Properties

Label 1134.2.f.s.757.1
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 757.1
Root \(-0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 1134.757
Dual form 1134.2.f.s.379.1

$q$-expansion

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

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

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
\(5\) −1.86603 + 3.23205i −0.834512 + 1.44542i 0.0599153 + 0.998203i \(0.480917\pi\)
−0.894427 + 0.447214i \(0.852416\pi\)
\(6\) 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 0.987020 + 0.160600i \(0.0513430\pi\)
−0.354426 + 0.935084i \(0.615324\pi\)
\(12\) 0 0
\(13\) −0.232051 + 0.401924i −0.0643593 + 0.111474i −0.896410 0.443227i \(-0.853834\pi\)
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
\(19\) −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 0.338078 + 0.941118i \(0.390223\pi\)
−0.984071 + 0.177775i \(0.943110\pi\)
\(24\) 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 −0.928477 0.371391i \(-0.878881\pi\)
0.142605 0.989780i \(-0.454452\pi\)
\(30\) 0 0
\(31\) 1.09808 1.90192i 0.197220 0.341596i −0.750406 0.660977i \(-0.770142\pi\)
0.947626 + 0.319382i \(0.103475\pi\)
\(32\) 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 0.213914 + 0.976853i \(0.431379\pi\)
−0.952936 + 0.303171i \(0.901955\pi\)
\(42\) 0 0
\(43\) −2.73205 4.73205i −0.416634 0.721631i 0.578965 0.815353i \(-0.303457\pi\)
−0.995598 + 0.0937217i \(0.970124\pi\)
\(44\) −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 \(-0.196144\pi\)
−0.908552 + 0.417772i \(0.862811\pi\)
\(48\) 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 \(-0.555723\pi\)
−0.174166 + 0.984716i \(0.555723\pi\)
\(54\) 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 \(-0.701184\pi\)
0.994126 + 0.108228i \(0.0345175\pi\)
\(60\) 0 0
\(61\) 4.96410 + 8.59808i 0.635588 + 1.10087i 0.986390 + 0.164421i \(0.0525756\pi\)
−0.350802 + 0.936450i \(0.614091\pi\)
\(62\) 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 −0.748784 0.662814i \(-0.769362\pi\)
0.948406 + 0.317059i \(0.102695\pi\)
\(68\) −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 \(-0.205391\pi\)
0.798947 + 0.601401i \(0.205391\pi\)
\(72\) 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 −0.880477 0.474089i \(-0.842778\pi\)
0.0296655 0.999560i \(-0.490556\pi\)
\(80\) 3.73205 0.417256
\(81\) 0 0
\(82\) −9.46410 −1.04514
\(83\) 7.29423 + 12.6340i 0.800646 + 1.38676i 0.919192 + 0.393810i \(0.128843\pi\)
−0.118546 + 0.992949i \(0.537823\pi\)
\(84\) 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 \(-0.566759\pi\)
−0.208194 + 0.978087i \(0.566759\pi\)
\(90\) 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 0.930731 0.365704i \(-0.119172\pi\)
−0.782074 + 0.623185i \(0.785838\pi\)
\(98\) −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 \(-0.0878172\pi\)
−0.716997 + 0.697076i \(0.754484\pi\)
\(102\) 0 0
\(103\) −6.19615 + 10.7321i −0.610525 + 1.05746i 0.380627 + 0.924729i \(0.375708\pi\)
−0.991152 + 0.132732i \(0.957625\pi\)
\(104\) 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 \(-0.799313\pi\)
0.914421 + 0.404763i \(0.132646\pi\)
\(114\) 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 0.178415 + 0.983955i \(0.442903\pi\)
−0.941338 + 0.337466i \(0.890430\pi\)
\(132\) 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 0.999999 + 0.00134965i \(0.000429606\pi\)
−0.498831 + 0.866699i \(0.666237\pi\)
\(138\) 0 0
\(139\) 3.36603 5.83013i 0.285503 0.494505i −0.687228 0.726441i \(-0.741173\pi\)
0.972731 + 0.231937i \(0.0745062\pi\)
\(140\) 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 \(-0.953515\pi\)
0.620701 + 0.784047i \(0.286848\pi\)
\(150\) 0 0
\(151\) 8.09808 + 14.0263i 0.659012 + 1.14144i 0.980872 + 0.194655i \(0.0623587\pi\)
−0.321860 + 0.946787i \(0.604308\pi\)
\(152\) 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 −0.845383 0.534160i \(-0.820628\pi\)
0.885288 + 0.465044i \(0.153961\pi\)
\(158\) 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 \(-0.676908\pi\)
0.999482 + 0.0321676i \(0.0102410\pi\)
\(168\) 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 \(-0.287294\pi\)
−0.989558 + 0.144132i \(0.953961\pi\)
\(174\) 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 \(-0.400907\pi\)
0.306305 + 0.951934i \(0.400907\pi\)
\(180\) 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 \(-0.305287\pi\)
−0.996121 + 0.0879965i \(0.971954\pi\)
\(192\) 0 0
\(193\) 4.42820 7.66987i 0.318749 0.552090i −0.661478 0.749964i \(-0.730071\pi\)
0.980227 + 0.197875i \(0.0634039\pi\)
\(194\) −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 \(-0.870630\pi\)
−0.918539 + 0.395331i \(0.870630\pi\)
\(198\) 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 −0.249860 0.968282i \(-0.580385\pi\)
0.963487 0.267756i \(-0.0862820\pi\)
\(212\) 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 0.989369 + 0.145427i \(0.0464555\pi\)
−0.368741 + 0.929532i \(0.620211\pi\)
\(224\) 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 \(-0.112835\pi\)
−0.769514 + 0.638631i \(0.779501\pi\)
\(228\) 0 0
\(229\) −2.23205 + 3.86603i −0.147498 + 0.255474i −0.930302 0.366794i \(-0.880455\pi\)
0.782804 + 0.622268i \(0.213789\pi\)
\(230\) 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 \(-0.642282\pi\)
−0.432254 + 0.901752i \(0.642282\pi\)
\(234\) 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 −0.0894638 + 0.995990i \(0.528515\pi\)
−0.817821 + 0.575473i \(0.804818\pi\)
\(240\) 0 0
\(241\) 8.86603 + 15.3564i 0.571111 + 0.989193i 0.996452 + 0.0841601i \(0.0268207\pi\)
−0.425341 + 0.905033i \(0.639846\pi\)
\(242\) −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 \(-0.330897\pi\)
0.506614 + 0.862173i \(0.330897\pi\)
\(252\) 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 \(-0.828726\pi\)
0.873172 + 0.487412i \(0.162059\pi\)
\(258\) 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 0.957105 + 0.289743i \(0.0935698\pi\)
−0.227628 + 0.973748i \(0.573097\pi\)
\(264\) 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 \(-0.784821\pi\)
−0.780078 + 0.625682i \(0.784821\pi\)
\(270\) 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 −0.973595 0.228284i \(-0.926688\pi\)
0.289097 0.957300i \(-0.406645\pi\)
\(278\) 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 \(-0.140015\pi\)
−0.821176 + 0.570676i \(0.806681\pi\)
\(282\) 0 0
\(283\) 9.66025 16.7321i 0.574242 0.994617i −0.421881 0.906651i \(-0.638630\pi\)
0.996123 0.0879660i \(-0.0280367\pi\)
\(284\) −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 0.388795 + 0.921324i \(0.372891\pi\)
−0.992288 + 0.123955i \(0.960442\pi\)
\(294\) 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 \(-0.831563\pi\)
0.868793 + 0.495176i \(0.164896\pi\)
\(312\) 0 0
\(313\) 2.79423 + 4.83975i 0.157939 + 0.273559i 0.934125 0.356945i \(-0.116182\pi\)
−0.776186 + 0.630504i \(0.782848\pi\)
\(314\) 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 \(-0.0703825\pi\)
−0.677760 + 0.735283i \(0.737049\pi\)
\(318\) 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 0.957997 0.286778i \(-0.0925842\pi\)
−0.727356 + 0.686261i \(0.759251\pi\)
\(332\) −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 −0.919622 0.392805i \(-0.871505\pi\)
0.799990 + 0.600014i \(0.204838\pi\)
\(338\) −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 \(-0.960915\pi\)
0.602307 + 0.798265i \(0.294248\pi\)
\(348\) 0 0
\(349\) 2.73205 + 4.73205i 0.146243 + 0.253301i 0.929836 0.367974i \(-0.119948\pi\)
−0.783593 + 0.621275i \(0.786615\pi\)
\(350\) 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 \(-0.00765819\pi\)
−0.520689 + 0.853746i \(0.674325\pi\)
\(354\) 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 \(-0.475379\pi\)
0.0772723 + 0.997010i \(0.475379\pi\)
\(360\) 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 0.984904 0.173100i \(-0.0553785\pi\)
−0.642361 + 0.766402i \(0.722045\pi\)
\(368\) 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 0.0213627 0.999772i \(-0.493200\pi\)
0.855146 0.518387i \(-0.173467\pi\)
\(374\) −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 0.101784 0.994807i \(-0.467545\pi\)
0.810636 0.585551i \(-0.199122\pi\)
\(384\) 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 \(-0.113681\pi\)
−0.771209 + 0.636582i \(0.780348\pi\)
\(390\) 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 −0.00831121 0.999965i \(-0.502646\pi\)
0.870151 0.492785i \(-0.164021\pi\)
\(402\) 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 0.0179330 + 0.999839i \(0.494291\pi\)
−0.874853 + 0.484389i \(0.839042\pi\)
\(410\) 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 \(-0.813604\pi\)
0.895334 + 0.445395i \(0.146937\pi\)
\(420\) 0 0
\(421\) 12.0622 + 20.8923i 0.587875 + 1.01823i 0.994510 + 0.104638i \(0.0333685\pi\)
−0.406636 + 0.913590i \(0.633298\pi\)
\(422\) 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 \(-0.672931\pi\)
−0.516945 + 0.856019i \(0.672931\pi\)
\(432\) 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 0.968900 0.247453i \(-0.0795936\pi\)
−0.698751 + 0.715365i \(0.746260\pi\)
\(440\) 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 \(-0.0198727\pi\)
−0.553058 + 0.833142i \(0.686539\pi\)
\(444\) 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 \(-0.590258\pi\)
−0.279769 + 0.960067i \(0.590258\pi\)
\(450\) 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 0.512091 0.858931i \(-0.328871\pi\)
−0.999902 + 0.0140182i \(0.995538\pi\)
\(458\) −4.46410 −0.208594
\(459\) 0 0
\(460\) 23.1244 1.07818
\(461\) −17.3923 30.1244i −0.810040 1.40303i −0.912835 0.408329i \(-0.866112\pi\)
0.102795 0.994703i \(-0.467222\pi\)
\(462\) 0 0
\(463\) 16.2942 28.2224i 0.757257 1.31161i −0.186987 0.982362i \(-0.559872\pi\)
0.944244 0.329245i \(-0.106794\pi\)
\(464\) −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 \(-0.390406\pi\)
0.337537 + 0.941312i \(0.390406\pi\)
\(468\) 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 −0.999051 0.0435628i \(-0.986129\pi\)
0.461799 0.886985i \(-0.347204\pi\)
\(480\) 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 0.190214 + 0.981743i \(0.439082\pi\)
−0.945321 + 0.326141i \(0.894252\pi\)
\(492\) 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 0.300327 + 0.953836i \(0.402904\pi\)
−0.976210 + 0.216827i \(0.930429\pi\)
\(500\) −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 \(-0.486176\pi\)
0.0434161 + 0.999057i \(0.486176\pi\)
\(504\) 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 \(-0.862605\pi\)
0.816451 + 0.577415i \(0.195939\pi\)
\(510\) 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 \(-0.728243\pi\)
−0.657162 + 0.753749i \(0.728243\pi\)
\(522\) 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 0.995100 0.0988779i \(-0.0315253\pi\)
−0.583181 + 0.812343i \(0.698192\pi\)
\(548\) −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 \(-0.431553\pi\)
0.213378 + 0.976970i \(0.431553\pi\)
\(558\) 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 −0.194022 0.980997i \(-0.562153\pi\)
0.946579 0.322471i \(-0.104514\pi\)
\(564\) 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 \(-0.253156\pi\)
−0.968444 + 0.249230i \(0.919822\pi\)
\(570\) 0 0
\(571\) 9.63397 16.6865i 0.403169 0.698310i −0.590937 0.806718i \(-0.701242\pi\)
0.994107 + 0.108408i \(0.0345752\pi\)
\(572\) 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 \(-0.241370\pi\)
−0.958555 + 0.284909i \(0.908037\pi\)
\(588\) 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 \(-0.191212\pi\)
0.824934 + 0.565229i \(0.191212\pi\)
\(594\) 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 \(-0.893017\pi\)
0.757644 + 0.652668i \(0.226350\pi\)
\(600\) 0 0
\(601\) −4.40192 7.62436i −0.179558 0.311004i 0.762171 0.647376i \(-0.224133\pi\)
−0.941729 + 0.336372i \(0.890800\pi\)
\(602\) 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 −0.925103 0.379715i \(-0.876022\pi\)
0.791395 + 0.611305i \(0.209355\pi\)
\(608\) −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 −0.111655 0.993747i \(-0.535615\pi\)
0.916438 0.400177i \(-0.131051\pi\)
\(618\) 0 0
\(619\) −15.8564 27.4641i −0.637323 1.10388i −0.986018 0.166639i \(-0.946708\pi\)
0.348695 0.937236i \(-0.386625\pi\)
\(620\) −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 \(-0.0412085\pi\)
−0.607619 + 0.794229i \(0.707875\pi\)
\(642\) 0 0
\(643\) 20.2942 35.1506i 0.800326 1.38621i −0.119075 0.992885i \(-0.537993\pi\)
0.919401 0.393320i \(-0.128674\pi\)
\(644\) 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 \(-0.395570\pi\)
0.322224 + 0.946663i \(0.395570\pi\)
\(648\) 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 \(-0.949555\pi\)
0.630405 + 0.776266i \(0.282889\pi\)
\(654\) 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 \(-0.0683461\pi\)
−0.673042 + 0.739604i \(0.735013\pi\)
\(660\) 0 0
\(661\) −7.42820 + 12.8660i −0.288924 + 0.500430i −0.973553 0.228461i \(-0.926631\pi\)
0.684629 + 0.728891i \(0.259964\pi\)
\(662\) −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 0.664788 0.747032i \(-0.268522\pi\)
−0.979343 + 0.202207i \(0.935189\pi\)
\(674\) −4.39230 −0.169185
\(675\) 0 0
\(676\) −12.7846 −0.491716
\(677\) −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
\(679\) −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 \(-0.335284\pi\)
0.494684 + 0.869073i \(0.335284\pi\)
\(684\) 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 0.999276 + 0.0380440i \(0.0121127\pi\)
−0.466691 + 0.884420i \(0.654554\pi\)
\(692\) 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 \(-0.460176\pi\)
0.124785 + 0.992184i \(0.460176\pi\)
\(702\) 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 0.999463 + 0.0327760i \(0.0104348\pi\)
−0.471347 + 0.881948i \(0.656232\pi\)
\(710\) −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 \(-0.515057\pi\)
−0.0472865 + 0.998881i \(0.515057\pi\)
\(720\) 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 0.668906 0.743347i \(-0.266763\pi\)
−0.978210 + 0.207616i \(0.933429\pi\)
\(728\) 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 −0.959029 0.283307i \(-0.908569\pi\)
0.724865 + 0.688890i \(0.241902\pi\)
\(734\) −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 \(-0.716223\pi\)
0.987905 + 0.155058i \(0.0495565\pi\)
\(744\) 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 0.0950825 0.995469i \(-0.469688\pi\)
0.814561 0.580079i \(-0.196978\pi\)
\(752\) −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 0.307103 + 0.951676i \(0.400640\pi\)
−0.977727 + 0.209879i \(0.932693\pi\)
\(762\) 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 −0.343382 0.939196i \(-0.611573\pi\)
0.985058 0.172220i \(-0.0550941\pi\)
\(770\) 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 \(-0.382124\pi\)
0.361911 + 0.932213i \(0.382124\pi\)
\(774\) 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