Properties

Label 1134.2.f.r.379.2
Level $1134$
Weight $2$
Character 1134.379
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 379.2
Root \(0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 1134.379
Dual form 1134.2.f.r.757.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(1.86603 + 3.23205i) q^{5} +(0.500000 - 0.866025i) q^{7} +1.00000 q^{8} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(1.86603 + 3.23205i) q^{5} +(0.500000 - 0.866025i) q^{7} +1.00000 q^{8} -3.73205 q^{10} +(-2.09808 + 3.63397i) q^{11} +(-0.232051 - 0.401924i) q^{13} +(0.500000 + 0.866025i) q^{14} +(-0.500000 + 0.866025i) q^{16} -7.00000 q^{17} -2.73205 q^{19} +(1.86603 - 3.23205i) q^{20} +(-2.09808 - 3.63397i) q^{22} +(3.09808 + 5.36603i) q^{23} +(-4.46410 + 7.73205i) q^{25} +0.464102 q^{26} -1.00000 q^{28} +(4.23205 - 7.33013i) q^{29} +(1.09808 + 1.90192i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(3.50000 - 6.06218i) q^{34} +3.73205 q^{35} -6.66025 q^{37} +(1.36603 - 2.36603i) q^{38} +(1.86603 + 3.23205i) q^{40} +(4.73205 + 8.19615i) q^{41} +(-2.73205 + 4.73205i) q^{43} +4.19615 q^{44} -6.19615 q^{46} +(0.633975 - 1.09808i) q^{47} +(-0.500000 - 0.866025i) q^{49} +(-4.46410 - 7.73205i) q^{50} +(-0.232051 + 0.401924i) q^{52} +2.53590 q^{53} -15.6603 q^{55} +(0.500000 - 0.866025i) q^{56} +(4.23205 + 7.33013i) q^{58} +(-3.09808 - 5.36603i) q^{59} +(4.96410 - 8.59808i) q^{61} -2.19615 q^{62} +1.00000 q^{64} +(0.866025 - 1.50000i) q^{65} +(1.63397 + 2.83013i) q^{67} +(3.50000 + 6.06218i) q^{68} +(-1.86603 + 3.23205i) q^{70} -13.4641 q^{71} +11.7321 q^{73} +(3.33013 - 5.76795i) q^{74} +(1.36603 + 2.36603i) q^{76} +(2.09808 + 3.63397i) q^{77} +(-7.56218 + 13.0981i) q^{79} -3.73205 q^{80} -9.46410 q^{82} +(-7.29423 + 12.6340i) q^{83} +(-13.0622 - 22.6244i) q^{85} +(-2.73205 - 4.73205i) q^{86} +(-2.09808 + 3.63397i) q^{88} +3.92820 q^{89} -0.464102 q^{91} +(3.09808 - 5.36603i) q^{92} +(0.633975 + 1.09808i) q^{94} +(-5.09808 - 8.83013i) q^{95} +(1.46410 - 2.53590i) q^{97} +1.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 2 q^{2} - 2 q^{4} + 4 q^{5} + 2 q^{7} + 4 q^{8}+O(q^{10}) \) 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 \(\left(\mathbb{Z}/1134\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(407\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 + 0.866025i −0.353553 + 0.612372i
\(3\) 0 0
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 1.86603 + 3.23205i 0.834512 + 1.44542i 0.894427 + 0.447214i \(0.147584\pi\)
−0.0599153 + 0.998203i \(0.519083\pi\)
\(6\) 0 0
\(7\) 0.500000 0.866025i 0.188982 0.327327i
\(8\) 1.00000 0.353553
\(9\) 0 0
\(10\) −3.73205 −1.18018
\(11\) −2.09808 + 3.63397i −0.632594 + 1.09568i 0.354426 + 0.935084i \(0.384676\pi\)
−0.987020 + 0.160600i \(0.948657\pi\)
\(12\) 0 0
\(13\) −0.232051 0.401924i −0.0643593 0.111474i 0.832050 0.554700i \(-0.187167\pi\)
−0.896410 + 0.443227i \(0.853834\pi\)
\(14\) 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 \(-0.822719\pi\)
−0.848875 + 0.528594i \(0.822719\pi\)
\(18\) 0 0
\(19\) −2.73205 −0.626775 −0.313388 0.949625i \(-0.601464\pi\)
−0.313388 + 0.949625i \(0.601464\pi\)
\(20\) 1.86603 3.23205i 0.417256 0.722709i
\(21\) 0 0
\(22\) −2.09808 3.63397i −0.447311 0.774766i
\(23\) 3.09808 + 5.36603i 0.645994 + 1.11889i 0.984071 + 0.177775i \(0.0568901\pi\)
−0.338078 + 0.941118i \(0.609777\pi\)
\(24\) 0 0
\(25\) −4.46410 + 7.73205i −0.892820 + 1.54641i
\(26\) 0.464102 0.0910178
\(27\) 0 0
\(28\) −1.00000 −0.188982
\(29\) 4.23205 7.33013i 0.785872 1.36117i −0.142605 0.989780i \(-0.545548\pi\)
0.928477 0.371391i \(-0.121119\pi\)
\(30\) 0 0
\(31\) 1.09808 + 1.90192i 0.197220 + 0.341596i 0.947626 0.319382i \(-0.103475\pi\)
−0.750406 + 0.660977i \(0.770142\pi\)
\(32\) −0.500000 0.866025i −0.0883883 0.153093i
\(33\) 0 0
\(34\) 3.50000 6.06218i 0.600245 1.03965i
\(35\) 3.73205 0.630832
\(36\) 0 0
\(37\) −6.66025 −1.09494 −0.547470 0.836826i \(-0.684409\pi\)
−0.547470 + 0.836826i \(0.684409\pi\)
\(38\) 1.36603 2.36603i 0.221599 0.383820i
\(39\) 0 0
\(40\) 1.86603 + 3.23205i 0.295045 + 0.511032i
\(41\) 4.73205 + 8.19615i 0.739022 + 1.28002i 0.952936 + 0.303171i \(0.0980455\pi\)
−0.213914 + 0.976853i \(0.568621\pi\)
\(42\) 0 0
\(43\) −2.73205 + 4.73205i −0.416634 + 0.721631i −0.995598 0.0937217i \(-0.970124\pi\)
0.578965 + 0.815353i \(0.303457\pi\)
\(44\) 4.19615 0.632594
\(45\) 0 0
\(46\) −6.19615 −0.913573
\(47\) 0.633975 1.09808i 0.0924747 0.160171i −0.816077 0.577943i \(-0.803856\pi\)
0.908552 + 0.417772i \(0.137189\pi\)
\(48\) 0 0
\(49\) −0.500000 0.866025i −0.0714286 0.123718i
\(50\) −4.46410 7.73205i −0.631319 1.09348i
\(51\) 0 0
\(52\) −0.232051 + 0.401924i −0.0321797 + 0.0557368i
\(53\) 2.53590 0.348332 0.174166 0.984716i \(-0.444277\pi\)
0.174166 + 0.984716i \(0.444277\pi\)
\(54\) 0 0
\(55\) −15.6603 −2.11163
\(56\) 0.500000 0.866025i 0.0668153 0.115728i
\(57\) 0 0
\(58\) 4.23205 + 7.33013i 0.555695 + 0.962493i
\(59\) −3.09808 5.36603i −0.403335 0.698597i 0.590791 0.806825i \(-0.298816\pi\)
−0.994126 + 0.108228i \(0.965482\pi\)
\(60\) 0 0
\(61\) 4.96410 8.59808i 0.635588 1.10087i −0.350802 0.936450i \(-0.614091\pi\)
0.986390 0.164421i \(-0.0525756\pi\)
\(62\) −2.19615 −0.278912
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 0.866025 1.50000i 0.107417 0.186052i
\(66\) 0 0
\(67\) 1.63397 + 2.83013i 0.199622 + 0.345755i 0.948406 0.317059i \(-0.102695\pi\)
−0.748784 + 0.662814i \(0.769362\pi\)
\(68\) 3.50000 + 6.06218i 0.424437 + 0.735147i
\(69\) 0 0
\(70\) −1.86603 + 3.23205i −0.223033 + 0.386304i
\(71\) −13.4641 −1.59789 −0.798947 0.601401i \(-0.794609\pi\)
−0.798947 + 0.601401i \(0.794609\pi\)
\(72\) 0 0
\(73\) 11.7321 1.37313 0.686566 0.727067i \(-0.259117\pi\)
0.686566 + 0.727067i \(0.259117\pi\)
\(74\) 3.33013 5.76795i 0.387119 0.670510i
\(75\) 0 0
\(76\) 1.36603 + 2.36603i 0.156694 + 0.271402i
\(77\) 2.09808 + 3.63397i 0.239098 + 0.414130i
\(78\) 0 0
\(79\) −7.56218 + 13.0981i −0.850811 + 1.47365i 0.0296655 + 0.999560i \(0.490556\pi\)
−0.880477 + 0.474089i \(0.842778\pi\)
\(80\) −3.73205 −0.417256
\(81\) 0 0
\(82\) −9.46410 −1.04514
\(83\) −7.29423 + 12.6340i −0.800646 + 1.38676i 0.118546 + 0.992949i \(0.462177\pi\)
−0.919192 + 0.393810i \(0.871157\pi\)
\(84\) 0 0
\(85\) −13.0622 22.6244i −1.41679 2.45396i
\(86\) −2.73205 4.73205i −0.294605 0.510270i
\(87\) 0 0
\(88\) −2.09808 + 3.63397i −0.223656 + 0.387383i
\(89\) 3.92820 0.416389 0.208194 0.978087i \(-0.433241\pi\)
0.208194 + 0.978087i \(0.433241\pi\)
\(90\) 0 0
\(91\) −0.464102 −0.0486511
\(92\) 3.09808 5.36603i 0.322997 0.559447i
\(93\) 0 0
\(94\) 0.633975 + 1.09808i 0.0653895 + 0.113258i
\(95\) −5.09808 8.83013i −0.523052 0.905952i
\(96\) 0 0
\(97\) 1.46410 2.53590i 0.148657 0.257481i −0.782074 0.623185i \(-0.785838\pi\)
0.930731 + 0.365704i \(0.119172\pi\)
\(98\) 1.00000 0.101015
\(99\) 0 0
\(100\) 8.92820 0.892820
\(101\) −2.46410 + 4.26795i −0.245187 + 0.424677i −0.962184 0.272399i \(-0.912183\pi\)
0.716997 + 0.697076i \(0.245516\pi\)
\(102\) 0 0
\(103\) −6.19615 10.7321i −0.610525 1.05746i −0.991152 0.132732i \(-0.957625\pi\)
0.380627 0.924729i \(-0.375708\pi\)
\(104\) −0.232051 0.401924i −0.0227545 0.0394119i
\(105\) 0 0
\(106\) −1.26795 + 2.19615i −0.123154 + 0.213309i
\(107\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(108\) 0 0
\(109\) −7.19615 −0.689266 −0.344633 0.938737i \(-0.611997\pi\)
−0.344633 + 0.938737i \(0.611997\pi\)
\(110\) 7.83013 13.5622i 0.746573 1.29310i
\(111\) 0 0
\(112\) 0.500000 + 0.866025i 0.0472456 + 0.0818317i
\(113\) −1.13397 1.96410i −0.106675 0.184767i 0.807746 0.589531i \(-0.200687\pi\)
−0.914421 + 0.404763i \(0.867354\pi\)
\(114\) 0 0
\(115\) −11.5622 + 20.0263i −1.07818 + 1.86746i
\(116\) −8.46410 −0.785872
\(117\) 0 0
\(118\) 6.19615 0.570402
\(119\) −3.50000 + 6.06218i −0.320844 + 0.555719i
\(120\) 0 0
\(121\) −3.30385 5.72243i −0.300350 0.520221i
\(122\) 4.96410 + 8.59808i 0.449429 + 0.778433i
\(123\) 0 0
\(124\) 1.09808 1.90192i 0.0986102 0.170798i
\(125\) −14.6603 −1.31125
\(126\) 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
\(131\) 8.73205 + 15.1244i 0.762923 + 1.32142i 0.941338 + 0.337466i \(0.109570\pi\)
−0.178415 + 0.983955i \(0.557097\pi\)
\(132\) 0 0
\(133\) −1.36603 + 2.36603i −0.118449 + 0.205160i
\(134\) −3.26795 −0.282308
\(135\) 0 0
\(136\) −7.00000 −0.600245
\(137\) −5.86603 + 10.1603i −0.501168 + 0.868049i 0.498831 + 0.866699i \(0.333763\pi\)
−0.999999 + 0.00134965i \(0.999570\pi\)
\(138\) 0 0
\(139\) 3.36603 + 5.83013i 0.285503 + 0.494505i 0.972731 0.231937i \(-0.0745062\pi\)
−0.687228 + 0.726441i \(0.741173\pi\)
\(140\) −1.86603 3.23205i −0.157708 0.273158i
\(141\) 0 0
\(142\) 6.73205 11.6603i 0.564941 0.978507i
\(143\) 1.94744 0.162853
\(144\) 0 0
\(145\) 31.5885 2.62328
\(146\) −5.86603 + 10.1603i −0.485476 + 0.840869i
\(147\) 0 0
\(148\) 3.33013 + 5.76795i 0.273735 + 0.474123i
\(149\) 4.50000 + 7.79423i 0.368654 + 0.638528i 0.989355 0.145519i \(-0.0464853\pi\)
−0.620701 + 0.784047i \(0.713152\pi\)
\(150\) 0 0
\(151\) 8.09808 14.0263i 0.659012 1.14144i −0.321860 0.946787i \(-0.604308\pi\)
0.980872 0.194655i \(-0.0623587\pi\)
\(152\) −2.73205 −0.221599
\(153\) 0 0
\(154\) −4.19615 −0.338136
\(155\) −4.09808 + 7.09808i −0.329165 + 0.570131i
\(156\) 0 0
\(157\) 0.500000 + 0.866025i 0.0399043 + 0.0691164i 0.885288 0.465044i \(-0.153961\pi\)
−0.845383 + 0.534160i \(0.820628\pi\)
\(158\) −7.56218 13.0981i −0.601615 1.04203i
\(159\) 0 0
\(160\) 1.86603 3.23205i 0.147522 0.255516i
\(161\) 6.19615 0.488325
\(162\) 0 0
\(163\) −6.53590 −0.511931 −0.255966 0.966686i \(-0.582393\pi\)
−0.255966 + 0.966686i \(0.582393\pi\)
\(164\) 4.73205 8.19615i 0.369511 0.640012i
\(165\) 0 0
\(166\) −7.29423 12.6340i −0.566142 0.980587i
\(167\) −6.09808 10.5622i −0.471883 0.817326i 0.527599 0.849493i \(-0.323092\pi\)
−0.999482 + 0.0321676i \(0.989759\pi\)
\(168\) 0 0
\(169\) 6.39230 11.0718i 0.491716 0.851677i
\(170\) 26.1244 2.00365
\(171\) 0 0
\(172\) 5.46410 0.416634
\(173\) 4.86603 8.42820i 0.369957 0.640784i −0.619601 0.784917i \(-0.712706\pi\)
0.989558 + 0.144132i \(0.0460391\pi\)
\(174\) 0 0
\(175\) 4.46410 + 7.73205i 0.337454 + 0.584488i
\(176\) −2.09808 3.63397i −0.158148 0.273921i
\(177\) 0 0
\(178\) −1.96410 + 3.40192i −0.147216 + 0.254985i
\(179\) −8.19615 −0.612609 −0.306305 0.951934i \(-0.599093\pi\)
−0.306305 + 0.951934i \(0.599093\pi\)
\(180\) 0 0
\(181\) 4.39230 0.326477 0.163239 0.986587i \(-0.447806\pi\)
0.163239 + 0.986587i \(0.447806\pi\)
\(182\) 0.232051 0.401924i 0.0172008 0.0297926i
\(183\) 0 0
\(184\) 3.09808 + 5.36603i 0.228393 + 0.395589i
\(185\) −12.4282 21.5263i −0.913740 1.58264i
\(186\) 0 0
\(187\) 14.6865 25.4378i 1.07399 1.86020i
\(188\) −1.26795 −0.0924747
\(189\) 0 0
\(190\) 10.1962 0.739707
\(191\) 5.83013 10.0981i 0.421853 0.730671i −0.574268 0.818668i \(-0.694713\pi\)
0.996121 + 0.0879965i \(0.0280464\pi\)
\(192\) 0 0
\(193\) 4.42820 + 7.66987i 0.318749 + 0.552090i 0.980227 0.197875i \(-0.0634039\pi\)
−0.661478 + 0.749964i \(0.730071\pi\)
\(194\) 1.46410 + 2.53590i 0.105116 + 0.182067i
\(195\) 0 0
\(196\) −0.500000 + 0.866025i −0.0357143 + 0.0618590i
\(197\) 25.7846 1.83708 0.918539 0.395331i \(-0.129370\pi\)
0.918539 + 0.395331i \(0.129370\pi\)
\(198\) 0 0
\(199\) 5.12436 0.363256 0.181628 0.983367i \(-0.441863\pi\)
0.181628 + 0.983367i \(0.441863\pi\)
\(200\) −4.46410 + 7.73205i −0.315660 + 0.546739i
\(201\) 0 0
\(202\) −2.46410 4.26795i −0.173374 0.300292i
\(203\) −4.23205 7.33013i −0.297032 0.514474i
\(204\) 0 0
\(205\) −17.6603 + 30.5885i −1.23345 + 2.13639i
\(206\) 12.3923 0.863413
\(207\) 0 0
\(208\) 0.464102 0.0321797
\(209\) 5.73205 9.92820i 0.396494 0.686748i
\(210\) 0 0
\(211\) 10.3660 + 17.9545i 0.713627 + 1.23604i 0.963487 + 0.267756i \(0.0862820\pi\)
−0.249860 + 0.968282i \(0.580385\pi\)
\(212\) −1.26795 2.19615i −0.0870831 0.150832i
\(213\) 0 0
\(214\) 0 0
\(215\) −20.3923 −1.39074
\(216\) 0 0
\(217\) 2.19615 0.149085
\(218\) 3.59808 6.23205i 0.243692 0.422088i
\(219\) 0 0
\(220\) 7.83013 + 13.5622i 0.527907 + 0.914362i
\(221\) 1.62436 + 2.81347i 0.109266 + 0.189254i
\(222\) 0 0
\(223\) 9.26795 16.0526i 0.620628 1.07496i −0.368741 0.929532i \(-0.620211\pi\)
0.989369 0.145427i \(-0.0464555\pi\)
\(224\) −1.00000 −0.0668153
\(225\) 0 0
\(226\) 2.26795 0.150862
\(227\) −2.53590 + 4.39230i −0.168313 + 0.291528i −0.937827 0.347103i \(-0.887165\pi\)
0.769514 + 0.638631i \(0.220499\pi\)
\(228\) 0 0
\(229\) −2.23205 3.86603i −0.147498 0.255474i 0.782804 0.622268i \(-0.213789\pi\)
−0.930302 + 0.366794i \(0.880455\pi\)
\(230\) −11.5622 20.0263i −0.762387 1.32049i
\(231\) 0 0
\(232\) 4.23205 7.33013i 0.277848 0.481246i
\(233\) 13.1962 0.864509 0.432254 0.901752i \(-0.357718\pi\)
0.432254 + 0.901752i \(0.357718\pi\)
\(234\) 0 0
\(235\) 4.73205 0.308685
\(236\) −3.09808 + 5.36603i −0.201668 + 0.349299i
\(237\) 0 0
\(238\) −3.50000 6.06218i −0.226871 0.392953i
\(239\) 14.0263 + 24.2942i 0.907285 + 1.57146i 0.817821 + 0.575473i \(0.195182\pi\)
0.0894638 + 0.995990i \(0.471485\pi\)
\(240\) 0 0
\(241\) 8.86603 15.3564i 0.571111 0.989193i −0.425341 0.905033i \(-0.639846\pi\)
0.996452 0.0841601i \(-0.0268207\pi\)
\(242\) 6.60770 0.424759
\(243\) 0 0
\(244\) −9.92820 −0.635588
\(245\) 1.86603 3.23205i 0.119216 0.206488i
\(246\) 0 0
\(247\) 0.633975 + 1.09808i 0.0403388 + 0.0698689i
\(248\) 1.09808 + 1.90192i 0.0697279 + 0.120772i
\(249\) 0 0
\(250\) 7.33013 12.6962i 0.463598 0.802975i
\(251\) −16.0526 −1.01323 −0.506614 0.862173i \(-0.669103\pi\)
−0.506614 + 0.862173i \(0.669103\pi\)
\(252\) 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
\(257\) −0.232051 0.401924i −0.0144749 0.0250713i 0.858697 0.512483i \(-0.171274\pi\)
−0.873172 + 0.487412i \(0.837941\pi\)
\(258\) 0 0
\(259\) −3.33013 + 5.76795i −0.206924 + 0.358403i
\(260\) −1.73205 −0.107417
\(261\) 0 0
\(262\) −17.4641 −1.07894
\(263\) −11.8301 + 20.4904i −0.729477 + 1.26349i 0.227628 + 0.973748i \(0.426903\pi\)
−0.957105 + 0.289743i \(0.906430\pi\)
\(264\) 0 0
\(265\) 4.73205 + 8.19615i 0.290688 + 0.503486i
\(266\) −1.36603 2.36603i −0.0837564 0.145070i
\(267\) 0 0
\(268\) 1.63397 2.83013i 0.0998109 0.172878i
\(269\) 25.5885 1.56016 0.780078 0.625682i \(-0.215179\pi\)
0.780078 + 0.625682i \(0.215179\pi\)
\(270\) 0 0
\(271\) 25.5167 1.55003 0.775013 0.631945i \(-0.217743\pi\)
0.775013 + 0.631945i \(0.217743\pi\)
\(272\) 3.50000 6.06218i 0.212219 0.367574i
\(273\) 0 0
\(274\) −5.86603 10.1603i −0.354380 0.613803i
\(275\) −18.7321 32.4449i −1.12959 1.95650i
\(276\) 0 0
\(277\) −11.3923 + 19.7321i −0.684497 + 1.18558i 0.289097 + 0.957300i \(0.406645\pi\)
−0.973595 + 0.228284i \(0.926688\pi\)
\(278\) −6.73205 −0.403762
\(279\) 0 0
\(280\) 3.73205 0.223033
\(281\) −1.40192 + 2.42820i −0.0836318 + 0.144854i −0.904807 0.425821i \(-0.859985\pi\)
0.821176 + 0.570676i \(0.193319\pi\)
\(282\) 0 0
\(283\) 9.66025 + 16.7321i 0.574242 + 0.994617i 0.996123 + 0.0879660i \(0.0280367\pi\)
−0.421881 + 0.906651i \(0.638630\pi\)
\(284\) 6.73205 + 11.6603i 0.399474 + 0.691909i
\(285\) 0 0
\(286\) −0.973721 + 1.68653i −0.0575773 + 0.0997268i
\(287\) 9.46410 0.558648
\(288\) 0 0
\(289\) 32.0000 1.88235
\(290\) −15.7942 + 27.3564i −0.927469 + 1.60642i
\(291\) 0 0
\(292\) −5.86603 10.1603i −0.343283 0.594584i
\(293\) 10.3301 + 17.8923i 0.603492 + 1.04528i 0.992288 + 0.123955i \(0.0395580\pi\)
−0.388795 + 0.921324i \(0.627109\pi\)
\(294\) 0 0
\(295\) 11.5622 20.0263i 0.673176 1.16598i
\(296\) −6.66025 −0.387119
\(297\) 0 0
\(298\) −9.00000 −0.521356
\(299\) 1.43782 2.49038i 0.0831514 0.144022i
\(300\) 0 0
\(301\) 2.73205 + 4.73205i 0.157473 + 0.272751i
\(302\) 8.09808 + 14.0263i 0.465992 + 0.807122i
\(303\) 0 0
\(304\) 1.36603 2.36603i 0.0783469 0.135701i
\(305\) 37.0526 2.12162
\(306\) 0 0
\(307\) 5.85641 0.334243 0.167121 0.985936i \(-0.446553\pi\)
0.167121 + 0.985936i \(0.446553\pi\)
\(308\) 2.09808 3.63397i 0.119549 0.207065i
\(309\) 0 0
\(310\) −4.09808 7.09808i −0.232755 0.403144i
\(311\) −0.0980762 0.169873i −0.00556139 0.00963261i 0.863231 0.504809i \(-0.168437\pi\)
−0.868793 + 0.495176i \(0.835104\pi\)
\(312\) 0 0
\(313\) 2.79423 4.83975i 0.157939 0.273559i −0.776186 0.630504i \(-0.782848\pi\)
0.934125 + 0.356945i \(0.116182\pi\)
\(314\) −1.00000 −0.0564333
\(315\) 0 0
\(316\) 15.1244 0.850811
\(317\) −5.30385 + 9.18653i −0.297894 + 0.515967i −0.975654 0.219316i \(-0.929617\pi\)
0.677760 + 0.735283i \(0.262951\pi\)
\(318\) 0 0
\(319\) 17.7583 + 30.7583i 0.994276 + 1.72214i
\(320\) 1.86603 + 3.23205i 0.104314 + 0.180677i
\(321\) 0 0
\(322\) −3.09808 + 5.36603i −0.172649 + 0.299037i
\(323\) 19.1244 1.06411
\(324\) 0 0
\(325\) 4.14359 0.229845
\(326\) 3.26795 5.66025i 0.180995 0.313492i
\(327\) 0 0
\(328\) 4.73205 + 8.19615i 0.261284 + 0.452557i
\(329\) −0.633975 1.09808i −0.0349522 0.0605389i
\(330\) 0 0
\(331\) 4.19615 7.26795i 0.230641 0.399483i −0.727356 0.686261i \(-0.759251\pi\)
0.957997 + 0.286778i \(0.0925842\pi\)
\(332\) 14.5885 0.800646
\(333\) 0 0
\(334\) 12.1962 0.667344
\(335\) −6.09808 + 10.5622i −0.333173 + 0.577073i
\(336\) 0 0
\(337\) −2.19615 3.80385i −0.119632 0.207209i 0.799990 0.600014i \(-0.204838\pi\)
−0.919622 + 0.392805i \(0.871505\pi\)
\(338\) 6.39230 + 11.0718i 0.347696 + 0.602226i
\(339\) 0 0
\(340\) −13.0622 + 22.6244i −0.708396 + 1.22698i
\(341\) −9.21539 −0.499041
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) −2.73205 + 4.73205i −0.147302 + 0.255135i
\(345\) 0 0
\(346\) 4.86603 + 8.42820i 0.261599 + 0.453103i
\(347\) 7.26795 + 12.5885i 0.390164 + 0.675784i 0.992471 0.122481i \(-0.0390850\pi\)
−0.602307 + 0.798265i \(0.705752\pi\)
\(348\) 0 0
\(349\) 2.73205 4.73205i 0.146243 0.253301i −0.783593 0.621275i \(-0.786615\pi\)
0.929836 + 0.367974i \(0.119948\pi\)
\(350\) −8.92820 −0.477233
\(351\) 0 0
\(352\) 4.19615 0.223656
\(353\) −9.00000 + 15.5885i −0.479022 + 0.829690i −0.999711 0.0240566i \(-0.992342\pi\)
0.520689 + 0.853746i \(0.325675\pi\)
\(354\) 0 0
\(355\) −25.1244 43.5167i −1.33346 2.30962i
\(356\) −1.96410 3.40192i −0.104097 0.180302i
\(357\) 0 0
\(358\) 4.09808 7.09808i 0.216590 0.375145i
\(359\) −2.92820 −0.154545 −0.0772723 0.997010i \(-0.524621\pi\)
−0.0772723 + 0.997010i \(0.524621\pi\)
\(360\) 0 0
\(361\) −11.5359 −0.607153
\(362\) −2.19615 + 3.80385i −0.115427 + 0.199926i
\(363\) 0 0
\(364\) 0.232051 + 0.401924i 0.0121628 + 0.0210665i
\(365\) 21.8923 + 37.9186i 1.14590 + 1.98475i
\(366\) 0 0
\(367\) 6.56218 11.3660i 0.342543 0.593302i −0.642361 0.766402i \(-0.722045\pi\)
0.984904 + 0.173100i \(0.0553785\pi\)
\(368\) −6.19615 −0.322997
\(369\) 0 0
\(370\) 24.8564 1.29222
\(371\) 1.26795 2.19615i 0.0658286 0.114019i
\(372\) 0 0
\(373\) 16.9282 + 29.3205i 0.876509 + 1.51816i 0.855146 + 0.518387i \(0.173467\pi\)
0.0213627 + 0.999772i \(0.493200\pi\)
\(374\) 14.6865 + 25.4378i 0.759423 + 1.31536i
\(375\) 0 0
\(376\) 0.633975 1.09808i 0.0326947 0.0566290i
\(377\) −3.92820 −0.202313
\(378\) 0 0
\(379\) 17.5167 0.899770 0.449885 0.893086i \(-0.351465\pi\)
0.449885 + 0.893086i \(0.351465\pi\)
\(380\) −5.09808 + 8.83013i −0.261526 + 0.452976i
\(381\) 0 0
\(382\) 5.83013 + 10.0981i 0.298295 + 0.516663i
\(383\) −17.8564 30.9282i −0.912420 1.58036i −0.810636 0.585551i \(-0.800878\pi\)
−0.101784 0.994807i \(-0.532455\pi\)
\(384\) 0 0
\(385\) −7.83013 + 13.5622i −0.399060 + 0.691193i
\(386\) −8.85641 −0.450779
\(387\) 0 0
\(388\) −2.92820 −0.148657
\(389\) −3.26795 + 5.66025i −0.165692 + 0.286986i −0.936901 0.349596i \(-0.886319\pi\)
0.771209 + 0.636582i \(0.219652\pi\)
\(390\) 0 0
\(391\) −21.6865 37.5622i −1.09674 1.89960i
\(392\) −0.500000 0.866025i −0.0252538 0.0437409i
\(393\) 0 0
\(394\) −12.8923 + 22.3301i −0.649505 + 1.12498i
\(395\) −56.4449 −2.84005
\(396\) 0 0
\(397\) −21.0000 −1.05396 −0.526980 0.849878i \(-0.676676\pi\)
−0.526980 + 0.849878i \(0.676676\pi\)
\(398\) −2.56218 + 4.43782i −0.128430 + 0.222448i
\(399\) 0 0
\(400\) −4.46410 7.73205i −0.223205 0.386603i
\(401\) −17.2583 29.8923i −0.861840 1.49275i −0.870151 0.492785i \(-0.835979\pi\)
0.00831121 0.999965i \(-0.497354\pi\)
\(402\) 0 0
\(403\) 0.509619 0.882686i 0.0253859 0.0439697i
\(404\) 4.92820 0.245187
\(405\) 0 0
\(406\) 8.46410 0.420066
\(407\) 13.9737 24.2032i 0.692652 1.19971i
\(408\) 0 0
\(409\) −17.3301 30.0167i −0.856920 1.48423i −0.874853 0.484389i \(-0.839042\pi\)
0.0179330 0.999839i \(-0.494291\pi\)
\(410\) −17.6603 30.5885i −0.872178 1.51066i
\(411\) 0 0
\(412\) −6.19615 + 10.7321i −0.305263 + 0.528730i
\(413\) −6.19615 −0.304893
\(414\) 0 0
\(415\) −54.4449 −2.67259
\(416\) −0.232051 + 0.401924i −0.0113772 + 0.0197059i
\(417\) 0 0
\(418\) 5.73205 + 9.92820i 0.280364 + 0.485604i
\(419\) −1.26795 2.19615i −0.0619434 0.107289i 0.833391 0.552684i \(-0.186396\pi\)
−0.895334 + 0.445395i \(0.853063\pi\)
\(420\) 0 0
\(421\) 12.0622 20.8923i 0.587875 1.01823i −0.406636 0.913590i \(-0.633298\pi\)
0.994510 0.104638i \(-0.0333685\pi\)
\(422\) −20.7321 −1.00922
\(423\) 0 0
\(424\) 2.53590 0.123154
\(425\) 31.2487 54.1244i 1.51579 2.62542i
\(426\) 0 0
\(427\) −4.96410 8.59808i −0.240230 0.416090i
\(428\) 0 0
\(429\) 0 0
\(430\) 10.1962 17.6603i 0.491702 0.851653i
\(431\) 21.4641 1.03389 0.516945 0.856019i \(-0.327069\pi\)
0.516945 + 0.856019i \(0.327069\pi\)
\(432\) 0 0
\(433\) 12.2679 0.589560 0.294780 0.955565i \(-0.404754\pi\)
0.294780 + 0.955565i \(0.404754\pi\)
\(434\) −1.09808 + 1.90192i −0.0527093 + 0.0912953i
\(435\) 0 0
\(436\) 3.59808 + 6.23205i 0.172317 + 0.298461i
\(437\) −8.46410 14.6603i −0.404893 0.701295i
\(438\) 0 0
\(439\) 5.66025 9.80385i 0.270149 0.467912i −0.698751 0.715365i \(-0.746260\pi\)
0.968900 + 0.247453i \(0.0795936\pi\)
\(440\) −15.6603 −0.746573
\(441\) 0 0
\(442\) −3.24871 −0.154525
\(443\) −9.36603 + 16.2224i −0.444993 + 0.770751i −0.998052 0.0623915i \(-0.980127\pi\)
0.553058 + 0.833142i \(0.313461\pi\)
\(444\) 0 0
\(445\) 7.33013 + 12.6962i 0.347481 + 0.601855i
\(446\) 9.26795 + 16.0526i 0.438850 + 0.760111i
\(447\) 0 0
\(448\) 0.500000 0.866025i 0.0236228 0.0409159i
\(449\) 11.8564 0.559538 0.279769 0.960067i \(-0.409742\pi\)
0.279769 + 0.960067i \(0.409742\pi\)
\(450\) 0 0
\(451\) −39.7128 −1.87000
\(452\) −1.13397 + 1.96410i −0.0533377 + 0.0923836i
\(453\) 0 0
\(454\) −2.53590 4.39230i −0.119016 0.206141i
\(455\) −0.866025 1.50000i −0.0405999 0.0703211i
\(456\) 0 0
\(457\) −10.4282 + 18.0622i −0.487811 + 0.844913i −0.999902 0.0140182i \(-0.995538\pi\)
0.512091 + 0.858931i \(0.328871\pi\)
\(458\) 4.46410 0.208594
\(459\) 0 0
\(460\) 23.1244 1.07818
\(461\) 17.3923 30.1244i 0.810040 1.40303i −0.102795 0.994703i \(-0.532778\pi\)
0.912835 0.408329i \(-0.133888\pi\)
\(462\) 0 0
\(463\) 16.2942 + 28.2224i 0.757257 + 1.31161i 0.944244 + 0.329245i \(0.106794\pi\)
−0.186987 + 0.982362i \(0.559872\pi\)
\(464\) 4.23205 + 7.33013i 0.196468 + 0.340293i
\(465\) 0 0
\(466\) −6.59808 + 11.4282i −0.305650 + 0.529401i
\(467\) −14.5885 −0.675073 −0.337537 0.941312i \(-0.609594\pi\)
−0.337537 + 0.941312i \(0.609594\pi\)
\(468\) 0 0
\(469\) 3.26795 0.150900
\(470\) −2.36603 + 4.09808i −0.109137 + 0.189030i
\(471\) 0 0
\(472\) −3.09808 5.36603i −0.142601 0.246991i
\(473\) −11.4641 19.8564i −0.527120 0.912999i
\(474\) 0 0
\(475\) 12.1962 21.1244i 0.559598 0.969252i
\(476\) 7.00000 0.320844
\(477\) 0 0
\(478\) −28.0526 −1.28309
\(479\) 11.7583 20.3660i 0.537252 0.930547i −0.461799 0.886985i \(-0.652796\pi\)
0.999051 0.0435628i \(-0.0138709\pi\)
\(480\) 0 0
\(481\) 1.54552 + 2.67691i 0.0704695 + 0.122057i
\(482\) 8.86603 + 15.3564i 0.403836 + 0.699465i
\(483\) 0 0
\(484\) −3.30385 + 5.72243i −0.150175 + 0.260111i
\(485\) 10.9282 0.496224
\(486\) 0 0
\(487\) −28.5885 −1.29547 −0.647733 0.761867i \(-0.724283\pi\)
−0.647733 + 0.761867i \(0.724283\pi\)
\(488\) 4.96410 8.59808i 0.224714 0.389217i
\(489\) 0 0
\(490\) 1.86603 + 3.23205i 0.0842984 + 0.146009i
\(491\) 16.7321 + 28.9808i 0.755107 + 1.30788i 0.945321 + 0.326141i \(0.105748\pi\)
−0.190214 + 0.981743i \(0.560918\pi\)
\(492\) 0 0
\(493\) −29.6244 + 51.3109i −1.33421 + 2.31093i
\(494\) −1.26795 −0.0570477
\(495\) 0 0
\(496\) −2.19615 −0.0986102
\(497\) −6.73205 + 11.6603i −0.301974 + 0.523034i
\(498\) 0 0
\(499\) −15.0981 26.1506i −0.675883 1.17066i −0.976210 0.216827i \(-0.930429\pi\)
0.300327 0.953836i \(-0.402904\pi\)
\(500\) 7.33013 + 12.6962i 0.327813 + 0.567789i
\(501\) 0 0
\(502\) 8.02628 13.9019i 0.358230 0.620473i
\(503\) −1.94744 −0.0868321 −0.0434161 0.999057i \(-0.513824\pi\)
−0.0434161 + 0.999057i \(0.513824\pi\)
\(504\) 0 0
\(505\) −18.3923 −0.818447
\(506\) 13.0000 22.5167i 0.577920 1.00099i
\(507\) 0 0
\(508\) −6.00000 10.3923i −0.266207 0.461084i
\(509\) 2.07180 + 3.58846i 0.0918308 + 0.159056i 0.908282 0.418360i \(-0.137395\pi\)
−0.816451 + 0.577415i \(0.804061\pi\)
\(510\) 0 0
\(511\) 5.86603 10.1603i 0.259498 0.449463i
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) 0.464102 0.0204706
\(515\) 23.1244 40.0526i 1.01898 1.76493i
\(516\) 0 0
\(517\) 2.66025 + 4.60770i 0.116998 + 0.202646i
\(518\) −3.33013 5.76795i −0.146317 0.253429i
\(519\) 0 0
\(520\) 0.866025 1.50000i 0.0379777 0.0657794i
\(521\) 30.0000 1.31432 0.657162 0.753749i \(-0.271757\pi\)
0.657162 + 0.753749i \(0.271757\pi\)
\(522\) 0 0
\(523\) −29.1769 −1.27582 −0.637909 0.770112i \(-0.720200\pi\)
−0.637909 + 0.770112i \(0.720200\pi\)
\(524\) 8.73205 15.1244i 0.381461 0.660711i
\(525\) 0 0
\(526\) −11.8301 20.4904i −0.515818 0.893423i
\(527\) −7.68653 13.3135i −0.334831 0.579944i
\(528\) 0 0
\(529\) −7.69615 + 13.3301i −0.334615 + 0.579571i
\(530\) −9.46410 −0.411094
\(531\) 0 0
\(532\) 2.73205 0.118449
\(533\) 2.19615 3.80385i 0.0951259 0.164763i
\(534\) 0 0
\(535\) 0 0
\(536\) 1.63397 + 2.83013i 0.0705770 + 0.122243i
\(537\) 0 0
\(538\) −12.7942 + 22.1603i −0.551598 + 0.955396i
\(539\) 4.19615 0.180741
\(540\) 0 0
\(541\) 20.6603 0.888254 0.444127 0.895964i \(-0.353514\pi\)
0.444127 + 0.895964i \(0.353514\pi\)
\(542\) −12.7583 + 22.0981i −0.548017 + 0.949194i
\(543\) 0 0
\(544\) 3.50000 + 6.06218i 0.150061 + 0.259914i
\(545\) −13.4282 23.2583i −0.575201 0.996277i
\(546\) 0 0
\(547\) 9.63397 16.6865i 0.411919 0.713465i −0.583181 0.812343i \(-0.698192\pi\)
0.995100 + 0.0988779i \(0.0315253\pi\)
\(548\) 11.7321 0.501168
\(549\) 0 0
\(550\) 37.4641 1.59747
\(551\) −11.5622 + 20.0263i −0.492565 + 0.853148i
\(552\) 0 0
\(553\) 7.56218 + 13.0981i 0.321577 + 0.556987i
\(554\) −11.3923 19.7321i −0.484013 0.838335i
\(555\) 0 0
\(556\) 3.36603 5.83013i 0.142751 0.247252i
\(557\) −10.0718 −0.426756 −0.213378 0.976970i \(-0.568447\pi\)
−0.213378 + 0.976970i \(0.568447\pi\)
\(558\) 0 0
\(559\) 2.53590 0.107257
\(560\) −1.86603 + 3.23205i −0.0788540 + 0.136579i
\(561\) 0 0
\(562\) −1.40192 2.42820i −0.0591366 0.102428i
\(563\) −17.8564 30.9282i −0.752558 1.30347i −0.946579 0.322471i \(-0.895486\pi\)
0.194022 0.980997i \(-0.437847\pi\)
\(564\) 0 0
\(565\) 4.23205 7.33013i 0.178044 0.308381i
\(566\) −19.3205 −0.812102
\(567\) 0 0
\(568\) −13.4641 −0.564941
\(569\) 6.40192 11.0885i 0.268383 0.464852i −0.700062 0.714082i \(-0.746844\pi\)
0.968444 + 0.249230i \(0.0801775\pi\)
\(570\) 0 0
\(571\) 9.63397 + 16.6865i 0.403169 + 0.698310i 0.994107 0.108408i \(-0.0345752\pi\)
−0.590937 + 0.806718i \(0.701242\pi\)
\(572\) −0.973721 1.68653i −0.0407133 0.0705175i
\(573\) 0 0
\(574\) −4.73205 + 8.19615i −0.197512 + 0.342101i
\(575\) −55.3205 −2.30702
\(576\) 0 0
\(577\) 7.33975 0.305558 0.152779 0.988260i \(-0.451178\pi\)
0.152779 + 0.988260i \(0.451178\pi\)
\(578\) −16.0000 + 27.7128i −0.665512 + 1.15270i
\(579\) 0 0
\(580\) −15.7942 27.3564i −0.655820 1.13591i
\(581\) 7.29423 + 12.6340i 0.302616 + 0.524146i
\(582\) 0 0
\(583\) −5.32051 + 9.21539i −0.220353 + 0.381662i
\(584\) 11.7321 0.485476
\(585\) 0 0
\(586\) −20.6603 −0.853467
\(587\) 5.63397 9.75833i 0.232539 0.402769i −0.726016 0.687678i \(-0.758630\pi\)
0.958555 + 0.284909i \(0.0919633\pi\)
\(588\) 0 0
\(589\) −3.00000 5.19615i −0.123613 0.214104i
\(590\) 11.5622 + 20.0263i 0.476007 + 0.824469i
\(591\) 0 0
\(592\) 3.33013 5.76795i 0.136867 0.237061i
\(593\) −40.1769 −1.64987 −0.824934 0.565229i \(-0.808788\pi\)
−0.824934 + 0.565229i \(0.808788\pi\)
\(594\) 0 0
\(595\) −26.1244 −1.07099
\(596\) 4.50000 7.79423i 0.184327 0.319264i
\(597\) 0 0
\(598\) 1.43782 + 2.49038i 0.0587969 + 0.101839i
\(599\) 4.56218 + 7.90192i 0.186406 + 0.322864i 0.944049 0.329805i \(-0.106983\pi\)
−0.757644 + 0.652668i \(0.773650\pi\)
\(600\) 0 0
\(601\) −4.40192 + 7.62436i −0.179558 + 0.311004i −0.941729 0.336372i \(-0.890800\pi\)
0.762171 + 0.647376i \(0.224133\pi\)
\(602\) −5.46410 −0.222700
\(603\) 0 0
\(604\) −16.1962 −0.659012
\(605\) 12.3301 21.3564i 0.501291 0.868261i
\(606\) 0 0
\(607\) −3.29423 5.70577i −0.133709 0.231590i 0.791395 0.611305i \(-0.209355\pi\)
−0.925103 + 0.379715i \(0.876022\pi\)
\(608\) 1.36603 + 2.36603i 0.0553996 + 0.0959550i
\(609\) 0 0
\(610\) −18.5263 + 32.0885i −0.750107 + 1.29922i
\(611\) −0.588457 −0.0238064
\(612\) 0 0
\(613\) −14.7846 −0.597145 −0.298572 0.954387i \(-0.596510\pi\)
−0.298572 + 0.954387i \(0.596510\pi\)
\(614\) −2.92820 + 5.07180i −0.118173 + 0.204681i
\(615\) 0 0
\(616\) 2.09808 + 3.63397i 0.0845339 + 0.146417i
\(617\) −19.9904 34.6244i −0.804782 1.39392i −0.916438 0.400177i \(-0.868949\pi\)
0.111655 0.993747i \(-0.464385\pi\)
\(618\) 0 0
\(619\) −15.8564 + 27.4641i −0.637323 + 1.10388i 0.348695 + 0.937236i \(0.386625\pi\)
−0.986018 + 0.166639i \(0.946708\pi\)
\(620\) 8.19615 0.329165
\(621\) 0 0
\(622\) 0.196152 0.00786500
\(623\) 1.96410 3.40192i 0.0786901 0.136295i
\(624\) 0 0
\(625\) −5.03590 8.72243i −0.201436 0.348897i
\(626\) 2.79423 + 4.83975i 0.111680 + 0.193435i
\(627\) 0 0
\(628\) 0.500000 0.866025i 0.0199522 0.0345582i
\(629\) 46.6218 1.85893
\(630\) 0 0
\(631\) 13.6603 0.543806 0.271903 0.962325i \(-0.412347\pi\)
0.271903 + 0.962325i \(0.412347\pi\)
\(632\) −7.56218 + 13.0981i −0.300807 + 0.521013i
\(633\) 0 0
\(634\) −5.30385 9.18653i −0.210643 0.364844i
\(635\) 22.3923 + 38.7846i 0.888612 + 1.53912i
\(636\) 0 0
\(637\) −0.232051 + 0.401924i −0.00919419 + 0.0159248i
\(638\) −35.5167 −1.40612
\(639\) 0 0
\(640\) −3.73205 −0.147522
\(641\) −9.72243 + 16.8397i −0.384013 + 0.665130i −0.991632 0.129099i \(-0.958792\pi\)
0.607619 + 0.794229i \(0.292125\pi\)
\(642\) 0 0
\(643\) 20.2942 + 35.1506i 0.800326 + 1.38621i 0.919401 + 0.393320i \(0.128674\pi\)
−0.119075 + 0.992885i \(0.537993\pi\)
\(644\) −3.09808 5.36603i −0.122081 0.211451i
\(645\) 0 0
\(646\) −9.56218 + 16.5622i −0.376219 + 0.651630i
\(647\) −16.3923 −0.644448 −0.322224 0.946663i \(-0.604430\pi\)
−0.322224 + 0.946663i \(0.604430\pi\)
\(648\) 0 0
\(649\) 26.0000 1.02059
\(650\) −2.07180 + 3.58846i −0.0812626 + 0.140751i
\(651\) 0 0
\(652\) 3.26795 + 5.66025i 0.127983 + 0.221673i
\(653\) 9.12436 + 15.8038i 0.357064 + 0.618452i 0.987469 0.157814i \(-0.0504446\pi\)
−0.630405 + 0.776266i \(0.717111\pi\)
\(654\) 0 0
\(655\) −32.5885 + 56.4449i −1.27334 + 2.20548i
\(656\) −9.46410 −0.369511
\(657\) 0 0
\(658\) 1.26795 0.0494298
\(659\) −7.80385 + 13.5167i −0.303995 + 0.526534i −0.977037 0.213070i \(-0.931654\pi\)
0.673042 + 0.739604i \(0.264987\pi\)
\(660\) 0 0
\(661\) −7.42820 12.8660i −0.288924 0.500430i 0.684629 0.728891i \(-0.259964\pi\)
−0.973553 + 0.228461i \(0.926631\pi\)
\(662\) 4.19615 + 7.26795i 0.163088 + 0.282477i
\(663\) 0 0
\(664\) −7.29423 + 12.6340i −0.283071 + 0.490293i
\(665\) −10.1962 −0.395390
\(666\) 0 0
\(667\) 52.4449 2.03067
\(668\) −6.09808 + 10.5622i −0.235942 + 0.408663i
\(669\) 0 0
\(670\) −6.09808 10.5622i −0.235589 0.408053i
\(671\) 20.8301 + 36.0788i 0.804138 + 1.39281i
\(672\) 0 0
\(673\) −8.16025 + 14.1340i −0.314555 + 0.544825i −0.979343 0.202207i \(-0.935189\pi\)
0.664788 + 0.747032i \(0.268522\pi\)
\(674\) 4.39230 0.169185
\(675\) 0 0
\(676\) −12.7846 −0.491716
\(677\) 18.0000 31.1769i 0.691796 1.19823i −0.279453 0.960159i \(-0.590153\pi\)
0.971249 0.238067i \(-0.0765137\pi\)
\(678\) 0 0
\(679\) −1.46410 2.53590i −0.0561871 0.0973188i
\(680\) −13.0622 22.6244i −0.500912 0.867604i
\(681\) 0 0
\(682\) 4.60770 7.98076i 0.176438 0.305599i
\(683\) −25.8564 −0.989368 −0.494684 0.869073i \(-0.664716\pi\)
−0.494684 + 0.869073i \(0.664716\pi\)
\(684\) 0 0
\(685\) −43.7846 −1.67292
\(686\) 0.500000 0.866025i 0.0190901 0.0330650i
\(687\) 0 0
\(688\) −2.73205 4.73205i −0.104158 0.180408i
\(689\) −0.588457 1.01924i −0.0224184 0.0388299i
\(690\) 0 0
\(691\) 14.0000 24.2487i 0.532585 0.922464i −0.466691 0.884420i \(-0.654554\pi\)
0.999276 0.0380440i \(-0.0121127\pi\)
\(692\) −9.73205 −0.369957
\(693\) 0 0
\(694\) −14.5359 −0.551775
\(695\) −12.5622 + 21.7583i −0.476511 + 0.825341i
\(696\) 0 0
\(697\) −33.1244 57.3731i −1.25467 2.17316i
\(698\) 2.73205 + 4.73205i 0.103410 + 0.179111i
\(699\) 0 0
\(700\) 4.46410 7.73205i 0.168727 0.292244i
\(701\) −6.60770 −0.249569 −0.124785 0.992184i \(-0.539824\pi\)
−0.124785 + 0.992184i \(0.539824\pi\)
\(702\) 0 0
\(703\) 18.1962 0.686281
\(704\) −2.09808 + 3.63397i −0.0790742 + 0.136961i
\(705\) 0 0
\(706\) −9.00000 15.5885i −0.338719 0.586679i
\(707\) 2.46410 + 4.26795i 0.0926721 + 0.160513i
\(708\) 0 0
\(709\) 14.0622 24.3564i 0.528116 0.914724i −0.471347 0.881948i \(-0.656232\pi\)
0.999463 0.0327760i \(-0.0104348\pi\)
\(710\) 50.2487 1.88580
\(711\) 0 0
\(712\) 3.92820 0.147216
\(713\) −6.80385 + 11.7846i −0.254806 + 0.441337i
\(714\) 0 0
\(715\) 3.63397 + 6.29423i 0.135903 + 0.235391i
\(716\) 4.09808 + 7.09808i 0.153152 + 0.265268i
\(717\) 0 0
\(718\) 1.46410 2.53590i 0.0546398 0.0946389i
\(719\) 2.53590 0.0945731 0.0472865 0.998881i \(-0.484943\pi\)
0.0472865 + 0.998881i \(0.484943\pi\)
\(720\) 0 0
\(721\) −12.3923 −0.461514
\(722\) 5.76795 9.99038i 0.214661 0.371803i
\(723\) 0 0
\(724\) −2.19615 3.80385i −0.0816194 0.141369i
\(725\) 37.7846 + 65.4449i 1.40329 + 2.43056i
\(726\) 0 0
\(727\) −8.33975 + 14.4449i −0.309304 + 0.535730i −0.978210 0.207616i \(-0.933429\pi\)
0.668906 + 0.743347i \(0.266763\pi\)
\(728\) −0.464102 −0.0172008
\(729\) 0 0
\(730\) −43.7846 −1.62054
\(731\) 19.1244 33.1244i 0.707340 1.22515i
\(732\) 0 0
\(733\) −6.33975 10.9808i −0.234164 0.405584i 0.724865 0.688890i \(-0.241902\pi\)
−0.959029 + 0.283307i \(0.908569\pi\)
\(734\) 6.56218 + 11.3660i 0.242214 + 0.419528i
\(735\) 0 0
\(736\) 3.09808 5.36603i 0.114197 0.197794i
\(737\) −13.7128 −0.505118
\(738\) 0 0
\(739\) −16.7321 −0.615498 −0.307749 0.951468i \(-0.599576\pi\)
−0.307749 + 0.951468i \(0.599576\pi\)
\(740\) −12.4282 + 21.5263i −0.456870 + 0.791322i
\(741\) 0 0
\(742\) 1.26795 + 2.19615i 0.0465479 + 0.0806233i
\(743\) −9.80385 16.9808i −0.359668 0.622964i 0.628237 0.778022i \(-0.283777\pi\)
−0.987905 + 0.155058i \(0.950443\pi\)
\(744\) 0 0
\(745\) −16.7942 + 29.0885i −0.615293 + 1.06572i
\(746\) −33.8564 −1.23957
\(747\) 0 0
\(748\) −29.3731 −1.07399
\(749\) 0 0
\(750\) 0 0
\(751\) 24.9282 + 43.1769i 0.909643 + 1.57555i 0.814561 + 0.580079i \(0.196978\pi\)
0.0950825 + 0.995469i \(0.469688\pi\)
\(752\) 0.633975 + 1.09808i 0.0231187 + 0.0400427i
\(753\) 0 0
\(754\) 1.96410 3.40192i 0.0715284 0.123891i
\(755\) 60.4449 2.19981
\(756\) 0 0
\(757\) −20.7846 −0.755429 −0.377715 0.925922i \(-0.623290\pi\)
−0.377715 + 0.925922i \(0.623290\pi\)
\(758\) −8.75833 + 15.1699i −0.318117 + 0.550995i
\(759\) 0 0
\(760\) −5.09808 8.83013i −0.184927 0.320302i
\(761\) 18.5000 + 32.0429i 0.670624 + 1.16156i 0.977727 + 0.209879i \(0.0673071\pi\)
−0.307103 + 0.951676i \(0.599360\pi\)
\(762\) 0 0
\(763\) −3.59808 + 6.23205i −0.130259 + 0.225615i
\(764\) −11.6603 −0.421853
\(765\) 0 0
\(766\) 35.7128 1.29036
\(767\) −1.43782 + 2.49038i −0.0519167 + 0.0899224i
\(768\) 0 0
\(769\) 17.7942 + 30.8205i 0.641676 + 1.11142i 0.985058 + 0.172220i \(0.0550941\pi\)
−0.343382 + 0.939196i \(0.611573\pi\)
\(770\) −7.83013 13.5622i −0.282178 0.488747i
\(771\) 0 0
\(772\) 4.42820 7.66987i 0.159375 0.276045i
\(773\) −20.1244 −0.723823 −0.361911 0.932213i \(-0.617876\pi\)
−0.361911 + 0.932213i \(0.617876\pi\)
\(774\) 0 0
\(775\) −19.6077 −0.704329
\(776\) 1.46410 2.53590i 0.0525582 0.0910334i
\(777\) 0 0
\(778\) −3.26795 5.66025i −0.117162 0.202930i
\(779\) −12.9282 22.3923i −0.463201 0.802288i
\(780\) 0 0
\(781\) 28.2487 48.9282i 1.01082 1.75079i
\(782\) 43.3731 1.55102
\(783\) 0 0
\(784\) 1.00000