0.719578\pi\)
\(524\) −9.00000 + 15.5885i −0.393167 + 0.680985i
\(525\) 0 0
\(526\) 18.0000 + 10.3923i 0.784837 + 0.453126i
\(527\) 9.00000 + 5.19615i 0.392046 + 0.226348i
\(528\) 0 0
\(529\) −6.50000 + 11.2583i −0.282609 + 0.489493i
\(530\) −4.50000 7.79423i −0.195468 0.338560i
\(531\) 0 0
\(532\) 0 0
\(533\) −4.50000 + 18.1865i −0.194917 + 0.787746i
\(534\) 0 0
\(535\) 9.00000 5.19615i 0.389104 0.224649i
\(536\) 3.00000 + 5.19615i 0.129580 + 0.224440i
\(537\) 0 0
\(538\) 10.3923i 0.448044i
\(539\) 0 0
\(540\) 0 0
\(541\) 29.4449i 1.26593i −0.774179 0.632967i \(-0.781837\pi\)
0.774179 0.632967i \(-0.218163\pi\)
\(542\) 18.0000 31.1769i 0.773166 1.33916i
\(543\) 0 0
\(544\) −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
\(549\) 0 0
\(550\) 0 0
\(551\) 10.3923i 0.442727i
\(552\) 0 0
\(553\) 0 0
\(554\) 12.1244i 0.515115i
\(555\) 0 0
\(556\) −2.00000 3.46410i −0.0848189 0.146911i
\(557\) 13.5000 7.79423i 0.572013 0.330252i −0.185940 0.982561i \(-0.559533\pi\)
0.757953 + 0.652309i \(0.226200\pi\)
\(558\) 0 0
\(559\) −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 \(0.166667\pi\)
\(564\) 0 0
\(565\) 22.5000 + 12.9904i 0.946582 + 0.546509i
\(566\) −6.00000 3.46410i −0.252199 0.145607i
\(567\) 0 0
\(568\) 3.00000 5.19615i 0.125877 0.218026i
\(569\) −21.0000 36.3731i −0.880366 1.52484i −0.850935 0.525271i \(-0.823964\pi\)
−0.0294311 0.999567i \(-0.509370\pi\)
\(570\) 0 0
\(571\) 40.0000 1.67395 0.836974 0.547243i \(-0.184323\pi\)
0.836974 + 0.547243i \(0.184323\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −6.00000 10.3923i −0.250217 0.433389i
\(576\) 0 0
\(577\) 19.0526i 0.793168i 0.917998 + 0.396584i \(0.129805\pi\)
−0.917998 + 0.396584i \(0.870195\pi\)
\(578\) 12.0000 + 6.92820i 0.499134 + 0.288175i
\(579\) 0 0
\(580\) 5.19615i 0.215758i
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) 3.00000 0.124141
\(585\) 0 0
\(586\) −9.00000 −0.371787
\(587\) 18.0000 10.3923i 0.742940 0.428936i −0.0801976 0.996779i \(-0.525555\pi\)
0.823137 + 0.567843i \(0.192222\pi\)
\(588\) 0 0
\(589\) −6.00000 + 10.3923i −0.247226 + 0.428207i
\(590\) 20.7846i 0.855689i
\(591\) 0 0
\(592\) 37.5000 + 21.6506i 1.54124 + 0.889836i
\(593\) 25.9808i 1.06690i −0.845831 0.533451i \(-0.820895\pi\)
0.845831 0.533451i \(-0.179105\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 16.5000 9.52628i 0.675866 0.390212i
\(597\) 0 0
\(598\) 36.0000 10.3923i 1.47215 0.424973i
\(599\) −30.0000 −1.22577 −0.612883 0.790173i \(-0.709990\pi\)
−0.612883 + 0.790173i \(0.709990\pi\)
\(600\) 0 0
\(601\) −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
\(603\) 0 0
\(604\) −15.0000 8.66025i −0.610341 0.352381i
\(605\) 16.5000 + 9.52628i 0.670820 + 0.387298i
\(606\) 0 0
\(607\) 17.0000 29.4449i 0.690009 1.19513i −0.281826 0.959466i \(-0.590940\pi\)
0.971834 0.235665i \(-0.0757267\pi\)
\(608\) −9.00000 15.5885i −0.364998 0.632195i
\(609\) 0 0
\(610\) 3.00000 0.121466
\(611\) 9.00000 + 8.66025i 0.364101 + 0.350356i
\(612\) 0 0
\(613\) −10.5000 + 6.06218i −0.424091 + 0.244849i −0.696826 0.717240i \(-0.745405\pi\)
0.272735 + 0.962089i \(0.412072\pi\)
\(614\) 15.0000 + 25.9808i 0.605351 + 1.04850i
\(615\) 0 0
\(616\) 0 0
\(617\) 19.5000 + 11.2583i 0.785040 + 0.453243i 0.838214 0.545342i \(-0.183600\pi\)
−0.0531732 + 0.998585i \(0.516934\pi\)
\(618\) 0 0
\(619\) 20.7846i 0.835404i 0.908584 + 0.417702i \(0.137164\pi\)
−0.908584 + 0.417702i \(0.862836\pi\)
\(620\) −3.00000 + 5.19615i −0.120483 + 0.208683i
\(621\) 0 0
\(622\) 45.0000 25.9808i 1.80434 1.04173i
\(623\) 0 0
\(624\) 0 0
\(625\) −11.0000 −0.440000
\(626\) 15.0000 8.66025i 0.599521 0.346133i
\(627\) 0 0
\(628\) −6.50000 + 11.2583i −0.259378 + 0.449256i
\(629\) 25.9808i 1.03592i
\(630\) 0 0
\(631\) −42.0000 24.2487i −1.67199 0.965326i −0.966521 0.256589i \(-0.917401\pi\)
−0.705473 0.708737i \(-0.749265\pi\)
\(632\) 6.92820i 0.275589i
\(633\) 0 0
\(634\) −4.50000 7.79423i −0.178718 0.309548i
\(635\) 3.00000 1.73205i 0.119051 0.0687343i
\(636\) 0 0
\(637\) 24.5000 + 6.06218i 0.970725 + 0.240192i
\(638\) 0 0
\(639\) 0 0
\(640\) 10.5000 + 18.1865i 0.415049 + 0.718886i
\(641\) 16.5000 28.5788i 0.651711 1.12880i −0.330997 0.943632i \(-0.607385\pi\)
0.982708 0.185164i \(-0.0592817\pi\)
\(642\) 0 0
\(643\) 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
\(645\) 0 0
\(646\) 9.00000 15.5885i 0.354100 0.613320i
\(647\) 9.00000 + 15.5885i 0.353827 + 0.612845i 0.986916 0.161233i \(-0.0515470\pi\)
−0.633090 + 0.774078i \(0.718214\pi\)
\(648\) 0 0
\(649\) 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 \(-0.966977\pi\)
0.407628 0.913148i \(-0.366356\pi\)
\(654\) 0 0
\(655\) 31.1769i 1.21818i
\(656\) 22.5000 + 12.9904i 0.878477 + 0.507189i
\(657\) 0 0
\(658\) 0 0
\(659\) −6.00000 + 10.3923i −0.233727 + 0.404827i −0.958902 0.283738i \(-0.908425\pi\)
0.725175 + 0.688565i \(0.241759\pi\)
\(660\) 0 0
\(661\) −40.5000 + 23.3827i −1.57527 + 0.909481i −0.579761 + 0.814787i \(0.696854\pi\)
−0.995506 + 0.0946945i \(0.969813\pi\)
\(662\) −48.0000 −1.86557
\(663\) 0 0
\(664\) −24.0000 −0.931381
\(665\) 0 0
\(666\) 0 0
\(667\) 9.00000 15.5885i 0.348481 0.603587i
\(668\) 13.8564i 0.536120i
\(669\) 0 0
\(670\) −9.00000 5.19615i −0.347700 0.200745i
\(671\) 0 0
\(672\) 0 0
\(673\) 9.50000 + 16.4545i 0.366198 + 0.634274i 0.988968 0.148132i \(-0.0473259\pi\)
−0.622770 + 0.782405i \(0.713993\pi\)
\(674\) −34.5000 + 19.9186i −1.32889 + 0.767235i
\(675\) 0 0
\(676\) −11.5000 6.06218i −0.442308 0.233161i
\(677\) 6.00000 0.230599 0.115299 0.993331i \(-0.463217\pi\)
0.115299 + 0.993331i \(0.463217\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) −4.50000 + 7.79423i −0.172567 + 0.298895i
\(681\) 0 0
\(682\) 0 0
\(683\) −21.0000 12.1244i −0.803543 0.463926i 0.0411658 0.999152i \(-0.486893\pi\)
−0.844708 + 0.535227i \(0.820226\pi\)
\(684\) 0 0
\(685\) 13.5000 23.3827i 0.515808 0.893407i
\(686\) 0 0
\(687\) 0 0
\(688\) −40.0000 −1.52499
\(689\) −7.50000 + 7.79423i −0.285727 + 0.296936i
\(690\) 0 0
\(691\) 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
\(695\) −6.00000 3.46410i −0.227593 0.131401i
\(696\) 0 0
\(697\) 15.5885i 0.590455i
\(698\) 12.0000 20.7846i 0.454207 0.786709i
\(699\) 0 0
\(700\) 0 0
\(701\) −18.0000 −0.679851 −0.339925 0.940452i \(-0.610402\pi\)
−0.339925 + 0.940452i \(0.610402\pi\)
\(702\) 0 0
\(703\) −30.0000 −1.13147
\(704\) 0 0
\(705\) 0 0
\(706\) −28.5000 + 49.3634i −1.07261 + 1.85782i
\(707\) 0 0
\(708\) 0 0
\(709\) −4.50000 2.59808i −0.169001 0.0975728i 0.413114 0.910679i \(-0.364441\pi\)
−0.582115 + 0.813107i \(0.697775\pi\)
\(710\) 10.3923i 0.390016i
\(711\) 0 0
\(712\) 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
\(717\) 0 0
\(718\) −6.00000 10.3923i −0.223918 0.387837i
\(719\) −24.0000 + 41.5692i −0.895049 + 1.55027i −0.0613050 + 0.998119i \(0.519526\pi\)
−0.833744 + 0.552151i \(0.813807\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −10.5000 6.06218i −0.390770 0.225611i
\(723\) 0 0
\(724\) 5.50000 9.52628i 0.204406 0.354041i
\(725\) 3.00000 + 5.19615i 0.111417 + 0.192980i
\(726\) 0 0
\(727\) −32.0000 −1.18681 −0.593407 0.804902i \(-0.702218\pi\)
−0.593407 + 0.804902i \(0.702218\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) −4.50000 + 2.59808i −0.166552 + 0.0961591i
\(731\) −12.0000 20.7846i −0.443836 0.768747i
\(732\) 0 0
\(733\) 12.1244i 0.447823i −0.974609 0.223912i \(-0.928117\pi\)
0.974609 0.223912i \(-0.0718827\pi\)
\(734\) 33.0000 + 19.0526i 1.21805 + 0.703243i
\(735\) 0 0
\(736\) 31.1769i 1.14920i
\(737\) 0 0
\(738\) 0 0
\(739\) −18.0000 + 10.3923i −0.662141 + 0.382287i −0.793092 0.609102i \(-0.791530\pi\)
0.130951 + 0.991389i \(0.458197\pi\)
\(740\) −15.0000 −0.551411
\(741\) 0 0
\(742\) 0 0
\(743\) 30.0000 17.3205i 1.10059 0.635428i 0.164216 0.986424i \(-0.447490\pi\)
0.936377 + 0.350997i \(0.114157\pi\)
\(744\) 0 0
\(745\) 16.5000 28.5788i 0.604513 1.04705i
\(746\) 32.9090i 1.20488i
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 8.00000 + 13.8564i 0.291924 + 0.505627i 0.974265 0.225407i \(-0.0723712\pi\)
−0.682341 + 0.731034i \(0.739038\pi\)
\(752\) 15.0000 8.66025i 0.546994 0.315807i
\(753\) 0 0
\(754\) −18.0000 + 5.19615i −0.655521 + 0.189233i
\(755\) −30.0000 −1.09181
\(756\) 0 0
\(757\) 13.0000 + 22.5167i 0.472493 + 0.818382i 0.999505 0.0314762i \(-0.0100208\pi\)
−0.527011 + 0.849858i \(0.676688\pi\)
\(758\) −21.0000 + 36.3731i −0.762754 + 1.32113i
\(759\) 0 0
\(760\) −9.00000 5.19615i −0.326464 0.188484i
\(761\) −30.0000 17.3205i −1.08750 0.627868i −0.154590 0.987979i \(-0.549406\pi\)
−0.932910 + 0.360111i \(0.882739\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −9.00000 15.5885i −0.325609 0.563971i
\(765\) 0 0
\(766\) 36.0000 1.30073
\(767\) 24.0000 6.92820i 0.866590 0.250163i
\(768\) 0 0
\(769\) 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
\(771\) 0 0
\(772\) 5.19615i 0.187014i
\(773\) 30.0000 + 17.3205i 1.07903 + 0.622975i 0.930633 0.365953i \(-0.119257\pi\)
0.148392 + 0.988929i \(0.452590\pi\)
\(774\) 0 0
\(775\) 6.92820i 0.248868i
\(776\) −6.00000 + 10.3923i −0.215387 + 0.373062i
\(777\) 0 0
\(778\) 13.5000 7.79423i 0.483998 0.279437i
\(779\) −18.0000 −0.644917
\(780\) 0 0
\(781\) 0 0
\(782\) 27.0000 15.5885i 0.965518 0.557442i
\(783\) 0 0
\(784\) 17.5000 30.3109i 0.625000 1.08253i
\(785\) 22.5167i 0.803654i
\(786\) 0 0
\(787\) 33.0000 + 19.0526i 1.17632 + 0.679150i 0.955161 0.296087i \(-0.0956817\pi\)
0.221162 + 0.975237i \(0.429015\pi\)