Properties

Label 1134.2.f.s.757.2
Level $1134$
Weight $2$
Character 1134.757
Analytic conductor $9.055$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1134,2,Mod(379,1134)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1134, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([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("1134.379");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1134 = 2 \cdot 3^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1134.f (of order \(3\), 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: \(9.05503558921\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\zeta_{12})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 757.2
Root \(0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 1134.757
Dual form 1134.2.f.s.379.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.133975 + 0.232051i) q^{5} +(0.500000 + 0.866025i) q^{7} -1.00000 q^{8} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.133975 + 0.232051i) q^{5} +(0.500000 + 0.866025i) q^{7} -1.00000 q^{8} -0.267949 q^{10} +(-3.09808 - 5.36603i) q^{11} +(3.23205 - 5.59808i) q^{13} +(-0.500000 + 0.866025i) q^{14} +(-0.500000 - 0.866025i) q^{16} +7.00000 q^{17} +0.732051 q^{19} +(-0.133975 - 0.232051i) q^{20} +(3.09808 - 5.36603i) q^{22} +(2.09808 - 3.63397i) q^{23} +(2.46410 + 4.26795i) q^{25} +6.46410 q^{26} -1.00000 q^{28} +(-0.767949 - 1.33013i) q^{29} +(-4.09808 + 7.09808i) q^{31} +(0.500000 - 0.866025i) q^{32} +(3.50000 + 6.06218i) q^{34} -0.267949 q^{35} +10.6603 q^{37} +(0.366025 + 0.633975i) q^{38} +(0.133975 - 0.232051i) q^{40} +(-1.26795 + 2.19615i) q^{41} +(0.732051 + 1.26795i) q^{43} +6.19615 q^{44} +4.19615 q^{46} +(-2.36603 - 4.09808i) q^{47} +(-0.500000 + 0.866025i) q^{49} +(-2.46410 + 4.26795i) q^{50} +(3.23205 + 5.59808i) q^{52} -9.46410 q^{53} +1.66025 q^{55} +(-0.500000 - 0.866025i) q^{56} +(0.767949 - 1.33013i) q^{58} +(-2.09808 + 3.63397i) q^{59} +(-1.96410 - 3.40192i) q^{61} -8.19615 q^{62} +1.00000 q^{64} +(0.866025 + 1.50000i) q^{65} +(3.36603 - 5.83013i) q^{67} +(-3.50000 + 6.06218i) q^{68} +(-0.133975 - 0.232051i) q^{70} +6.53590 q^{71} +8.26795 q^{73} +(5.33013 + 9.23205i) q^{74} +(-0.366025 + 0.633975i) q^{76} +(3.09808 - 5.36603i) q^{77} +(4.56218 + 7.90192i) q^{79} +0.267949 q^{80} -2.53590 q^{82} +(-8.29423 - 14.3660i) q^{83} +(-0.937822 + 1.62436i) q^{85} +(-0.732051 + 1.26795i) q^{86} +(3.09808 + 5.36603i) q^{88} +9.92820 q^{89} +6.46410 q^{91} +(2.09808 + 3.63397i) q^{92} +(2.36603 - 4.09808i) q^{94} +(-0.0980762 + 0.169873i) q^{95} +(-5.46410 - 9.46410i) q^{97} -1.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 2 q^{2} - 2 q^{4} - 4 q^{5} + 2 q^{7} - 4 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 2 q^{2} - 2 q^{4} - 4 q^{5} + 2 q^{7} - 4 q^{8} - 8 q^{10} - 2 q^{11} + 6 q^{13} - 2 q^{14} - 2 q^{16} + 28 q^{17} - 4 q^{19} - 4 q^{20} + 2 q^{22} - 2 q^{23} - 4 q^{25} + 12 q^{26} - 4 q^{28} - 10 q^{29} - 6 q^{31} + 2 q^{32} + 14 q^{34} - 8 q^{35} + 8 q^{37} - 2 q^{38} + 4 q^{40} - 12 q^{41} - 4 q^{43} + 4 q^{44} - 4 q^{46} - 6 q^{47} - 2 q^{49} + 4 q^{50} + 6 q^{52} - 24 q^{53} - 28 q^{55} - 2 q^{56} + 10 q^{58} + 2 q^{59} + 6 q^{61} - 12 q^{62} + 4 q^{64} + 10 q^{67} - 14 q^{68} - 4 q^{70} + 40 q^{71} + 40 q^{73} + 4 q^{74} + 2 q^{76} + 2 q^{77} - 6 q^{79} + 8 q^{80} - 24 q^{82} - 2 q^{83} - 28 q^{85} + 4 q^{86} + 2 q^{88} + 12 q^{89} + 12 q^{91} - 2 q^{92} + 6 q^{94} + 10 q^{95} - 8 q^{97} - 4 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1134\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(407\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 + 0.866025i 0.353553 + 0.612372i
\(3\) 0 0
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) −0.133975 + 0.232051i −0.0599153 + 0.103776i −0.894427 0.447214i \(-0.852416\pi\)
0.834512 + 0.550990i \(0.185750\pi\)
\(6\) 0 0
\(7\) 0.500000 + 0.866025i 0.188982 + 0.327327i
\(8\) −1.00000 −0.353553
\(9\) 0 0
\(10\) −0.267949 −0.0847330
\(11\) −3.09808 5.36603i −0.934105 1.61792i −0.776222 0.630460i \(-0.782866\pi\)
−0.157883 0.987458i \(-0.550467\pi\)
\(12\) 0 0
\(13\) 3.23205 5.59808i 0.896410 1.55263i 0.0643593 0.997927i \(-0.479500\pi\)
0.832050 0.554700i \(-0.187167\pi\)
\(14\) −0.500000 + 0.866025i −0.133631 + 0.231455i
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 7.00000 1.69775 0.848875 0.528594i \(-0.177281\pi\)
0.848875 + 0.528594i \(0.177281\pi\)
\(18\) 0 0
\(19\) 0.732051 0.167944 0.0839720 0.996468i \(-0.473239\pi\)
0.0839720 + 0.996468i \(0.473239\pi\)
\(20\) −0.133975 0.232051i −0.0299576 0.0518881i
\(21\) 0 0
\(22\) 3.09808 5.36603i 0.660512 1.14404i
\(23\) 2.09808 3.63397i 0.437479 0.757736i −0.560015 0.828482i \(-0.689205\pi\)
0.997494 + 0.0707462i \(0.0225381\pi\)
\(24\) 0 0
\(25\) 2.46410 + 4.26795i 0.492820 + 0.853590i
\(26\) 6.46410 1.26771
\(27\) 0 0
\(28\) −1.00000 −0.188982
\(29\) −0.767949 1.33013i −0.142605 0.246998i 0.785872 0.618389i \(-0.212214\pi\)
−0.928477 + 0.371391i \(0.878881\pi\)
\(30\) 0 0
\(31\) −4.09808 + 7.09808i −0.736036 + 1.27485i 0.218231 + 0.975897i \(0.429971\pi\)
−0.954267 + 0.298955i \(0.903362\pi\)
\(32\) 0.500000 0.866025i 0.0883883 0.153093i
\(33\) 0 0
\(34\) 3.50000 + 6.06218i 0.600245 + 1.03965i
\(35\) −0.267949 −0.0452917
\(36\) 0 0
\(37\) 10.6603 1.75253 0.876267 0.481825i \(-0.160026\pi\)
0.876267 + 0.481825i \(0.160026\pi\)
\(38\) 0.366025 + 0.633975i 0.0593772 + 0.102844i
\(39\) 0 0
\(40\) 0.133975 0.232051i 0.0211832 0.0366905i
\(41\) −1.26795 + 2.19615i −0.198020 + 0.342981i −0.947886 0.318608i \(-0.896785\pi\)
0.749866 + 0.661590i \(0.230118\pi\)
\(42\) 0 0
\(43\) 0.732051 + 1.26795i 0.111637 + 0.193360i 0.916430 0.400194i \(-0.131057\pi\)
−0.804794 + 0.593555i \(0.797724\pi\)
\(44\) 6.19615 0.934105
\(45\) 0 0
\(46\) 4.19615 0.618689
\(47\) −2.36603 4.09808i −0.345120 0.597766i 0.640255 0.768162i \(-0.278829\pi\)
−0.985376 + 0.170396i \(0.945495\pi\)
\(48\) 0 0
\(49\) −0.500000 + 0.866025i −0.0714286 + 0.123718i
\(50\) −2.46410 + 4.26795i −0.348477 + 0.603579i
\(51\) 0 0
\(52\) 3.23205 + 5.59808i 0.448205 + 0.776313i
\(53\) −9.46410 −1.29999 −0.649997 0.759937i \(-0.725230\pi\)
−0.649997 + 0.759937i \(0.725230\pi\)
\(54\) 0 0
\(55\) 1.66025 0.223869
\(56\) −0.500000 0.866025i −0.0668153 0.115728i
\(57\) 0 0
\(58\) 0.767949 1.33013i 0.100837 0.174654i
\(59\) −2.09808 + 3.63397i −0.273146 + 0.473103i −0.969666 0.244435i \(-0.921398\pi\)
0.696520 + 0.717538i \(0.254731\pi\)
\(60\) 0 0
\(61\) −1.96410 3.40192i −0.251477 0.435572i 0.712455 0.701717i \(-0.247583\pi\)
−0.963933 + 0.266146i \(0.914250\pi\)
\(62\) −8.19615 −1.04091
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 0.866025 + 1.50000i 0.107417 + 0.186052i
\(66\) 0 0
\(67\) 3.36603 5.83013i 0.411225 0.712263i −0.583799 0.811899i \(-0.698434\pi\)
0.995024 + 0.0996351i \(0.0317676\pi\)
\(68\) −3.50000 + 6.06218i −0.424437 + 0.735147i
\(69\) 0 0
\(70\) −0.133975 0.232051i −0.0160130 0.0277354i
\(71\) 6.53590 0.775668 0.387834 0.921729i \(-0.373223\pi\)
0.387834 + 0.921729i \(0.373223\pi\)
\(72\) 0 0
\(73\) 8.26795 0.967690 0.483845 0.875154i \(-0.339240\pi\)
0.483845 + 0.875154i \(0.339240\pi\)
\(74\) 5.33013 + 9.23205i 0.619615 + 1.07320i
\(75\) 0 0
\(76\) −0.366025 + 0.633975i −0.0419860 + 0.0727219i
\(77\) 3.09808 5.36603i 0.353059 0.611515i
\(78\) 0 0
\(79\) 4.56218 + 7.90192i 0.513285 + 0.889036i 0.999881 + 0.0154089i \(0.00490499\pi\)
−0.486596 + 0.873627i \(0.661762\pi\)
\(80\) 0.267949 0.0299576
\(81\) 0 0
\(82\) −2.53590 −0.280043
\(83\) −8.29423 14.3660i −0.910410 1.57688i −0.813486 0.581584i \(-0.802433\pi\)
−0.0969238 0.995292i \(-0.530900\pi\)
\(84\) 0 0
\(85\) −0.937822 + 1.62436i −0.101721 + 0.176186i
\(86\) −0.732051 + 1.26795i −0.0789391 + 0.136726i
\(87\) 0 0
\(88\) 3.09808 + 5.36603i 0.330256 + 0.572020i
\(89\) 9.92820 1.05239 0.526194 0.850365i \(-0.323619\pi\)
0.526194 + 0.850365i \(0.323619\pi\)
\(90\) 0 0
\(91\) 6.46410 0.677622
\(92\) 2.09808 + 3.63397i 0.218740 + 0.378868i
\(93\) 0 0
\(94\) 2.36603 4.09808i 0.244037 0.422684i
\(95\) −0.0980762 + 0.169873i −0.0100624 + 0.0174286i
\(96\) 0 0
\(97\) −5.46410 9.46410i −0.554795 0.960934i −0.997919 0.0644736i \(-0.979463\pi\)
0.443124 0.896460i \(-0.353870\pi\)
\(98\) −1.00000 −0.101015
\(99\) 0 0
\(100\) −4.92820 −0.492820
\(101\) −4.46410 7.73205i −0.444195 0.769368i 0.553801 0.832649i \(-0.313177\pi\)
−0.997996 + 0.0632812i \(0.979843\pi\)
\(102\) 0 0
\(103\) 4.19615 7.26795i 0.413459 0.716132i −0.581806 0.813327i \(-0.697654\pi\)
0.995265 + 0.0971952i \(0.0309871\pi\)
\(104\) −3.23205 + 5.59808i −0.316929 + 0.548937i
\(105\) 0 0
\(106\) −4.73205 8.19615i −0.459617 0.796081i
\(107\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(108\) 0 0
\(109\) 3.19615 0.306136 0.153068 0.988216i \(-0.451085\pi\)
0.153068 + 0.988216i \(0.451085\pi\)
\(110\) 0.830127 + 1.43782i 0.0791495 + 0.137091i
\(111\) 0 0
\(112\) 0.500000 0.866025i 0.0472456 0.0818317i
\(113\) 2.86603 4.96410i 0.269613 0.466983i −0.699149 0.714976i \(-0.746438\pi\)
0.968762 + 0.247993i \(0.0797709\pi\)
\(114\) 0 0
\(115\) 0.562178 + 0.973721i 0.0524234 + 0.0907999i
\(116\) 1.53590 0.142605
\(117\) 0 0
\(118\) −4.19615 −0.386287
\(119\) 3.50000 + 6.06218i 0.320844 + 0.555719i
\(120\) 0 0
\(121\) −13.6962 + 23.7224i −1.24510 + 2.15658i
\(122\) 1.96410 3.40192i 0.177821 0.307996i
\(123\) 0 0
\(124\) −4.09808 7.09808i −0.368018 0.637426i
\(125\) −2.66025 −0.237940
\(126\) 0 0
\(127\) 12.0000 1.06483 0.532414 0.846484i \(-0.321285\pi\)
0.532414 + 0.846484i \(0.321285\pi\)
\(128\) 0.500000 + 0.866025i 0.0441942 + 0.0765466i
\(129\) 0 0
\(130\) −0.866025 + 1.50000i −0.0759555 + 0.131559i
\(131\) −5.26795 + 9.12436i −0.460263 + 0.797199i −0.998974 0.0452920i \(-0.985578\pi\)
0.538711 + 0.842491i \(0.318912\pi\)
\(132\) 0 0
\(133\) 0.366025 + 0.633975i 0.0317384 + 0.0549726i
\(134\) 6.73205 0.581561
\(135\) 0 0
\(136\) −7.00000 −0.600245
\(137\) 4.13397 + 7.16025i 0.353189 + 0.611742i 0.986806 0.161905i \(-0.0517638\pi\)
−0.633617 + 0.773647i \(0.718430\pi\)
\(138\) 0 0
\(139\) 1.63397 2.83013i 0.138592 0.240048i −0.788372 0.615199i \(-0.789076\pi\)
0.926964 + 0.375151i \(0.122409\pi\)
\(140\) 0.133975 0.232051i 0.0113229 0.0196119i
\(141\) 0 0
\(142\) 3.26795 + 5.66025i 0.274240 + 0.474998i
\(143\) −40.0526 −3.34936
\(144\) 0 0
\(145\) 0.411543 0.0341768
\(146\) 4.13397 + 7.16025i 0.342130 + 0.592587i
\(147\) 0 0
\(148\) −5.33013 + 9.23205i −0.438134 + 0.758870i
\(149\) −4.50000 + 7.79423i −0.368654 + 0.638528i −0.989355 0.145519i \(-0.953515\pi\)
0.620701 + 0.784047i \(0.286848\pi\)
\(150\) 0 0
\(151\) 2.90192 + 5.02628i 0.236155 + 0.409033i 0.959608 0.281341i \(-0.0907793\pi\)
−0.723453 + 0.690374i \(0.757446\pi\)
\(152\) −0.732051 −0.0593772
\(153\) 0 0
\(154\) 6.19615 0.499300
\(155\) −1.09808 1.90192i −0.0881996 0.152766i
\(156\) 0 0
\(157\) 0.500000 0.866025i 0.0399043 0.0691164i −0.845383 0.534160i \(-0.820628\pi\)
0.885288 + 0.465044i \(0.153961\pi\)
\(158\) −4.56218 + 7.90192i −0.362947 + 0.628643i
\(159\) 0 0
\(160\) 0.133975 + 0.232051i 0.0105916 + 0.0183452i
\(161\) 4.19615 0.330703
\(162\) 0 0
\(163\) −13.4641 −1.05459 −0.527295 0.849682i \(-0.676794\pi\)
−0.527295 + 0.849682i \(0.676794\pi\)
\(164\) −1.26795 2.19615i −0.0990102 0.171491i
\(165\) 0 0
\(166\) 8.29423 14.3660i 0.643757 1.11502i
\(167\) 0.901924 1.56218i 0.0697930 0.120885i −0.829017 0.559223i \(-0.811099\pi\)
0.898810 + 0.438338i \(0.144433\pi\)
\(168\) 0 0
\(169\) −14.3923 24.9282i −1.10710 1.91755i
\(170\) −1.87564 −0.143855
\(171\) 0 0
\(172\) −1.46410 −0.111637
\(173\) −3.13397 5.42820i −0.238272 0.412699i 0.721947 0.691949i \(-0.243248\pi\)
−0.960218 + 0.279250i \(0.909914\pi\)
\(174\) 0 0
\(175\) −2.46410 + 4.26795i −0.186269 + 0.322627i
\(176\) −3.09808 + 5.36603i −0.233526 + 0.404479i
\(177\) 0 0
\(178\) 4.96410 + 8.59808i 0.372075 + 0.644453i
\(179\) −2.19615 −0.164148 −0.0820741 0.996626i \(-0.526154\pi\)
−0.0820741 + 0.996626i \(0.526154\pi\)
\(180\) 0 0
\(181\) −16.3923 −1.21843 −0.609215 0.793005i \(-0.708515\pi\)
−0.609215 + 0.793005i \(0.708515\pi\)
\(182\) 3.23205 + 5.59808i 0.239576 + 0.414957i
\(183\) 0 0
\(184\) −2.09808 + 3.63397i −0.154672 + 0.267900i
\(185\) −1.42820 + 2.47372i −0.105004 + 0.181872i
\(186\) 0 0
\(187\) −21.6865 37.5622i −1.58588 2.74682i
\(188\) 4.73205 0.345120
\(189\) 0 0
\(190\) −0.196152 −0.0142304
\(191\) 2.83013 + 4.90192i 0.204781 + 0.354691i 0.950063 0.312059i \(-0.101019\pi\)
−0.745282 + 0.666749i \(0.767685\pi\)
\(192\) 0 0
\(193\) −9.42820 + 16.3301i −0.678657 + 1.17547i 0.296729 + 0.954962i \(0.404104\pi\)
−0.975386 + 0.220506i \(0.929229\pi\)
\(194\) 5.46410 9.46410i 0.392300 0.679483i
\(195\) 0 0
\(196\) −0.500000 0.866025i −0.0357143 0.0618590i
\(197\) 15.7846 1.12461 0.562303 0.826931i \(-0.309915\pi\)
0.562303 + 0.826931i \(0.309915\pi\)
\(198\) 0 0
\(199\) −19.1244 −1.35569 −0.677845 0.735205i \(-0.737086\pi\)
−0.677845 + 0.735205i \(0.737086\pi\)
\(200\) −2.46410 4.26795i −0.174238 0.301790i
\(201\) 0 0
\(202\) 4.46410 7.73205i 0.314093 0.544025i
\(203\) 0.767949 1.33013i 0.0538995 0.0933566i
\(204\) 0 0
\(205\) −0.339746 0.588457i −0.0237289 0.0410996i
\(206\) 8.39230 0.584720
\(207\) 0 0
\(208\) −6.46410 −0.448205
\(209\) −2.26795 3.92820i −0.156877 0.271719i
\(210\) 0 0
\(211\) 8.63397 14.9545i 0.594387 1.02951i −0.399246 0.916844i \(-0.630728\pi\)
0.993633 0.112665i \(-0.0359387\pi\)
\(212\) 4.73205 8.19615i 0.324999 0.562914i
\(213\) 0 0
\(214\) 0 0
\(215\) −0.392305 −0.0267550
\(216\) 0 0
\(217\) −8.19615 −0.556391
\(218\) 1.59808 + 2.76795i 0.108235 + 0.187469i
\(219\) 0 0
\(220\) −0.830127 + 1.43782i −0.0559672 + 0.0969380i
\(221\) 22.6244 39.1865i 1.52188 2.63597i
\(222\) 0 0
\(223\) 12.7321 + 22.0526i 0.852601 + 1.47675i 0.878853 + 0.477093i \(0.158310\pi\)
−0.0262515 + 0.999655i \(0.508357\pi\)
\(224\) 1.00000 0.0668153
\(225\) 0 0
\(226\) 5.73205 0.381290
\(227\) 9.46410 + 16.3923i 0.628154 + 1.08800i 0.987922 + 0.154953i \(0.0495227\pi\)
−0.359767 + 0.933042i \(0.617144\pi\)
\(228\) 0 0
\(229\) 1.23205 2.13397i 0.0814162 0.141017i −0.822442 0.568849i \(-0.807389\pi\)
0.903858 + 0.427832i \(0.140722\pi\)
\(230\) −0.562178 + 0.973721i −0.0370689 + 0.0642052i
\(231\) 0 0
\(232\) 0.767949 + 1.33013i 0.0504183 + 0.0873271i
\(233\) −2.80385 −0.183686 −0.0918431 0.995773i \(-0.529276\pi\)
−0.0918431 + 0.995773i \(0.529276\pi\)
\(234\) 0 0
\(235\) 1.26795 0.0827119
\(236\) −2.09808 3.63397i −0.136573 0.236552i
\(237\) 0 0
\(238\) −3.50000 + 6.06218i −0.226871 + 0.392953i
\(239\) 5.02628 8.70577i 0.325123 0.563130i −0.656414 0.754401i \(-0.727928\pi\)
0.981537 + 0.191271i \(0.0612610\pi\)
\(240\) 0 0
\(241\) 7.13397 + 12.3564i 0.459540 + 0.795946i 0.998937 0.0461056i \(-0.0146811\pi\)
−0.539397 + 0.842052i \(0.681348\pi\)
\(242\) −27.3923 −1.76084
\(243\) 0 0
\(244\) 3.92820 0.251477
\(245\) −0.133975 0.232051i −0.00855932 0.0148252i
\(246\) 0 0
\(247\) 2.36603 4.09808i 0.150547 0.260754i
\(248\) 4.09808 7.09808i 0.260228 0.450728i
\(249\) 0 0
\(250\) −1.33013 2.30385i −0.0841246 0.145708i
\(251\) −22.0526 −1.39195 −0.695973 0.718068i \(-0.745027\pi\)
−0.695973 + 0.718068i \(0.745027\pi\)
\(252\) 0 0
\(253\) −26.0000 −1.63461
\(254\) 6.00000 + 10.3923i 0.376473 + 0.652071i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −3.23205 + 5.59808i −0.201610 + 0.349198i −0.949047 0.315134i \(-0.897951\pi\)
0.747437 + 0.664332i \(0.231284\pi\)
\(258\) 0 0
\(259\) 5.33013 + 9.23205i 0.331198 + 0.573652i
\(260\) −1.73205 −0.107417
\(261\) 0 0
\(262\) −10.5359 −0.650910
\(263\) 3.16987 + 5.49038i 0.195463 + 0.338551i 0.947052 0.321080i \(-0.104046\pi\)
−0.751589 + 0.659631i \(0.770712\pi\)
\(264\) 0 0
\(265\) 1.26795 2.19615i 0.0778895 0.134909i
\(266\) −0.366025 + 0.633975i −0.0224425 + 0.0388715i
\(267\) 0 0
\(268\) 3.36603 + 5.83013i 0.205613 + 0.356132i
\(269\) 5.58846 0.340734 0.170367 0.985381i \(-0.445505\pi\)
0.170367 + 0.985381i \(0.445505\pi\)
\(270\) 0 0
\(271\) −19.5167 −1.18555 −0.592776 0.805367i \(-0.701968\pi\)
−0.592776 + 0.805367i \(0.701968\pi\)
\(272\) −3.50000 6.06218i −0.212219 0.367574i
\(273\) 0 0
\(274\) −4.13397 + 7.16025i −0.249743 + 0.432567i
\(275\) 15.2679 26.4449i 0.920692 1.59469i
\(276\) 0 0
\(277\) 9.39230 + 16.2679i 0.564329 + 0.977446i 0.997112 + 0.0759481i \(0.0241983\pi\)
−0.432783 + 0.901498i \(0.642468\pi\)
\(278\) 3.26795 0.195999
\(279\) 0 0
\(280\) 0.267949 0.0160130
\(281\) 6.59808 + 11.4282i 0.393608 + 0.681749i 0.992922 0.118764i \(-0.0378933\pi\)
−0.599314 + 0.800514i \(0.704560\pi\)
\(282\) 0 0
\(283\) −7.66025 + 13.2679i −0.455355 + 0.788698i −0.998709 0.0508062i \(-0.983821\pi\)
0.543354 + 0.839504i \(0.317154\pi\)
\(284\) −3.26795 + 5.66025i −0.193917 + 0.335874i
\(285\) 0 0
\(286\) −20.0263 34.6865i −1.18418 2.05106i
\(287\) −2.53590 −0.149689
\(288\) 0 0
\(289\) 32.0000 1.88235
\(290\) 0.205771 + 0.356406i 0.0120833 + 0.0209289i
\(291\) 0 0
\(292\) −4.13397 + 7.16025i −0.241923 + 0.419022i
\(293\) −1.66987 + 2.89230i −0.0975550 + 0.168970i −0.910672 0.413130i \(-0.864436\pi\)
0.813117 + 0.582100i \(0.197769\pi\)
\(294\) 0 0
\(295\) −0.562178 0.973721i −0.0327313 0.0566922i
\(296\) −10.6603 −0.619615
\(297\) 0 0
\(298\) −9.00000 −0.521356
\(299\) −13.5622 23.4904i −0.784321 1.35848i
\(300\) 0 0
\(301\) −0.732051 + 1.26795i −0.0421947 + 0.0730834i
\(302\) −2.90192 + 5.02628i −0.166987 + 0.289230i
\(303\) 0 0
\(304\) −0.366025 0.633975i −0.0209930 0.0363609i
\(305\) 1.05256 0.0602693
\(306\) 0 0
\(307\) −21.8564 −1.24741 −0.623706 0.781659i \(-0.714374\pi\)
−0.623706 + 0.781659i \(0.714374\pi\)
\(308\) 3.09808 + 5.36603i 0.176529 + 0.305758i
\(309\) 0 0
\(310\) 1.09808 1.90192i 0.0623665 0.108022i
\(311\) −5.09808 + 8.83013i −0.289085 + 0.500711i −0.973592 0.228296i \(-0.926684\pi\)
0.684506 + 0.729007i \(0.260018\pi\)
\(312\) 0 0
\(313\) −12.7942 22.1603i −0.723173 1.25257i −0.959722 0.280952i \(-0.909350\pi\)
0.236549 0.971620i \(-0.423984\pi\)
\(314\) 1.00000 0.0564333
\(315\) 0 0
\(316\) −9.12436 −0.513285
\(317\) 15.6962 + 27.1865i 0.881584 + 1.52695i 0.849580 + 0.527460i \(0.176856\pi\)
0.0320039 + 0.999488i \(0.489811\pi\)
\(318\) 0 0
\(319\) −4.75833 + 8.24167i −0.266415 + 0.461445i
\(320\) −0.133975 + 0.232051i −0.00748941 + 0.0129720i
\(321\) 0 0
\(322\) 2.09808 + 3.63397i 0.116921 + 0.202513i
\(323\) 5.12436 0.285127
\(324\) 0 0
\(325\) 31.8564 1.76708
\(326\) −6.73205 11.6603i −0.372854 0.645802i
\(327\) 0 0
\(328\) 1.26795 2.19615i 0.0700108 0.121262i
\(329\) 2.36603 4.09808i 0.130443 0.225934i
\(330\) 0 0
\(331\) −6.19615 10.7321i −0.340571 0.589887i 0.643968 0.765053i \(-0.277287\pi\)
−0.984539 + 0.175166i \(0.943954\pi\)
\(332\) 16.5885 0.910410
\(333\) 0 0
\(334\) 1.80385 0.0987021
\(335\) 0.901924 + 1.56218i 0.0492774 + 0.0853509i
\(336\) 0 0
\(337\) 8.19615 14.1962i 0.446473 0.773314i −0.551681 0.834055i \(-0.686013\pi\)
0.998154 + 0.0607417i \(0.0193466\pi\)
\(338\) 14.3923 24.9282i 0.782838 1.35592i
\(339\) 0 0
\(340\) −0.937822 1.62436i −0.0508605 0.0880931i
\(341\) 50.7846 2.75014
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) −0.732051 1.26795i −0.0394695 0.0683632i
\(345\) 0 0
\(346\) 3.13397 5.42820i 0.168484 0.291822i
\(347\) −10.7321 + 18.5885i −0.576127 + 0.997881i 0.419792 + 0.907621i \(0.362103\pi\)
−0.995918 + 0.0902601i \(0.971230\pi\)
\(348\) 0 0
\(349\) −0.732051 1.26795i −0.0391858 0.0678718i 0.845767 0.533552i \(-0.179143\pi\)
−0.884953 + 0.465680i \(0.845810\pi\)
\(350\) −4.92820 −0.263424
\(351\) 0 0
\(352\) −6.19615 −0.330256
\(353\) 9.00000 + 15.5885i 0.479022 + 0.829690i 0.999711 0.0240566i \(-0.00765819\pi\)
−0.520689 + 0.853746i \(0.674325\pi\)
\(354\) 0 0
\(355\) −0.875644 + 1.51666i −0.0464744 + 0.0804960i
\(356\) −4.96410 + 8.59808i −0.263097 + 0.455697i
\(357\) 0 0
\(358\) −1.09808 1.90192i −0.0580351 0.100520i
\(359\) −10.9282 −0.576769 −0.288384 0.957515i \(-0.593118\pi\)
−0.288384 + 0.957515i \(0.593118\pi\)
\(360\) 0 0
\(361\) −18.4641 −0.971795
\(362\) −8.19615 14.1962i −0.430780 0.746133i
\(363\) 0 0
\(364\) −3.23205 + 5.59808i −0.169405 + 0.293419i
\(365\) −1.10770 + 1.91858i −0.0579794 + 0.100423i
\(366\) 0 0
\(367\) −5.56218 9.63397i −0.290343 0.502889i 0.683548 0.729906i \(-0.260436\pi\)
−0.973891 + 0.227017i \(0.927103\pi\)
\(368\) −4.19615 −0.218740
\(369\) 0 0
\(370\) −2.85641 −0.148498
\(371\) −4.73205 8.19615i −0.245676 0.425523i
\(372\) 0 0
\(373\) 3.07180 5.32051i 0.159052 0.275485i −0.775475 0.631378i \(-0.782490\pi\)
0.934527 + 0.355892i \(0.115823\pi\)
\(374\) 21.6865 37.5622i 1.12138 1.94229i
\(375\) 0 0
\(376\) 2.36603 + 4.09808i 0.122018 + 0.211342i
\(377\) −9.92820 −0.511328
\(378\) 0 0
\(379\) −27.5167 −1.41344 −0.706718 0.707495i \(-0.749825\pi\)
−0.706718 + 0.707495i \(0.749825\pi\)
\(380\) −0.0980762 0.169873i −0.00503120 0.00871430i
\(381\) 0 0
\(382\) −2.83013 + 4.90192i −0.144802 + 0.250804i
\(383\) −9.85641 + 17.0718i −0.503639 + 0.872328i 0.496352 + 0.868121i \(0.334672\pi\)
−0.999991 + 0.00420688i \(0.998661\pi\)
\(384\) 0 0
\(385\) 0.830127 + 1.43782i 0.0423072 + 0.0732782i
\(386\) −18.8564 −0.959766
\(387\) 0 0
\(388\) 10.9282 0.554795
\(389\) 6.73205 + 11.6603i 0.341329 + 0.591198i 0.984680 0.174373i \(-0.0557898\pi\)
−0.643351 + 0.765571i \(0.722456\pi\)
\(390\) 0 0
\(391\) 14.6865 25.4378i 0.742730 1.28645i
\(392\) 0.500000 0.866025i 0.0252538 0.0437409i
\(393\) 0 0
\(394\) 7.89230 + 13.6699i 0.397609 + 0.688678i
\(395\) −2.44486 −0.123014
\(396\) 0 0
\(397\) −21.0000 −1.05396 −0.526980 0.849878i \(-0.676676\pi\)
−0.526980 + 0.849878i \(0.676676\pi\)
\(398\) −9.56218 16.5622i −0.479309 0.830187i
\(399\) 0 0
\(400\) 2.46410 4.26795i 0.123205 0.213397i
\(401\) −5.25833 + 9.10770i −0.262588 + 0.454817i −0.966929 0.255046i \(-0.917909\pi\)
0.704341 + 0.709862i \(0.251243\pi\)
\(402\) 0 0
\(403\) 26.4904 + 45.8827i 1.31958 + 2.28558i
\(404\) 8.92820 0.444195
\(405\) 0 0
\(406\) 1.53590 0.0762254
\(407\) −33.0263 57.2032i −1.63705 2.83546i
\(408\) 0 0
\(409\) −8.66987 + 15.0167i −0.428698 + 0.742526i −0.996758 0.0804610i \(-0.974361\pi\)
0.568060 + 0.822987i \(0.307694\pi\)
\(410\) 0.339746 0.588457i 0.0167789 0.0290618i
\(411\) 0 0
\(412\) 4.19615 + 7.26795i 0.206730 + 0.358066i
\(413\) −4.19615 −0.206479
\(414\) 0 0
\(415\) 4.44486 0.218190
\(416\) −3.23205 5.59808i −0.158464 0.274468i
\(417\) 0 0
\(418\) 2.26795 3.92820i 0.110929 0.192135i
\(419\) 4.73205 8.19615i 0.231176 0.400408i −0.726979 0.686660i \(-0.759076\pi\)
0.958154 + 0.286252i \(0.0924094\pi\)
\(420\) 0 0
\(421\) −0.0621778 0.107695i −0.00303036 0.00524874i 0.864506 0.502622i \(-0.167631\pi\)
−0.867537 + 0.497373i \(0.834298\pi\)
\(422\) 17.2679 0.840591
\(423\) 0 0
\(424\) 9.46410 0.459617
\(425\) 17.2487 + 29.8756i 0.836685 + 1.44918i
\(426\) 0 0
\(427\) 1.96410 3.40192i 0.0950495 0.164631i
\(428\) 0 0
\(429\) 0 0
\(430\) −0.196152 0.339746i −0.00945931 0.0163840i
\(431\) −14.5359 −0.700170 −0.350085 0.936718i \(-0.613847\pi\)
−0.350085 + 0.936718i \(0.613847\pi\)
\(432\) 0 0
\(433\) 15.7321 0.756034 0.378017 0.925799i \(-0.376606\pi\)
0.378017 + 0.925799i \(0.376606\pi\)
\(434\) −4.09808 7.09808i −0.196714 0.340719i
\(435\) 0 0
\(436\) −1.59808 + 2.76795i −0.0765340 + 0.132561i
\(437\) 1.53590 2.66025i 0.0734720 0.127257i
\(438\) 0 0
\(439\) −11.6603 20.1962i −0.556514 0.963910i −0.997784 0.0665356i \(-0.978805\pi\)
0.441270 0.897374i \(-0.354528\pi\)
\(440\) −1.66025 −0.0791495
\(441\) 0 0
\(442\) 45.2487 2.15226
\(443\) 7.63397 + 13.2224i 0.362701 + 0.628217i 0.988404 0.151844i \(-0.0485213\pi\)
−0.625703 + 0.780061i \(0.715188\pi\)
\(444\) 0 0
\(445\) −1.33013 + 2.30385i −0.0630541 + 0.109213i
\(446\) −12.7321 + 22.0526i −0.602880 + 1.04422i
\(447\) 0 0
\(448\) 0.500000 + 0.866025i 0.0236228 + 0.0409159i
\(449\) 15.8564 0.748310 0.374155 0.927366i \(-0.377933\pi\)
0.374155 + 0.927366i \(0.377933\pi\)
\(450\) 0 0
\(451\) 15.7128 0.739887
\(452\) 2.86603 + 4.96410i 0.134806 + 0.233492i
\(453\) 0 0
\(454\) −9.46410 + 16.3923i −0.444172 + 0.769329i
\(455\) −0.866025 + 1.50000i −0.0405999 + 0.0703211i
\(456\) 0 0
\(457\) 3.42820 + 5.93782i 0.160365 + 0.277760i 0.934999 0.354649i \(-0.115400\pi\)
−0.774635 + 0.632409i \(0.782066\pi\)
\(458\) 2.46410 0.115140
\(459\) 0 0
\(460\) −1.12436 −0.0524234
\(461\) 3.39230 + 5.87564i 0.157995 + 0.273656i 0.934146 0.356892i \(-0.116164\pi\)
−0.776150 + 0.630548i \(0.782830\pi\)
\(462\) 0 0
\(463\) 0.705771 1.22243i 0.0328000 0.0568112i −0.849159 0.528137i \(-0.822891\pi\)
0.881959 + 0.471325i \(0.156224\pi\)
\(464\) −0.767949 + 1.33013i −0.0356511 + 0.0617496i
\(465\) 0 0
\(466\) −1.40192 2.42820i −0.0649429 0.112484i
\(467\) −16.5885 −0.767622 −0.383811 0.923412i \(-0.625389\pi\)
−0.383811 + 0.923412i \(0.625389\pi\)
\(468\) 0 0
\(469\) 6.73205 0.310857
\(470\) 0.633975 + 1.09808i 0.0292431 + 0.0506505i
\(471\) 0 0
\(472\) 2.09808 3.63397i 0.0965718 0.167267i
\(473\) 4.53590 7.85641i 0.208561 0.361238i
\(474\) 0 0
\(475\) 1.80385 + 3.12436i 0.0827662 + 0.143355i
\(476\) −7.00000 −0.320844
\(477\) 0 0
\(478\) 10.0526 0.459793
\(479\) 10.7583 + 18.6340i 0.491561 + 0.851408i 0.999953 0.00971765i \(-0.00309327\pi\)
−0.508392 + 0.861126i \(0.669760\pi\)
\(480\) 0 0
\(481\) 34.4545 59.6769i 1.57099 2.72103i
\(482\) −7.13397 + 12.3564i −0.324944 + 0.562819i
\(483\) 0 0
\(484\) −13.6962 23.7224i −0.622552 1.07829i
\(485\) 2.92820 0.132963
\(486\) 0 0
\(487\) 2.58846 0.117294 0.0586471 0.998279i \(-0.481321\pi\)
0.0586471 + 0.998279i \(0.481321\pi\)
\(488\) 1.96410 + 3.40192i 0.0889107 + 0.153998i
\(489\) 0 0
\(490\) 0.133975 0.232051i 0.00605236 0.0104830i
\(491\) −13.2679 + 22.9808i −0.598774 + 1.03711i 0.394228 + 0.919013i \(0.371012\pi\)
−0.993002 + 0.118095i \(0.962321\pi\)
\(492\) 0 0
\(493\) −5.37564 9.31089i −0.242107 0.419341i
\(494\) 4.73205 0.212905
\(495\) 0 0
\(496\) 8.19615 0.368018
\(497\) 3.26795 + 5.66025i 0.146588 + 0.253897i
\(498\) 0 0
\(499\) −9.90192 + 17.1506i −0.443271 + 0.767768i −0.997930 0.0643099i \(-0.979515\pi\)
0.554659 + 0.832078i \(0.312849\pi\)
\(500\) 1.33013 2.30385i 0.0594851 0.103031i
\(501\) 0 0
\(502\) −11.0263 19.0981i −0.492127 0.852389i
\(503\) 40.0526 1.78586 0.892928 0.450200i \(-0.148647\pi\)
0.892928 + 0.450200i \(0.148647\pi\)
\(504\) 0 0
\(505\) 2.39230 0.106456
\(506\) −13.0000 22.5167i −0.577920 1.00099i
\(507\) 0 0
\(508\) −6.00000 + 10.3923i −0.266207 + 0.461084i
\(509\) −15.9282 + 27.5885i −0.706005 + 1.22284i 0.260322 + 0.965522i \(0.416171\pi\)
−0.966328 + 0.257315i \(0.917162\pi\)
\(510\) 0 0
\(511\) 4.13397 + 7.16025i 0.182876 + 0.316751i
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) −6.46410 −0.285119
\(515\) 1.12436 + 1.94744i 0.0495450 + 0.0858145i
\(516\) 0 0
\(517\) −14.6603 + 25.3923i −0.644757 + 1.11675i
\(518\) −5.33013 + 9.23205i −0.234192 + 0.405633i
\(519\) 0 0
\(520\) −0.866025 1.50000i −0.0379777 0.0657794i
\(521\) −30.0000 −1.31432 −0.657162 0.753749i \(-0.728243\pi\)
−0.657162 + 0.753749i \(0.728243\pi\)
\(522\) 0 0
\(523\) 33.1769 1.45073 0.725363 0.688367i \(-0.241672\pi\)
0.725363 + 0.688367i \(0.241672\pi\)
\(524\) −5.26795 9.12436i −0.230131 0.398599i
\(525\) 0 0
\(526\) −3.16987 + 5.49038i −0.138213 + 0.239392i
\(527\) −28.6865 + 49.6865i −1.24961 + 2.16438i
\(528\) 0 0
\(529\) 2.69615 + 4.66987i 0.117224 + 0.203038i
\(530\) 2.53590 0.110152
\(531\) 0 0
\(532\) −0.732051 −0.0317384
\(533\) 8.19615 + 14.1962i 0.355015 + 0.614904i
\(534\) 0 0
\(535\) 0 0
\(536\) −3.36603 + 5.83013i −0.145390 + 0.251823i
\(537\) 0 0
\(538\) 2.79423 + 4.83975i 0.120468 + 0.208656i
\(539\) 6.19615 0.266887
\(540\) 0 0
\(541\) 3.33975 0.143587 0.0717934 0.997420i \(-0.477128\pi\)
0.0717934 + 0.997420i \(0.477128\pi\)
\(542\) −9.75833 16.9019i −0.419156 0.726000i
\(543\) 0 0
\(544\) 3.50000 6.06218i 0.150061 0.259914i
\(545\) −0.428203 + 0.741670i −0.0183422 + 0.0317696i
\(546\) 0 0
\(547\) 11.3660 + 19.6865i 0.485976 + 0.841735i 0.999870 0.0161183i \(-0.00513085\pi\)
−0.513894 + 0.857854i \(0.671798\pi\)
\(548\) −8.26795 −0.353189
\(549\) 0 0
\(550\) 30.5359 1.30206
\(551\) −0.562178 0.973721i −0.0239496 0.0414819i
\(552\) 0 0
\(553\) −4.56218 + 7.90192i −0.194004 + 0.336024i
\(554\) −9.39230 + 16.2679i −0.399041 + 0.691159i
\(555\) 0 0
\(556\) 1.63397 + 2.83013i 0.0692960 + 0.120024i
\(557\) 23.9282 1.01387 0.506935 0.861984i \(-0.330778\pi\)
0.506935 + 0.861984i \(0.330778\pi\)
\(558\) 0 0
\(559\) 9.46410 0.400289
\(560\) 0.133975 + 0.232051i 0.00566146 + 0.00980594i
\(561\) 0 0
\(562\) −6.59808 + 11.4282i −0.278323 + 0.482070i
\(563\) −9.85641 + 17.0718i −0.415398 + 0.719490i −0.995470 0.0950747i \(-0.969691\pi\)
0.580072 + 0.814565i \(0.303024\pi\)
\(564\) 0 0
\(565\) 0.767949 + 1.33013i 0.0323079 + 0.0559589i
\(566\) −15.3205 −0.643969
\(567\) 0 0
\(568\) −6.53590 −0.274240
\(569\) −11.5981 20.0885i −0.486217 0.842152i 0.513658 0.857995i \(-0.328290\pi\)
−0.999874 + 0.0158432i \(0.994957\pi\)
\(570\) 0 0
\(571\) 11.3660 19.6865i 0.475653 0.823856i −0.523958 0.851744i \(-0.675545\pi\)
0.999611 + 0.0278885i \(0.00887834\pi\)
\(572\) 20.0263 34.6865i 0.837341 1.45032i
\(573\) 0 0
\(574\) −1.26795 2.19615i −0.0529232 0.0916656i
\(575\) 20.6795 0.862394
\(576\) 0 0
\(577\) 24.6603 1.02662 0.513310 0.858203i \(-0.328419\pi\)
0.513310 + 0.858203i \(0.328419\pi\)
\(578\) 16.0000 + 27.7128i 0.665512 + 1.15270i
\(579\) 0 0
\(580\) −0.205771 + 0.356406i −0.00854419 + 0.0147990i
\(581\) 8.29423 14.3660i 0.344103 0.596003i
\(582\) 0 0
\(583\) 29.3205 + 50.7846i 1.21433 + 2.10328i
\(584\) −8.26795 −0.342130
\(585\) 0 0
\(586\) −3.33975 −0.137964
\(587\) −7.36603 12.7583i −0.304028 0.526593i 0.673016 0.739628i \(-0.264998\pi\)
−0.977045 + 0.213035i \(0.931665\pi\)
\(588\) 0 0
\(589\) −3.00000 + 5.19615i −0.123613 + 0.214104i
\(590\) 0.562178 0.973721i 0.0231445 0.0400874i
\(591\) 0 0
\(592\) −5.33013 9.23205i −0.219067 0.379435i
\(593\) −22.1769 −0.910697 −0.455348 0.890313i \(-0.650485\pi\)
−0.455348 + 0.890313i \(0.650485\pi\)
\(594\) 0 0
\(595\) −1.87564 −0.0768939
\(596\) −4.50000 7.79423i −0.184327 0.319264i
\(597\) 0 0
\(598\) 13.5622 23.4904i 0.554599 0.960593i
\(599\) 7.56218 13.0981i 0.308982 0.535173i −0.669158 0.743120i \(-0.733345\pi\)
0.978140 + 0.207947i \(0.0666783\pi\)
\(600\) 0 0
\(601\) −9.59808 16.6244i −0.391514 0.678122i 0.601136 0.799147i \(-0.294715\pi\)
−0.992649 + 0.121025i \(0.961382\pi\)
\(602\) −1.46410 −0.0596723
\(603\) 0 0
\(604\) −5.80385 −0.236155
\(605\) −3.66987 6.35641i −0.149202 0.258425i
\(606\) 0 0
\(607\) 12.2942 21.2942i 0.499007 0.864306i −0.500992 0.865452i \(-0.667031\pi\)
0.999999 + 0.00114584i \(0.000364732\pi\)
\(608\) 0.366025 0.633975i 0.0148443 0.0257111i
\(609\) 0 0
\(610\) 0.526279 + 0.911543i 0.0213084 + 0.0369073i
\(611\) −30.5885 −1.23748
\(612\) 0 0
\(613\) 26.7846 1.08182 0.540910 0.841080i \(-0.318080\pi\)
0.540910 + 0.841080i \(0.318080\pi\)
\(614\) −10.9282 18.9282i −0.441026 0.763880i
\(615\) 0 0
\(616\) −3.09808 + 5.36603i −0.124825 + 0.216203i
\(617\) −5.99038 + 10.3756i −0.241164 + 0.417708i −0.961046 0.276388i \(-0.910862\pi\)
0.719882 + 0.694096i \(0.244196\pi\)
\(618\) 0 0
\(619\) 11.8564 + 20.5359i 0.476549 + 0.825407i 0.999639 0.0268702i \(-0.00855407\pi\)
−0.523090 + 0.852278i \(0.675221\pi\)
\(620\) 2.19615 0.0881996
\(621\) 0 0
\(622\) −10.1962 −0.408828
\(623\) 4.96410 + 8.59808i 0.198883 + 0.344475i
\(624\) 0 0
\(625\) −11.9641 + 20.7224i −0.478564 + 0.828897i
\(626\) 12.7942 22.1603i 0.511360 0.885702i
\(627\) 0 0
\(628\) 0.500000 + 0.866025i 0.0199522 + 0.0345582i
\(629\) 74.6218 2.97537
\(630\) 0 0
\(631\) −3.66025 −0.145712 −0.0728562 0.997342i \(-0.523211\pi\)
−0.0728562 + 0.997342i \(0.523211\pi\)
\(632\) −4.56218 7.90192i −0.181474 0.314322i
\(633\) 0 0
\(634\) −15.6962 + 27.1865i −0.623374 + 1.07972i
\(635\) −1.60770 + 2.78461i −0.0637994 + 0.110504i
\(636\) 0 0
\(637\) 3.23205 + 5.59808i 0.128059 + 0.221804i
\(638\) −9.51666 −0.376768
\(639\) 0 0
\(640\) −0.267949 −0.0105916
\(641\) −19.7224 34.1603i −0.778989 1.34925i −0.932525 0.361106i \(-0.882399\pi\)
0.153536 0.988143i \(-0.450934\pi\)
\(642\) 0 0
\(643\) 4.70577 8.15064i 0.185578 0.321430i −0.758193 0.652030i \(-0.773918\pi\)
0.943771 + 0.330600i \(0.107251\pi\)
\(644\) −2.09808 + 3.63397i −0.0826758 + 0.143199i
\(645\) 0 0
\(646\) 2.56218 + 4.43782i 0.100808 + 0.174604i
\(647\) −4.39230 −0.172679 −0.0863397 0.996266i \(-0.527517\pi\)
−0.0863397 + 0.996266i \(0.527517\pi\)
\(648\) 0 0
\(649\) 26.0000 1.02059
\(650\) 15.9282 + 27.5885i 0.624756 + 1.08211i
\(651\) 0 0
\(652\) 6.73205 11.6603i 0.263647 0.456651i
\(653\) 15.1244 26.1962i 0.591862 1.02513i −0.402120 0.915587i \(-0.631726\pi\)
0.993982 0.109548i \(-0.0349402\pi\)
\(654\) 0 0
\(655\) −1.41154 2.44486i −0.0551535 0.0955287i
\(656\) 2.53590 0.0990102
\(657\) 0 0
\(658\) 4.73205 0.184475
\(659\) 18.1962 + 31.5167i 0.708821 + 1.22771i 0.965295 + 0.261163i \(0.0841061\pi\)
−0.256473 + 0.966551i \(0.582561\pi\)
\(660\) 0 0
\(661\) 6.42820 11.1340i 0.250028 0.433061i −0.713505 0.700650i \(-0.752893\pi\)
0.963533 + 0.267589i \(0.0862268\pi\)
\(662\) 6.19615 10.7321i 0.240820 0.417113i
\(663\) 0 0
\(664\) 8.29423 + 14.3660i 0.321878 + 0.557510i
\(665\) −0.196152 −0.00760646
\(666\) 0 0
\(667\) −6.44486 −0.249546
\(668\) 0.901924 + 1.56218i 0.0348965 + 0.0604425i
\(669\) 0 0
\(670\) −0.901924 + 1.56218i −0.0348444 + 0.0603522i
\(671\) −12.1699 + 21.0788i −0.469813 + 0.813740i
\(672\) 0 0
\(673\) 9.16025 + 15.8660i 0.353102 + 0.611590i 0.986791 0.161997i \(-0.0517936\pi\)
−0.633689 + 0.773588i \(0.718460\pi\)
\(674\) 16.3923 0.631408
\(675\) 0 0
\(676\) 28.7846 1.10710
\(677\) −18.0000 31.1769i −0.691796 1.19823i −0.971249 0.238067i \(-0.923486\pi\)
0.279453 0.960159i \(-0.409847\pi\)
\(678\) 0 0
\(679\) 5.46410 9.46410i 0.209693 0.363199i
\(680\) 0.937822 1.62436i 0.0359638 0.0622912i
\(681\) 0 0
\(682\) 25.3923 + 43.9808i 0.972322 + 1.68411i
\(683\) −1.85641 −0.0710334 −0.0355167 0.999369i \(-0.511308\pi\)
−0.0355167 + 0.999369i \(0.511308\pi\)
\(684\) 0 0
\(685\) −2.21539 −0.0846457
\(686\) −0.500000 0.866025i −0.0190901 0.0330650i
\(687\) 0 0
\(688\) 0.732051 1.26795i 0.0279092 0.0483401i
\(689\) −30.5885 + 52.9808i −1.16533 + 2.01841i
\(690\) 0 0
\(691\) 14.0000 + 24.2487i 0.532585 + 0.922464i 0.999276 + 0.0380440i \(0.0121127\pi\)
−0.466691 + 0.884420i \(0.654554\pi\)
\(692\) 6.26795 0.238272
\(693\) 0 0
\(694\) −21.4641 −0.814766
\(695\) 0.437822 + 0.758330i 0.0166075 + 0.0287651i
\(696\) 0 0
\(697\) −8.87564 + 15.3731i −0.336189 + 0.582296i
\(698\) 0.732051 1.26795i 0.0277085 0.0479926i
\(699\) 0 0
\(700\) −2.46410 4.26795i −0.0931343 0.161313i
\(701\) 27.3923 1.03459 0.517297 0.855806i \(-0.326938\pi\)
0.517297 + 0.855806i \(0.326938\pi\)
\(702\) 0 0
\(703\) 7.80385 0.294328
\(704\) −3.09808 5.36603i −0.116763 0.202240i
\(705\) 0 0
\(706\) −9.00000 + 15.5885i −0.338719 + 0.586679i
\(707\) 4.46410 7.73205i 0.167890 0.290794i
\(708\) 0 0
\(709\) 1.93782 + 3.35641i 0.0727764 + 0.126052i 0.900117 0.435648i \(-0.143481\pi\)
−0.827341 + 0.561700i \(0.810147\pi\)
\(710\) −1.75129 −0.0657247
\(711\) 0 0
\(712\) −9.92820 −0.372075
\(713\) 17.1962 + 29.7846i 0.644001 + 1.11544i
\(714\) 0 0
\(715\) 5.36603 9.29423i 0.200678 0.347584i
\(716\) 1.09808 1.90192i 0.0410370 0.0710782i
\(717\) 0 0
\(718\) −5.46410 9.46410i −0.203918 0.353197i
\(719\) −9.46410 −0.352951 −0.176476 0.984305i \(-0.556470\pi\)
−0.176476 + 0.984305i \(0.556470\pi\)
\(720\) 0 0
\(721\) 8.39230 0.312546
\(722\) −9.23205 15.9904i −0.343581 0.595100i
\(723\) 0 0
\(724\) 8.19615 14.1962i 0.304608 0.527596i
\(725\) 3.78461 6.55514i 0.140557 0.243452i
\(726\) 0 0
\(727\) −25.6603 44.4449i −0.951686 1.64837i −0.741776 0.670648i \(-0.766016\pi\)
−0.209911 0.977721i \(-0.567317\pi\)
\(728\) −6.46410 −0.239576
\(729\) 0 0
\(730\) −2.21539 −0.0819953
\(731\) 5.12436 + 8.87564i 0.189531 + 0.328278i
\(732\) 0 0
\(733\) −23.6603 + 40.9808i −0.873911 + 1.51366i −0.0159936 + 0.999872i \(0.505091\pi\)
−0.857918 + 0.513787i \(0.828242\pi\)
\(734\) 5.56218 9.63397i 0.205304 0.355596i
\(735\) 0 0
\(736\) −2.09808 3.63397i −0.0773361 0.133950i
\(737\) −41.7128 −1.53651
\(738\) 0 0
\(739\) −13.2679 −0.488069 −0.244035 0.969767i \(-0.578471\pi\)
−0.244035 + 0.969767i \(0.578471\pi\)
\(740\) −1.42820 2.47372i −0.0525018 0.0909358i
\(741\) 0 0
\(742\) 4.73205 8.19615i 0.173719 0.300890i
\(743\) 20.1962 34.9808i 0.740925 1.28332i −0.211150 0.977454i \(-0.567721\pi\)
0.952075 0.305866i \(-0.0989459\pi\)
\(744\) 0 0
\(745\) −1.20577 2.08846i −0.0441760 0.0765152i
\(746\) 6.14359 0.224933
\(747\) 0 0
\(748\) 43.3731 1.58588
\(749\) 0 0
\(750\) 0 0
\(751\) 11.0718 19.1769i 0.404016 0.699776i −0.590191 0.807264i \(-0.700947\pi\)
0.994206 + 0.107488i \(0.0342808\pi\)
\(752\) −2.36603 + 4.09808i −0.0862801 + 0.149441i
\(753\) 0 0
\(754\) −4.96410 8.59808i −0.180782 0.313123i
\(755\) −1.55514 −0.0565972
\(756\) 0 0
\(757\) 20.7846 0.755429 0.377715 0.925922i \(-0.376710\pi\)
0.377715 + 0.925922i \(0.376710\pi\)
\(758\) −13.7583 23.8301i −0.499725 0.865549i
\(759\) 0 0
\(760\) 0.0980762 0.169873i 0.00355760 0.00616194i
\(761\) −18.5000 + 32.0429i −0.670624 + 1.16156i 0.307103 + 0.951676i \(0.400640\pi\)
−0.977727 + 0.209879i \(0.932693\pi\)
\(762\) 0 0
\(763\) 1.59808 + 2.76795i 0.0578542 + 0.100206i
\(764\) −5.66025 −0.204781
\(765\) 0 0
\(766\) −19.7128 −0.712253
\(767\) 13.5622 + 23.4904i 0.489702 + 0.848189i
\(768\) 0 0
\(769\) 2.20577 3.82051i 0.0795421 0.137771i −0.823510 0.567301i \(-0.807988\pi\)
0.903052 + 0.429530i \(0.141321\pi\)
\(770\) −0.830127 + 1.43782i −0.0299157 + 0.0518155i
\(771\) 0 0
\(772\) −9.42820 16.3301i −0.339328 0.587734i
\(773\) −4.12436 −0.148343 −0.0741714 0.997246i \(-0.523631\pi\)
−0.0741714 + 0.997246i \(0.523631\pi\)
\(774\) 0 0
\(775\) −40.3923 −1.45093
\(776\) 5.46410 + 9.46410i 0.196150 + 0.339741i
\(777\) 0 0
\(778\) −6.73205 + 11.6603i −0.241356 + 0.418040i
\(779\) −0.928203 + 1.60770i −0.0332563 + 0.0576017i
\(780\) 0 0
\(781\) −20.2487 35.0718i −0.724556 1.25497i
\(782\) 29.3731 1.05038
\(783\) 0 0