Properties

Label 1638.2.bj.g.127.6
Level $1638$
Weight $2$
Character 1638.127
Analytic conductor $13.079$
Analytic rank $0$
Dimension $12$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1638,2,Mod(127,1638)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1638, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1638.127");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1638.bj (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(13.0794958511\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 6 x^{11} + 39 x^{10} - 140 x^{9} + 460 x^{8} - 1066 x^{7} + 2127 x^{6} - 3172 x^{5} + \cdots + 169 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 182)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 127.6
Root \(0.500000 + 2.47866i\) of defining polynomial
Character \(\chi\) \(=\) 1638.127
Dual form 1638.2.bj.g.1135.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +1.56356i q^{5} +(-0.866025 - 0.500000i) q^{7} -1.00000i q^{8} +O(q^{10})\) \(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +1.56356i q^{5} +(-0.866025 - 0.500000i) q^{7} -1.00000i q^{8} +(0.781779 + 1.35408i) q^{10} +(2.48215 - 1.43307i) q^{11} +(2.99598 - 2.00602i) q^{13} -1.00000 q^{14} +(-0.500000 - 0.866025i) q^{16} +(1.11481 - 1.93090i) q^{17} +(-6.26657 - 3.61801i) q^{19} +(1.35408 + 0.781779i) q^{20} +(1.43307 - 2.48215i) q^{22} +(0.833676 + 1.44397i) q^{23} +2.55529 q^{25} +(1.59158 - 3.23525i) q^{26} +(-0.866025 + 0.500000i) q^{28} +(2.41379 + 4.18080i) q^{29} +0.597963i q^{31} +(-0.866025 - 0.500000i) q^{32} -2.22961i q^{34} +(0.781779 - 1.35408i) q^{35} +(0.0333971 - 0.0192818i) q^{37} -7.23602 q^{38} +1.56356 q^{40} +(6.88896 - 3.97734i) q^{41} +(5.04571 - 8.73942i) q^{43} -2.86614i q^{44} +(1.44397 + 0.833676i) q^{46} +7.02636i q^{47} +(0.500000 + 0.866025i) q^{49} +(2.21294 - 1.27764i) q^{50} +(-0.239275 - 3.59760i) q^{52} +5.98404 q^{53} +(2.24069 + 3.88098i) q^{55} +(-0.500000 + 0.866025i) q^{56} +(4.18080 + 2.41379i) q^{58} +(-0.776138 - 0.448103i) q^{59} +(7.12846 - 12.3469i) q^{61} +(0.298982 + 0.517851i) q^{62} -1.00000 q^{64} +(3.13653 + 4.68438i) q^{65} +(-1.42103 + 0.820432i) q^{67} +(-1.11481 - 1.93090i) q^{68} -1.56356i q^{70} +(1.98724 + 1.14733i) q^{71} -11.2277i q^{73} +(0.0192818 - 0.0333971i) q^{74} +(-6.26657 + 3.61801i) q^{76} -2.86614 q^{77} +4.26098 q^{79} +(1.35408 - 0.781779i) q^{80} +(3.97734 - 6.88896i) q^{82} -4.94829i q^{83} +(3.01907 + 1.74306i) q^{85} -10.0914i q^{86} +(-1.43307 - 2.48215i) q^{88} +(-2.09682 + 1.21060i) q^{89} +(-3.59760 + 0.239275i) q^{91} +1.66735 q^{92} +(3.51318 + 6.08501i) q^{94} +(5.65696 - 9.79815i) q^{95} +(-4.23338 - 2.44414i) q^{97} +(0.866025 + 0.500000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 6 q^{4}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 6 q^{4} - 2 q^{10} + 18 q^{11} - 8 q^{13} - 12 q^{14} - 6 q^{16} - 4 q^{17} + 12 q^{19} - 2 q^{22} + 6 q^{23} - 24 q^{25} + 14 q^{26} + 10 q^{29} - 2 q^{35} - 6 q^{37} - 8 q^{38} - 4 q^{40} + 24 q^{41} + 26 q^{43} - 6 q^{46} + 6 q^{49} + 12 q^{50} - 4 q^{52} - 36 q^{53} - 6 q^{55} - 6 q^{56} + 24 q^{58} - 6 q^{59} - 28 q^{61} + 2 q^{62} - 12 q^{64} + 34 q^{65} - 42 q^{67} + 4 q^{68} - 48 q^{71} + 12 q^{76} + 4 q^{77} + 44 q^{79} + 6 q^{82} + 54 q^{85} + 2 q^{88} - 12 q^{89} - 16 q^{91} + 12 q^{92} + 8 q^{94} - 32 q^{95} + 60 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(379\) \(703\) \(911\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(1\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.866025 0.500000i 0.612372 0.353553i
\(3\) 0 0
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) 1.56356i 0.699244i 0.936891 + 0.349622i \(0.113690\pi\)
−0.936891 + 0.349622i \(0.886310\pi\)
\(6\) 0 0
\(7\) −0.866025 0.500000i −0.327327 0.188982i
\(8\) 1.00000i 0.353553i
\(9\) 0 0
\(10\) 0.781779 + 1.35408i 0.247220 + 0.428198i
\(11\) 2.48215 1.43307i 0.748396 0.432087i −0.0767180 0.997053i \(-0.524444\pi\)
0.825114 + 0.564966i \(0.191111\pi\)
\(12\) 0 0
\(13\) 2.99598 2.00602i 0.830935 0.556370i
\(14\) −1.00000 −0.267261
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 1.11481 1.93090i 0.270380 0.468312i −0.698579 0.715533i \(-0.746184\pi\)
0.968959 + 0.247221i \(0.0795173\pi\)
\(18\) 0 0
\(19\) −6.26657 3.61801i −1.43765 0.830028i −0.439964 0.898015i \(-0.645009\pi\)
−0.997686 + 0.0679872i \(0.978342\pi\)
\(20\) 1.35408 + 0.781779i 0.302782 + 0.174811i
\(21\) 0 0
\(22\) 1.43307 2.48215i 0.305531 0.529196i
\(23\) 0.833676 + 1.44397i 0.173833 + 0.301088i 0.939757 0.341843i \(-0.111051\pi\)
−0.765924 + 0.642932i \(0.777718\pi\)
\(24\) 0 0
\(25\) 2.55529 0.511058
\(26\) 1.59158 3.23525i 0.312135 0.634485i
\(27\) 0 0
\(28\) −0.866025 + 0.500000i −0.163663 + 0.0944911i
\(29\) 2.41379 + 4.18080i 0.448229 + 0.776356i 0.998271 0.0587816i \(-0.0187216\pi\)
−0.550042 + 0.835137i \(0.685388\pi\)
\(30\) 0 0
\(31\) 0.597963i 0.107397i 0.998557 + 0.0536987i \(0.0171010\pi\)
−0.998557 + 0.0536987i \(0.982899\pi\)
\(32\) −0.866025 0.500000i −0.153093 0.0883883i
\(33\) 0 0
\(34\) 2.22961i 0.382375i
\(35\) 0.781779 1.35408i 0.132145 0.228881i
\(36\) 0 0
\(37\) 0.0333971 0.0192818i 0.00549045 0.00316991i −0.497252 0.867606i \(-0.665658\pi\)
0.502743 + 0.864436i \(0.332324\pi\)
\(38\) −7.23602 −1.17384
\(39\) 0 0
\(40\) 1.56356 0.247220
\(41\) 6.88896 3.97734i 1.07588 0.621157i 0.146095 0.989271i \(-0.453330\pi\)
0.929781 + 0.368114i \(0.119996\pi\)
\(42\) 0 0
\(43\) 5.04571 8.73942i 0.769463 1.33275i −0.168391 0.985720i \(-0.553857\pi\)
0.937854 0.347029i \(-0.112809\pi\)
\(44\) 2.86614i 0.432087i
\(45\) 0 0
\(46\) 1.44397 + 0.833676i 0.212902 + 0.122919i
\(47\) 7.02636i 1.02490i 0.858717 + 0.512450i \(0.171262\pi\)
−0.858717 + 0.512450i \(0.828738\pi\)
\(48\) 0 0
\(49\) 0.500000 + 0.866025i 0.0714286 + 0.123718i
\(50\) 2.21294 1.27764i 0.312958 0.180686i
\(51\) 0 0
\(52\) −0.239275 3.59760i −0.0331814 0.498898i
\(53\) 5.98404 0.821971 0.410985 0.911642i \(-0.365185\pi\)
0.410985 + 0.911642i \(0.365185\pi\)
\(54\) 0 0
\(55\) 2.24069 + 3.88098i 0.302134 + 0.523312i
\(56\) −0.500000 + 0.866025i −0.0668153 + 0.115728i
\(57\) 0 0
\(58\) 4.18080 + 2.41379i 0.548966 + 0.316946i
\(59\) −0.776138 0.448103i −0.101044 0.0583381i 0.448626 0.893719i \(-0.351913\pi\)
−0.549671 + 0.835381i \(0.685247\pi\)
\(60\) 0 0
\(61\) 7.12846 12.3469i 0.912706 1.58085i 0.102481 0.994735i \(-0.467322\pi\)
0.810225 0.586119i \(-0.199345\pi\)
\(62\) 0.298982 + 0.517851i 0.0379707 + 0.0657672i
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 3.13653 + 4.68438i 0.389038 + 0.581026i
\(66\) 0 0
\(67\) −1.42103 + 0.820432i −0.173606 + 0.100232i −0.584285 0.811548i \(-0.698625\pi\)
0.410679 + 0.911780i \(0.365292\pi\)
\(68\) −1.11481 1.93090i −0.135190 0.234156i
\(69\) 0 0
\(70\) 1.56356i 0.186881i
\(71\) 1.98724 + 1.14733i 0.235841 + 0.136163i 0.613264 0.789878i \(-0.289856\pi\)
−0.377422 + 0.926041i \(0.623190\pi\)
\(72\) 0 0
\(73\) 11.2277i 1.31411i −0.753844 0.657054i \(-0.771802\pi\)
0.753844 0.657054i \(-0.228198\pi\)
\(74\) 0.0192818 0.0333971i 0.00224147 0.00388233i
\(75\) 0 0
\(76\) −6.26657 + 3.61801i −0.718825 + 0.415014i
\(77\) −2.86614 −0.326627
\(78\) 0 0
\(79\) 4.26098 0.479397 0.239699 0.970847i \(-0.422951\pi\)
0.239699 + 0.970847i \(0.422951\pi\)
\(80\) 1.35408 0.781779i 0.151391 0.0874055i
\(81\) 0 0
\(82\) 3.97734 6.88896i 0.439224 0.760759i
\(83\) 4.94829i 0.543145i −0.962418 0.271572i \(-0.912456\pi\)
0.962418 0.271572i \(-0.0875437\pi\)
\(84\) 0 0
\(85\) 3.01907 + 1.74306i 0.327465 + 0.189062i
\(86\) 10.0914i 1.08818i
\(87\) 0 0
\(88\) −1.43307 2.48215i −0.152766 0.264598i
\(89\) −2.09682 + 1.21060i −0.222263 + 0.128323i −0.606997 0.794704i \(-0.707626\pi\)
0.384735 + 0.923027i \(0.374293\pi\)
\(90\) 0 0
\(91\) −3.59760 + 0.239275i −0.377131 + 0.0250828i
\(92\) 1.66735 0.173833
\(93\) 0 0
\(94\) 3.51318 + 6.08501i 0.362357 + 0.627621i
\(95\) 5.65696 9.79815i 0.580392 1.00527i
\(96\) 0 0
\(97\) −4.23338 2.44414i −0.429835 0.248165i 0.269442 0.963017i \(-0.413161\pi\)
−0.699276 + 0.714852i \(0.746494\pi\)
\(98\) 0.866025 + 0.500000i 0.0874818 + 0.0505076i
\(99\) 0 0
\(100\) 1.27764 2.21294i 0.127764 0.221294i
\(101\) −3.68373 6.38042i −0.366545 0.634875i 0.622478 0.782638i \(-0.286126\pi\)
−0.989023 + 0.147763i \(0.952793\pi\)
\(102\) 0 0
\(103\) −5.78525 −0.570038 −0.285019 0.958522i \(-0.592000\pi\)
−0.285019 + 0.958522i \(0.592000\pi\)
\(104\) −2.00602 2.99598i −0.196706 0.293780i
\(105\) 0 0
\(106\) 5.18233 2.99202i 0.503352 0.290611i
\(107\) −0.514478 0.891102i −0.0497365 0.0861461i 0.840085 0.542454i \(-0.182505\pi\)
−0.889822 + 0.456308i \(0.849171\pi\)
\(108\) 0 0
\(109\) 14.1535i 1.35566i 0.735220 + 0.677829i \(0.237079\pi\)
−0.735220 + 0.677829i \(0.762921\pi\)
\(110\) 3.88098 + 2.24069i 0.370037 + 0.213641i
\(111\) 0 0
\(112\) 1.00000i 0.0944911i
\(113\) −6.77051 + 11.7269i −0.636916 + 1.10317i 0.349189 + 0.937052i \(0.386457\pi\)
−0.986106 + 0.166119i \(0.946876\pi\)
\(114\) 0 0
\(115\) −2.25773 + 1.30350i −0.210534 + 0.121552i
\(116\) 4.82757 0.448229
\(117\) 0 0
\(118\) −0.896206 −0.0825025
\(119\) −1.93090 + 1.11481i −0.177005 + 0.102194i
\(120\) 0 0
\(121\) −1.39263 + 2.41210i −0.126602 + 0.219282i
\(122\) 14.2569i 1.29076i
\(123\) 0 0
\(124\) 0.517851 + 0.298982i 0.0465044 + 0.0268493i
\(125\) 11.8131i 1.05660i
\(126\) 0 0
\(127\) 4.92583 + 8.53178i 0.437096 + 0.757073i 0.997464 0.0711707i \(-0.0226735\pi\)
−0.560368 + 0.828244i \(0.689340\pi\)
\(128\) −0.866025 + 0.500000i −0.0765466 + 0.0441942i
\(129\) 0 0
\(130\) 5.05850 + 2.48853i 0.443660 + 0.218259i
\(131\) −14.7923 −1.29241 −0.646204 0.763165i \(-0.723645\pi\)
−0.646204 + 0.763165i \(0.723645\pi\)
\(132\) 0 0
\(133\) 3.61801 + 6.26657i 0.313721 + 0.543381i
\(134\) −0.820432 + 1.42103i −0.0708746 + 0.122758i
\(135\) 0 0
\(136\) −1.93090 1.11481i −0.165573 0.0955938i
\(137\) −0.397503 0.229499i −0.0339610 0.0196074i 0.482923 0.875663i \(-0.339575\pi\)
−0.516884 + 0.856055i \(0.672908\pi\)
\(138\) 0 0
\(139\) −7.65731 + 13.2628i −0.649485 + 1.12494i 0.333762 + 0.942658i \(0.391682\pi\)
−0.983246 + 0.182283i \(0.941651\pi\)
\(140\) −0.781779 1.35408i −0.0660724 0.114441i
\(141\) 0 0
\(142\) 2.29466 0.192564
\(143\) 4.56170 9.27268i 0.381468 0.775421i
\(144\) 0 0
\(145\) −6.53693 + 3.77410i −0.542862 + 0.313422i
\(146\) −5.61387 9.72351i −0.464607 0.804723i
\(147\) 0 0
\(148\) 0.0385636i 0.00316991i
\(149\) −8.86563 5.11858i −0.726301 0.419330i 0.0907665 0.995872i \(-0.471068\pi\)
−0.817067 + 0.576542i \(0.804402\pi\)
\(150\) 0 0
\(151\) 15.2110i 1.23785i 0.785448 + 0.618927i \(0.212432\pi\)
−0.785448 + 0.618927i \(0.787568\pi\)
\(152\) −3.61801 + 6.26657i −0.293459 + 0.508286i
\(153\) 0 0
\(154\) −2.48215 + 1.43307i −0.200017 + 0.115480i
\(155\) −0.934950 −0.0750970
\(156\) 0 0
\(157\) −2.27419 −0.181500 −0.0907500 0.995874i \(-0.528926\pi\)
−0.0907500 + 0.995874i \(0.528926\pi\)
\(158\) 3.69011 2.13049i 0.293570 0.169493i
\(159\) 0 0
\(160\) 0.781779 1.35408i 0.0618050 0.107049i
\(161\) 1.66735i 0.131406i
\(162\) 0 0
\(163\) 0.00848066 + 0.00489631i 0.000664256 + 0.000383509i 0.500332 0.865834i \(-0.333211\pi\)
−0.499668 + 0.866217i \(0.666545\pi\)
\(164\) 7.95469i 0.621157i
\(165\) 0 0
\(166\) −2.47414 4.28534i −0.192031 0.332607i
\(167\) −21.6080 + 12.4754i −1.67208 + 0.965376i −0.705608 + 0.708603i \(0.749326\pi\)
−0.966472 + 0.256773i \(0.917341\pi\)
\(168\) 0 0
\(169\) 4.95177 12.0200i 0.380906 0.924614i
\(170\) 3.48613 0.267374
\(171\) 0 0
\(172\) −5.04571 8.73942i −0.384731 0.666374i
\(173\) 1.60275 2.77604i 0.121855 0.211058i −0.798644 0.601803i \(-0.794449\pi\)
0.920499 + 0.390745i \(0.127782\pi\)
\(174\) 0 0
\(175\) −2.21294 1.27764i −0.167283 0.0965808i
\(176\) −2.48215 1.43307i −0.187099 0.108022i
\(177\) 0 0
\(178\) −1.21060 + 2.09682i −0.0907383 + 0.157163i
\(179\) 7.89998 + 13.6832i 0.590472 + 1.02273i 0.994169 + 0.107835i \(0.0343917\pi\)
−0.403697 + 0.914893i \(0.632275\pi\)
\(180\) 0 0
\(181\) 9.11907 0.677815 0.338908 0.940820i \(-0.389943\pi\)
0.338908 + 0.940820i \(0.389943\pi\)
\(182\) −2.99598 + 2.00602i −0.222077 + 0.148696i
\(183\) 0 0
\(184\) 1.44397 0.833676i 0.106451 0.0614594i
\(185\) 0.0301482 + 0.0522183i 0.00221654 + 0.00383916i
\(186\) 0 0
\(187\) 6.39038i 0.467311i
\(188\) 6.08501 + 3.51318i 0.443795 + 0.256225i
\(189\) 0 0
\(190\) 11.3139i 0.820799i
\(191\) −1.63068 + 2.82443i −0.117992 + 0.204368i −0.918972 0.394323i \(-0.870979\pi\)
0.800980 + 0.598691i \(0.204312\pi\)
\(192\) 0 0
\(193\) 19.1158 11.0365i 1.37599 0.794426i 0.384313 0.923203i \(-0.374438\pi\)
0.991674 + 0.128777i \(0.0411051\pi\)
\(194\) −4.88829 −0.350959
\(195\) 0 0
\(196\) 1.00000 0.0714286
\(197\) 4.56660 2.63653i 0.325357 0.187845i −0.328421 0.944531i \(-0.606516\pi\)
0.653778 + 0.756687i \(0.273183\pi\)
\(198\) 0 0
\(199\) 4.43381 7.67958i 0.314304 0.544391i −0.664985 0.746857i \(-0.731562\pi\)
0.979289 + 0.202466i \(0.0648954\pi\)
\(200\) 2.55529i 0.180686i
\(201\) 0 0
\(202\) −6.38042 3.68373i −0.448924 0.259187i
\(203\) 4.82757i 0.338829i
\(204\) 0 0
\(205\) 6.21881 + 10.7713i 0.434340 + 0.752300i
\(206\) −5.01017 + 2.89263i −0.349075 + 0.201539i
\(207\) 0 0
\(208\) −3.23525 1.59158i −0.224324 0.110356i
\(209\) −20.7394 −1.43458
\(210\) 0 0
\(211\) −3.28453 5.68898i −0.226117 0.391646i 0.730537 0.682873i \(-0.239270\pi\)
−0.956654 + 0.291227i \(0.905936\pi\)
\(212\) 2.99202 5.18233i 0.205493 0.355924i
\(213\) 0 0
\(214\) −0.891102 0.514478i −0.0609145 0.0351690i
\(215\) 13.6646 + 7.88925i 0.931917 + 0.538043i
\(216\) 0 0
\(217\) 0.298982 0.517851i 0.0202962 0.0351540i
\(218\) 7.07674 + 12.2573i 0.479297 + 0.830167i
\(219\) 0 0
\(220\) 4.48137 0.302134
\(221\) −0.533490 8.02126i −0.0358864 0.539568i
\(222\) 0 0
\(223\) −14.6463 + 8.45606i −0.980790 + 0.566260i −0.902509 0.430672i \(-0.858277\pi\)
−0.0782817 + 0.996931i \(0.524943\pi\)
\(224\) 0.500000 + 0.866025i 0.0334077 + 0.0578638i
\(225\) 0 0
\(226\) 13.5410i 0.900736i
\(227\) 13.9709 + 8.06611i 0.927282 + 0.535367i 0.885951 0.463779i \(-0.153507\pi\)
0.0413312 + 0.999146i \(0.486840\pi\)
\(228\) 0 0
\(229\) 6.91184i 0.456747i 0.973574 + 0.228374i \(0.0733408\pi\)
−0.973574 + 0.228374i \(0.926659\pi\)
\(230\) −1.30350 + 2.25773i −0.0859502 + 0.148870i
\(231\) 0 0
\(232\) 4.18080 2.41379i 0.274483 0.158473i
\(233\) −7.47405 −0.489641 −0.244821 0.969568i \(-0.578729\pi\)
−0.244821 + 0.969568i \(0.578729\pi\)
\(234\) 0 0
\(235\) −10.9861 −0.716656
\(236\) −0.776138 + 0.448103i −0.0505222 + 0.0291690i
\(237\) 0 0
\(238\) −1.11481 + 1.93090i −0.0722621 + 0.125162i
\(239\) 19.8696i 1.28526i −0.766179 0.642628i \(-0.777844\pi\)
0.766179 0.642628i \(-0.222156\pi\)
\(240\) 0 0
\(241\) −9.21842 5.32226i −0.593811 0.342837i 0.172792 0.984958i \(-0.444721\pi\)
−0.766603 + 0.642121i \(0.778054\pi\)
\(242\) 2.78525i 0.179043i
\(243\) 0 0
\(244\) −7.12846 12.3469i −0.456353 0.790427i
\(245\) −1.35408 + 0.781779i −0.0865090 + 0.0499460i
\(246\) 0 0
\(247\) −26.0323 + 1.73140i −1.65640 + 0.110166i
\(248\) 0.597963 0.0379707
\(249\) 0 0
\(250\) 5.90656 + 10.2305i 0.373564 + 0.647032i
\(251\) −7.95696 + 13.7819i −0.502239 + 0.869904i 0.497757 + 0.867316i \(0.334157\pi\)
−0.999997 + 0.00258749i \(0.999176\pi\)
\(252\) 0 0
\(253\) 4.13861 + 2.38943i 0.260192 + 0.150222i
\(254\) 8.53178 + 4.92583i 0.535332 + 0.309074i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 15.5509 + 26.9350i 0.970039 + 1.68016i 0.695420 + 0.718603i \(0.255218\pi\)
0.274619 + 0.961553i \(0.411448\pi\)
\(258\) 0 0
\(259\) −0.0385636 −0.00239623
\(260\) 5.62506 0.374120i 0.348851 0.0232019i
\(261\) 0 0
\(262\) −12.8105 + 7.39614i −0.791435 + 0.456935i
\(263\) −14.1873 24.5732i −0.874829 1.51525i −0.856945 0.515408i \(-0.827640\pi\)
−0.0178837 0.999840i \(-0.505693\pi\)
\(264\) 0 0
\(265\) 9.35639i 0.574758i
\(266\) 6.26657 + 3.61801i 0.384228 + 0.221834i
\(267\) 0 0
\(268\) 1.64086i 0.100232i
\(269\) −10.7008 + 18.5344i −0.652441 + 1.13006i 0.330088 + 0.943950i \(0.392922\pi\)
−0.982529 + 0.186111i \(0.940412\pi\)
\(270\) 0 0
\(271\) 4.97667 2.87328i 0.302311 0.174539i −0.341170 0.940002i \(-0.610823\pi\)
0.643481 + 0.765462i \(0.277490\pi\)
\(272\) −2.22961 −0.135190
\(273\) 0 0
\(274\) −0.458997 −0.0277290
\(275\) 6.34260 3.66190i 0.382473 0.220821i
\(276\) 0 0
\(277\) 13.3010 23.0380i 0.799180 1.38422i −0.120971 0.992656i \(-0.538601\pi\)
0.920151 0.391564i \(-0.128066\pi\)
\(278\) 15.3146i 0.918510i
\(279\) 0 0
\(280\) −1.35408 0.781779i −0.0809218 0.0467202i
\(281\) 6.69143i 0.399177i −0.979880 0.199589i \(-0.936039\pi\)
0.979880 0.199589i \(-0.0639606\pi\)
\(282\) 0 0
\(283\) 9.96692 + 17.2632i 0.592472 + 1.02619i 0.993898 + 0.110300i \(0.0351812\pi\)
−0.401426 + 0.915891i \(0.631485\pi\)
\(284\) 1.98724 1.14733i 0.117921 0.0680816i
\(285\) 0 0
\(286\) −0.685794 10.3112i −0.0405519 0.609716i
\(287\) −7.95469 −0.469550
\(288\) 0 0
\(289\) 6.01442 + 10.4173i 0.353789 + 0.612781i
\(290\) −3.77410 + 6.53693i −0.221623 + 0.383861i
\(291\) 0 0
\(292\) −9.72351 5.61387i −0.569025 0.328527i
\(293\) 7.67375 + 4.43044i 0.448305 + 0.258829i 0.707114 0.707099i \(-0.249997\pi\)
−0.258809 + 0.965929i \(0.583330\pi\)
\(294\) 0 0
\(295\) 0.700635 1.21354i 0.0407926 0.0706548i
\(296\) −0.0192818 0.0333971i −0.00112073 0.00194117i
\(297\) 0 0
\(298\) −10.2372 −0.593022
\(299\) 5.39430 + 2.65373i 0.311961 + 0.153469i
\(300\) 0 0
\(301\) −8.73942 + 5.04571i −0.503732 + 0.290830i
\(302\) 7.60551 + 13.1731i 0.437648 + 0.758028i
\(303\) 0 0
\(304\) 7.23602i 0.415014i
\(305\) 19.3050 + 11.1458i 1.10540 + 0.638205i
\(306\) 0 0
\(307\) 8.34636i 0.476352i −0.971222 0.238176i \(-0.923450\pi\)
0.971222 0.238176i \(-0.0765495\pi\)
\(308\) −1.43307 + 2.48215i −0.0816567 + 0.141434i
\(309\) 0 0
\(310\) −0.809690 + 0.467475i −0.0459873 + 0.0265508i
\(311\) 6.68896 0.379296 0.189648 0.981852i \(-0.439265\pi\)
0.189648 + 0.981852i \(0.439265\pi\)
\(312\) 0 0
\(313\) −21.3788 −1.20840 −0.604199 0.796833i \(-0.706507\pi\)
−0.604199 + 0.796833i \(0.706507\pi\)
\(314\) −1.96950 + 1.13709i −0.111146 + 0.0641699i
\(315\) 0 0
\(316\) 2.13049 3.69011i 0.119849 0.207585i
\(317\) 31.6776i 1.77919i 0.456748 + 0.889596i \(0.349014\pi\)
−0.456748 + 0.889596i \(0.650986\pi\)
\(318\) 0 0
\(319\) 11.9828 + 6.91825i 0.670906 + 0.387348i
\(320\) 1.56356i 0.0874055i
\(321\) 0 0
\(322\) −0.833676 1.44397i −0.0464589 0.0804692i
\(323\) −13.9720 + 8.06675i −0.777424 + 0.448846i
\(324\) 0 0
\(325\) 7.65559 5.12596i 0.424656 0.284337i
\(326\) 0.00979262 0.000542363
\(327\) 0 0
\(328\) −3.97734 6.88896i −0.219612 0.380379i
\(329\) 3.51318 6.08501i 0.193688 0.335477i
\(330\) 0 0
\(331\) −21.3644 12.3347i −1.17429 0.677979i −0.219606 0.975589i \(-0.570477\pi\)
−0.954688 + 0.297609i \(0.903811\pi\)
\(332\) −4.28534 2.47414i −0.235189 0.135786i
\(333\) 0 0
\(334\) −12.4754 + 21.6080i −0.682624 + 1.18234i
\(335\) −1.28279 2.22186i −0.0700865 0.121393i
\(336\) 0 0
\(337\) 28.0871 1.53000 0.765002 0.644028i \(-0.222738\pi\)
0.765002 + 0.644028i \(0.222738\pi\)
\(338\) −1.72163 12.8855i −0.0936444 0.700879i
\(339\) 0 0
\(340\) 3.01907 1.74306i 0.163732 0.0945309i
\(341\) 0.856923 + 1.48423i 0.0464050 + 0.0803757i
\(342\) 0 0
\(343\) 1.00000i 0.0539949i
\(344\) −8.73942 5.04571i −0.471198 0.272046i
\(345\) 0 0
\(346\) 3.20550i 0.172329i
\(347\) −5.05398 + 8.75374i −0.271312 + 0.469926i −0.969198 0.246283i \(-0.920791\pi\)
0.697886 + 0.716209i \(0.254124\pi\)
\(348\) 0 0
\(349\) −15.0596 + 8.69465i −0.806121 + 0.465414i −0.845607 0.533806i \(-0.820761\pi\)
0.0394863 + 0.999220i \(0.487428\pi\)
\(350\) −2.55529 −0.136586
\(351\) 0 0
\(352\) −2.86614 −0.152766
\(353\) −2.88091 + 1.66329i −0.153335 + 0.0885282i −0.574704 0.818361i \(-0.694883\pi\)
0.421369 + 0.906889i \(0.361550\pi\)
\(354\) 0 0
\(355\) −1.79392 + 3.10716i −0.0952113 + 0.164911i
\(356\) 2.42120i 0.128323i
\(357\) 0 0
\(358\) 13.6832 + 7.89998i 0.723177 + 0.417527i
\(359\) 8.02414i 0.423498i −0.977324 0.211749i \(-0.932084\pi\)
0.977324 0.211749i \(-0.0679159\pi\)
\(360\) 0 0
\(361\) 16.6800 + 28.8905i 0.877893 + 1.52055i
\(362\) 7.89735 4.55954i 0.415075 0.239644i
\(363\) 0 0
\(364\) −1.59158 + 3.23525i −0.0834216 + 0.169573i
\(365\) 17.5552 0.918882
\(366\) 0 0
\(367\) −0.519540 0.899869i −0.0271198 0.0469728i 0.852147 0.523302i \(-0.175300\pi\)
−0.879267 + 0.476330i \(0.841967\pi\)
\(368\) 0.833676 1.44397i 0.0434583 0.0752721i
\(369\) 0 0
\(370\) 0.0522183 + 0.0301482i 0.00271470 + 0.00156733i
\(371\) −5.18233 2.99202i −0.269053 0.155338i
\(372\) 0 0
\(373\) −13.6562 + 23.6532i −0.707092 + 1.22472i 0.258840 + 0.965920i \(0.416660\pi\)
−0.965931 + 0.258798i \(0.916673\pi\)
\(374\) −3.19519 5.53423i −0.165219 0.286168i
\(375\) 0 0
\(376\) 7.02636 0.362357
\(377\) 15.6184 + 7.68349i 0.804390 + 0.395720i
\(378\) 0 0
\(379\) −1.91535 + 1.10583i −0.0983850 + 0.0568026i −0.548385 0.836226i \(-0.684757\pi\)
0.450000 + 0.893028i \(0.351424\pi\)
\(380\) −5.65696 9.79815i −0.290196 0.502634i
\(381\) 0 0
\(382\) 3.26137i 0.166866i
\(383\) −19.3458 11.1693i −0.988522 0.570724i −0.0836900 0.996492i \(-0.526671\pi\)
−0.904832 + 0.425768i \(0.860004\pi\)
\(384\) 0 0
\(385\) 4.48137i 0.228392i
\(386\) 11.0365 19.1158i 0.561744 0.972969i
\(387\) 0 0
\(388\) −4.23338 + 2.44414i −0.214917 + 0.124083i
\(389\) 12.2604 0.621629 0.310814 0.950471i \(-0.399398\pi\)
0.310814 + 0.950471i \(0.399398\pi\)
\(390\) 0 0
\(391\) 3.71755 0.188004
\(392\) 0.866025 0.500000i 0.0437409 0.0252538i
\(393\) 0 0
\(394\) 2.63653 4.56660i 0.132826 0.230062i
\(395\) 6.66228i 0.335216i
\(396\) 0 0
\(397\) 2.54193 + 1.46759i 0.127576 + 0.0736561i 0.562430 0.826845i \(-0.309867\pi\)
−0.434854 + 0.900501i \(0.643200\pi\)
\(398\) 8.86762i 0.444493i
\(399\) 0 0
\(400\) −1.27764 2.21294i −0.0638822 0.110647i
\(401\) −18.9229 + 10.9251i −0.944963 + 0.545575i −0.891513 0.452996i \(-0.850355\pi\)
−0.0534502 + 0.998571i \(0.517022\pi\)
\(402\) 0 0
\(403\) 1.19953 + 1.79148i 0.0597526 + 0.0892402i
\(404\) −7.36747 −0.366545
\(405\) 0 0
\(406\) −2.41379 4.18080i −0.119794 0.207490i
\(407\) 0.0552644 0.0957207i 0.00273935 0.00474470i
\(408\) 0 0
\(409\) −6.39292 3.69095i −0.316109 0.182506i 0.333548 0.942733i \(-0.391754\pi\)
−0.649657 + 0.760227i \(0.725088\pi\)
\(410\) 10.7713 + 6.21881i 0.531956 + 0.307125i
\(411\) 0 0
\(412\) −2.89263 + 5.01017i −0.142509 + 0.246834i
\(413\) 0.448103 + 0.776138i 0.0220497 + 0.0381912i
\(414\) 0 0
\(415\) 7.73693 0.379791
\(416\) −3.59760 + 0.239275i −0.176387 + 0.0117314i
\(417\) 0 0
\(418\) −17.9609 + 10.3697i −0.878495 + 0.507199i
\(419\) −4.29137 7.43287i −0.209647 0.363119i 0.741956 0.670448i \(-0.233898\pi\)
−0.951603 + 0.307329i \(0.900565\pi\)
\(420\) 0 0
\(421\) 7.49525i 0.365296i −0.983178 0.182648i \(-0.941533\pi\)
0.983178 0.182648i \(-0.0584669\pi\)
\(422\) −5.68898 3.28453i −0.276935 0.159889i
\(423\) 0 0
\(424\) 5.98404i 0.290611i
\(425\) 2.84865 4.93401i 0.138180 0.239334i
\(426\) 0 0
\(427\) −12.3469 + 7.12846i −0.597507 + 0.344971i
\(428\) −1.02896 −0.0497365
\(429\) 0 0
\(430\) 15.7785 0.760907
\(431\) 14.2713 8.23956i 0.687426 0.396886i −0.115221 0.993340i \(-0.536758\pi\)
0.802647 + 0.596454i \(0.203424\pi\)
\(432\) 0 0
\(433\) −12.7805 + 22.1365i −0.614192 + 1.06381i 0.376333 + 0.926484i \(0.377185\pi\)
−0.990526 + 0.137328i \(0.956149\pi\)
\(434\) 0.597963i 0.0287031i
\(435\) 0 0
\(436\) 12.2573 + 7.07674i 0.587017 + 0.338914i
\(437\) 12.0650i 0.577146i
\(438\) 0 0
\(439\) 4.60420 + 7.97470i 0.219746 + 0.380612i 0.954730 0.297473i \(-0.0961437\pi\)
−0.734984 + 0.678084i \(0.762810\pi\)
\(440\) 3.88098 2.24069i 0.185019 0.106821i
\(441\) 0 0
\(442\) −4.47264 6.67987i −0.212742 0.317729i
\(443\) 6.20759 0.294931 0.147466 0.989067i \(-0.452888\pi\)
0.147466 + 0.989067i \(0.452888\pi\)
\(444\) 0 0
\(445\) −1.89284 3.27850i −0.0897294 0.155416i
\(446\) −8.45606 + 14.6463i −0.400406 + 0.693523i
\(447\) 0 0
\(448\) 0.866025 + 0.500000i 0.0409159 + 0.0236228i
\(449\) −4.51968 2.60944i −0.213297 0.123147i 0.389546 0.921007i \(-0.372632\pi\)
−0.602843 + 0.797860i \(0.705965\pi\)
\(450\) 0 0
\(451\) 11.3996 19.7447i 0.536787 0.929743i
\(452\) 6.77051 + 11.7269i 0.318458 + 0.551586i
\(453\) 0 0
\(454\) 16.1322 0.757123
\(455\) −0.374120 5.62506i −0.0175390 0.263707i
\(456\) 0 0
\(457\) −29.3870 + 16.9666i −1.37467 + 0.793664i −0.991511 0.130021i \(-0.958496\pi\)
−0.383155 + 0.923684i \(0.625162\pi\)
\(458\) 3.45592 + 5.98583i 0.161484 + 0.279699i
\(459\) 0 0
\(460\) 2.60700i 0.121552i
\(461\) −0.731583 0.422380i −0.0340732 0.0196722i 0.482867 0.875694i \(-0.339596\pi\)
−0.516940 + 0.856022i \(0.672929\pi\)
\(462\) 0 0
\(463\) 6.50221i 0.302183i 0.988520 + 0.151092i \(0.0482789\pi\)
−0.988520 + 0.151092i \(0.951721\pi\)
\(464\) 2.41379 4.18080i 0.112057 0.194089i
\(465\) 0 0
\(466\) −6.47272 + 3.73702i −0.299843 + 0.173114i
\(467\) −9.52759 −0.440884 −0.220442 0.975400i \(-0.570750\pi\)
−0.220442 + 0.975400i \(0.570750\pi\)
\(468\) 0 0
\(469\) 1.64086 0.0757681
\(470\) −9.51426 + 5.49306i −0.438860 + 0.253376i
\(471\) 0 0
\(472\) −0.448103 + 0.776138i −0.0206256 + 0.0357246i
\(473\) 28.9234i 1.32990i
\(474\) 0 0
\(475\) −16.0129 9.24505i −0.734722 0.424192i
\(476\) 2.22961i 0.102194i
\(477\) 0 0
\(478\) −9.93478 17.2075i −0.454406 0.787055i
\(479\) 2.46123 1.42099i 0.112457 0.0649268i −0.442717 0.896662i \(-0.645985\pi\)
0.555173 + 0.831735i \(0.312652\pi\)
\(480\) 0 0
\(481\) 0.0613773 0.124763i 0.00279856 0.00568871i
\(482\) −10.6445 −0.484844
\(483\) 0 0
\(484\) 1.39263 + 2.41210i 0.0633011 + 0.109641i
\(485\) 3.82156 6.61913i 0.173528 0.300559i
\(486\) 0 0
\(487\) −4.55853 2.63187i −0.206567 0.119261i 0.393148 0.919475i \(-0.371386\pi\)
−0.599715 + 0.800214i \(0.704719\pi\)
\(488\) −12.3469 7.12846i −0.558916 0.322690i
\(489\) 0 0
\(490\) −0.781779 + 1.35408i −0.0353172 + 0.0611711i
\(491\) −11.4457 19.8245i −0.516536 0.894666i −0.999816 0.0192004i \(-0.993888\pi\)
0.483280 0.875466i \(-0.339445\pi\)
\(492\) 0 0
\(493\) 10.7636 0.484769
\(494\) −21.6789 + 14.5156i −0.975382 + 0.653087i
\(495\) 0 0
\(496\) 0.517851 0.298982i 0.0232522 0.0134247i
\(497\) −1.14733 1.98724i −0.0514648 0.0891397i
\(498\) 0 0
\(499\) 6.79877i 0.304355i −0.988353 0.152177i \(-0.951372\pi\)
0.988353 0.152177i \(-0.0486285\pi\)
\(500\) 10.2305 + 5.90656i 0.457520 + 0.264150i
\(501\) 0 0
\(502\) 15.9139i 0.710273i
\(503\) 5.40300 9.35827i 0.240908 0.417265i −0.720065 0.693906i \(-0.755888\pi\)
0.960973 + 0.276642i \(0.0892215\pi\)
\(504\) 0 0
\(505\) 9.97615 5.75973i 0.443933 0.256305i
\(506\) 4.77886 0.212446
\(507\) 0 0
\(508\) 9.85165 0.437096
\(509\) 23.6593 13.6597i 1.04868 0.605455i 0.126400 0.991979i \(-0.459658\pi\)
0.922279 + 0.386524i \(0.126324\pi\)
\(510\) 0 0
\(511\) −5.61387 + 9.72351i −0.248343 + 0.430143i
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) 26.9350 + 15.5509i 1.18805 + 0.685921i
\(515\) 9.04557i 0.398595i
\(516\) 0 0
\(517\) 10.0693 + 17.4405i 0.442846 + 0.767031i
\(518\) −0.0333971 + 0.0192818i −0.00146738 + 0.000847194i
\(519\) 0 0
\(520\) 4.68438 3.13653i 0.205424 0.137546i
\(521\) 3.63580 0.159287 0.0796437 0.996823i \(-0.474622\pi\)
0.0796437 + 0.996823i \(0.474622\pi\)
\(522\) 0 0
\(523\) 3.59223 + 6.22193i 0.157077 + 0.272066i 0.933813 0.357760i \(-0.116459\pi\)
−0.776736 + 0.629826i \(0.783126\pi\)
\(524\) −7.39614 + 12.8105i −0.323102 + 0.559629i
\(525\) 0 0
\(526\) −24.5732 14.1873i −1.07144 0.618597i
\(527\) 1.15461 + 0.666613i 0.0502955 + 0.0290381i
\(528\) 0 0
\(529\) 10.1100 17.5110i 0.439564 0.761347i
\(530\) 4.67819 + 8.10287i 0.203208 + 0.351966i
\(531\) 0 0
\(532\) 7.23602 0.313721
\(533\) 12.6606 25.7354i 0.548389 1.11473i
\(534\) 0 0
\(535\) 1.39329 0.804416i 0.0602371 0.0347779i
\(536\) 0.820432 + 1.42103i 0.0354373 + 0.0613792i
\(537\) 0 0
\(538\) 21.4017i 0.922691i
\(539\) 2.48215 + 1.43307i 0.106914 + 0.0617267i
\(540\) 0 0
\(541\) 0.445063i 0.0191347i −0.999954 0.00956737i \(-0.996955\pi\)
0.999954 0.00956737i \(-0.00304543\pi\)
\(542\) 2.87328 4.97667i 0.123418 0.213766i
\(543\) 0 0
\(544\) −1.93090 + 1.11481i −0.0827867 + 0.0477969i
\(545\) −22.1298 −0.947935
\(546\) 0 0
\(547\) −5.67129 −0.242487 −0.121243 0.992623i \(-0.538688\pi\)
−0.121243 + 0.992623i \(0.538688\pi\)
\(548\) −0.397503 + 0.229499i −0.0169805 + 0.00980370i
\(549\) 0 0
\(550\) 3.66190 6.34260i 0.156144 0.270450i
\(551\) 34.9324i 1.48817i
\(552\) 0 0
\(553\) −3.69011 2.13049i −0.156920 0.0905976i
\(554\) 26.6020i 1.13021i
\(555\) 0 0
\(556\) 7.65731 + 13.2628i 0.324742 + 0.562470i
\(557\) −22.9561 + 13.2537i −0.972683 + 0.561579i −0.900053 0.435780i \(-0.856472\pi\)
−0.0726298 + 0.997359i \(0.523139\pi\)
\(558\) 0 0
\(559\) −2.41462 36.3049i −0.102128 1.53553i
\(560\) −1.56356 −0.0660724
\(561\) 0 0
\(562\) −3.34571 5.79495i −0.141130 0.244445i
\(563\) 5.76880 9.99186i 0.243126 0.421107i −0.718477 0.695551i \(-0.755160\pi\)
0.961603 + 0.274444i \(0.0884938\pi\)
\(564\) 0 0
\(565\) −18.3356 10.5861i −0.771386 0.445360i
\(566\) 17.2632 + 9.96692i 0.725627 + 0.418941i
\(567\) 0 0
\(568\) 1.14733 1.98724i 0.0481409 0.0833826i
\(569\) 16.0791 + 27.8497i 0.674069 + 1.16752i 0.976740 + 0.214427i \(0.0687883\pi\)
−0.302671 + 0.953095i \(0.597878\pi\)
\(570\) 0 0
\(571\) −11.5540 −0.483521 −0.241761 0.970336i \(-0.577725\pi\)
−0.241761 + 0.970336i \(0.577725\pi\)
\(572\) −5.74953 8.58689i −0.240400 0.359036i
\(573\) 0 0
\(574\) −6.88896 + 3.97734i −0.287540 + 0.166011i
\(575\) 2.13028 + 3.68976i 0.0888389 + 0.153873i
\(576\) 0 0
\(577\) 9.14050i 0.380524i 0.981733 + 0.190262i \(0.0609337\pi\)
−0.981733 + 0.190262i \(0.939066\pi\)
\(578\) 10.4173 + 6.01442i 0.433301 + 0.250167i
\(579\) 0 0
\(580\) 7.54819i 0.313422i
\(581\) −2.47414 + 4.28534i −0.102645 + 0.177786i
\(582\) 0 0
\(583\) 14.8533 8.57554i 0.615160 0.355163i
\(584\) −11.2277 −0.464607
\(585\) 0 0
\(586\) 8.86088 0.366040
\(587\) −37.0629 + 21.3983i −1.52975 + 0.883201i −0.530378 + 0.847761i \(0.677950\pi\)
−0.999372 + 0.0354398i \(0.988717\pi\)
\(588\) 0 0
\(589\) 2.16344 3.74718i 0.0891428 0.154400i
\(590\) 1.40127i 0.0576894i
\(591\) 0 0
\(592\) −0.0333971 0.0192818i −0.00137261 0.000792478i
\(593\) 14.2439i 0.584927i 0.956277 + 0.292463i \(0.0944750\pi\)
−0.956277 + 0.292463i \(0.905525\pi\)
\(594\) 0 0
\(595\) −1.74306 3.01907i −0.0714586 0.123770i
\(596\) −8.86563 + 5.11858i −0.363150 + 0.209665i
\(597\) 0 0
\(598\) 5.99847 0.398955i 0.245296 0.0163145i
\(599\) −3.74735 −0.153113 −0.0765563 0.997065i \(-0.524392\pi\)
−0.0765563 + 0.997065i \(0.524392\pi\)
\(600\) 0 0
\(601\) −5.33462 9.23984i −0.217604 0.376901i 0.736471 0.676469i \(-0.236491\pi\)
−0.954075 + 0.299568i \(0.903157\pi\)
\(602\) −5.04571 + 8.73942i −0.205648 + 0.356192i
\(603\) 0 0
\(604\) 13.1731 + 7.60551i 0.536007 + 0.309464i
\(605\) −3.77145 2.17745i −0.153331 0.0885259i
\(606\) 0 0
\(607\) −4.82628 + 8.35936i −0.195893 + 0.339296i −0.947193 0.320665i \(-0.896094\pi\)
0.751300 + 0.659961i \(0.229427\pi\)
\(608\) 3.61801 + 6.26657i 0.146730 + 0.254143i
\(609\) 0 0
\(610\) 22.2915 0.902558
\(611\) 14.0950 + 21.0508i 0.570223 + 0.851625i
\(612\) 0 0
\(613\) −3.45968 + 1.99745i −0.139735 + 0.0806761i −0.568238 0.822864i \(-0.692375\pi\)
0.428503 + 0.903541i \(0.359041\pi\)
\(614\) −4.17318 7.22816i −0.168416 0.291705i
\(615\) 0 0
\(616\) 2.86614i 0.115480i
\(617\) −2.80199 1.61773i −0.112804 0.0651273i 0.442537 0.896750i \(-0.354079\pi\)
−0.555340 + 0.831623i \(0.687412\pi\)
\(618\) 0 0
\(619\) 39.2679i 1.57831i −0.614193 0.789156i \(-0.710518\pi\)
0.614193 0.789156i \(-0.289482\pi\)
\(620\) −0.467475 + 0.809690i −0.0187742 + 0.0325179i
\(621\) 0 0
\(622\) 5.79281 3.34448i 0.232270 0.134101i
\(623\) 2.42120 0.0970033
\(624\) 0 0
\(625\) −5.69406 −0.227763
\(626\) −18.5145 + 10.6894i −0.739990 + 0.427233i
\(627\) 0 0
\(628\) −1.13709 + 1.96950i −0.0453750 + 0.0785918i
\(629\) 0.0859819i 0.00342832i
\(630\) 0 0
\(631\) 25.4983 + 14.7215i 1.01507 + 0.586052i 0.912673 0.408691i \(-0.134015\pi\)
0.102400 + 0.994743i \(0.467348\pi\)
\(632\) 4.26098i 0.169493i
\(633\) 0 0
\(634\) 15.8388 + 27.4336i 0.629040 + 1.08953i
\(635\) −13.3399 + 7.70181i −0.529379 + 0.305637i
\(636\) 0 0
\(637\) 3.23525 + 1.59158i 0.128185 + 0.0630608i
\(638\) 13.8365 0.547792
\(639\) 0 0
\(640\) −0.781779 1.35408i −0.0309025 0.0535247i
\(641\) −2.04559 + 3.54307i −0.0807961 + 0.139943i −0.903592 0.428394i \(-0.859080\pi\)
0.822796 + 0.568337i \(0.192413\pi\)
\(642\) 0 0
\(643\) 19.2672 + 11.1239i 0.759825 + 0.438685i 0.829233 0.558903i \(-0.188778\pi\)
−0.0694080 + 0.997588i \(0.522111\pi\)
\(644\) −1.44397 0.833676i −0.0569003 0.0328514i
\(645\) 0 0
\(646\) −8.06675 + 13.9720i −0.317382 + 0.549722i
\(647\) 24.9292 + 43.1786i 0.980066 + 1.69752i 0.662086 + 0.749427i \(0.269671\pi\)
0.317980 + 0.948097i \(0.396996\pi\)
\(648\) 0 0
\(649\) −2.56865 −0.100828
\(650\) 4.06695 8.26700i 0.159519 0.324259i
\(651\) 0 0
\(652\) 0.00848066 0.00489631i 0.000332128 0.000191754i
\(653\) 3.70177 + 6.41165i 0.144861 + 0.250907i 0.929321 0.369272i \(-0.120393\pi\)
−0.784460 + 0.620180i \(0.787060\pi\)
\(654\) 0 0
\(655\) 23.1286i 0.903709i
\(656\) −6.88896 3.97734i −0.268969 0.155289i
\(657\) 0 0
\(658\) 7.02636i 0.273916i
\(659\) 15.0410 26.0518i 0.585914 1.01483i −0.408847 0.912603i \(-0.634069\pi\)
0.994761 0.102230i \(-0.0325977\pi\)
\(660\) 0 0
\(661\) 23.0639 13.3160i 0.897082 0.517931i 0.0208300 0.999783i \(-0.493369\pi\)
0.876252 + 0.481852i \(0.160036\pi\)
\(662\) −24.6695 −0.958807
\(663\) 0 0
\(664\) −4.94829 −0.192031
\(665\) −9.79815 + 5.65696i −0.379956 + 0.219368i
\(666\) 0 0
\(667\) −4.02463 + 6.97087i −0.155834 + 0.269913i
\(668\) 24.9508i 0.965376i
\(669\) 0 0
\(670\) −2.22186 1.28279i −0.0858380 0.0495586i
\(671\) 40.8623i 1.57747i
\(672\) 0 0
\(673\) −1.84652 3.19827i −0.0711783 0.123284i 0.828240 0.560374i \(-0.189343\pi\)
−0.899418 + 0.437090i \(0.856009\pi\)
\(674\) 24.3242 14.0436i 0.936932 0.540938i
\(675\) 0 0
\(676\) −7.93372 10.2984i −0.305143 0.396090i
\(677\) 35.6533 1.37027 0.685134 0.728417i \(-0.259744\pi\)
0.685134 + 0.728417i \(0.259744\pi\)
\(678\) 0 0
\(679\) 2.44414 + 4.23338i 0.0937976 + 0.162462i
\(680\) 1.74306 3.01907i 0.0668434 0.115776i
\(681\) 0 0
\(682\) 1.48423 + 0.856923i 0.0568342 + 0.0328133i
\(683\) 26.2105 + 15.1326i 1.00292 + 0.579034i 0.909110 0.416557i \(-0.136763\pi\)
0.0938062 + 0.995590i \(0.470097\pi\)
\(684\) 0 0
\(685\) 0.358834 0.621519i 0.0137104 0.0237470i
\(686\) −0.500000 0.866025i −0.0190901 0.0330650i
\(687\) 0 0
\(688\) −10.0914 −0.384731
\(689\) 17.9280 12.0041i 0.683004 0.457320i
\(690\) 0 0
\(691\) 3.03377 1.75155i 0.115410 0.0666320i −0.441184 0.897417i \(-0.645441\pi\)
0.556594 + 0.830785i \(0.312108\pi\)
\(692\) −1.60275 2.77604i −0.0609273 0.105529i
\(693\) 0 0
\(694\) 10.1080i 0.383693i
\(695\) −20.7372 11.9726i −0.786608 0.454148i
\(696\) 0 0
\(697\) 17.7359i 0.671794i
\(698\) −8.69465 + 15.0596i −0.329097 + 0.570013i
\(699\) 0 0
\(700\) −2.21294 + 1.27764i −0.0836414 + 0.0482904i
\(701\) 45.2243 1.70810 0.854048 0.520194i \(-0.174140\pi\)
0.854048 + 0.520194i \(0.174140\pi\)
\(702\) 0 0
\(703\) −0.279047 −0.0105245
\(704\) −2.48215 + 1.43307i −0.0935495 + 0.0540108i
\(705\) 0 0
\(706\) −1.66329 + 2.88091i −0.0625989 + 0.108424i
\(707\) 7.36747i 0.277082i
\(708\) 0 0
\(709\) 2.59657 + 1.49913i 0.0975161 + 0.0563009i 0.547965 0.836501i \(-0.315403\pi\)
−0.450449 + 0.892802i \(0.648736\pi\)
\(710\) 3.58784i 0.134649i
\(711\) 0 0
\(712\) 1.21060 + 2.09682i 0.0453692 + 0.0785817i
\(713\) −0.863440 + 0.498507i −0.0323361 + 0.0186692i
\(714\) 0 0
\(715\) 14.4984 + 7.13248i 0.542208 + 0.266740i
\(716\) 15.8000 0.590472
\(717\) 0 0
\(718\) −4.01207 6.94911i −0.149729 0.259339i
\(719\) 10.0397 17.3892i 0.374417 0.648509i −0.615823 0.787885i \(-0.711176\pi\)
0.990240 + 0.139376i \(0.0445096\pi\)
\(720\) 0 0
\(721\) 5.01017 + 2.89263i 0.186589 + 0.107727i
\(722\) 28.8905 + 16.6800i 1.07519 + 0.620764i
\(723\) 0 0
\(724\) 4.55954 7.89735i 0.169454 0.293503i
\(725\) 6.16792 + 10.6832i 0.229071 + 0.396762i
\(726\) 0 0
\(727\) −32.5895 −1.20868 −0.604338 0.796728i \(-0.706562\pi\)
−0.604338 + 0.796728i \(0.706562\pi\)
\(728\) 0.239275 + 3.59760i 0.00886811 + 0.133336i
\(729\) 0 0
\(730\) 15.2033 8.77761i 0.562698 0.324874i
\(731\) −11.2500 19.4855i −0.416095 0.720698i
\(732\) 0 0
\(733\) 18.5190i 0.684017i 0.939697 + 0.342008i \(0.111107\pi\)
−0.939697 + 0.342008i \(0.888893\pi\)
\(734\) −0.899869 0.519540i −0.0332148 0.0191766i
\(735\) 0 0
\(736\) 1.66735i 0.0614594i
\(737\) −2.35147 + 4.07287i −0.0866176 + 0.150026i
\(738\) 0 0
\(739\) 13.7968 7.96559i 0.507524 0.293019i −0.224291 0.974522i \(-0.572007\pi\)
0.731815 + 0.681503i \(0.238673\pi\)
\(740\) 0.0602965 0.00221654
\(741\) 0 0
\(742\) −5.98404 −0.219681
\(743\) −10.5962 + 6.11773i −0.388738 + 0.224438i −0.681613 0.731713i \(-0.738721\pi\)
0.292875 + 0.956151i \(0.405388\pi\)
\(744\) 0 0
\(745\) 8.00319 13.8619i 0.293214 0.507862i
\(746\) 27.3124i 0.999979i
\(747\) 0 0
\(748\) −5.53423 3.19519i −0.202351 0.116828i
\(749\) 1.02896i 0.0375972i
\(750\) 0 0
\(751\) −10.4107 18.0318i −0.379891 0.657990i 0.611155 0.791511i \(-0.290705\pi\)
−0.991046 + 0.133521i \(0.957372\pi\)
\(752\) 6.08501 3.51318i 0.221897 0.128113i
\(753\) 0 0
\(754\) 17.3677 1.15512i 0.632494 0.0420669i
\(755\) −23.7833 −0.865563
\(756\) 0 0
\(757\) −13.5575 23.4823i −0.492757 0.853480i 0.507208 0.861824i \(-0.330678\pi\)
−0.999965 + 0.00834344i \(0.997344\pi\)
\(758\) −1.10583 + 1.91535i −0.0401655 + 0.0695687i
\(759\) 0 0
\(760\) −9.79815 5.65696i −0.355416 0.205200i
\(761\) −41.8920 24.1864i −1.51858 0.876755i −0.999761 0.0218739i \(-0.993037\pi\)
−0.518824 0.854881i \(-0.673630\pi\)
\(762\) 0 0
\(763\) 7.07674 12.2573i 0.256195 0.443743i
\(764\) 1.63068 + 2.82443i 0.0589961 + 0.102184i
\(765\) 0 0
\(766\) −22.3386 −0.807125
\(767\) −3.22419 + 0.214439i −0.116419 + 0.00774296i
\(768\) 0 0
\(769\) −15.0214 + 8.67264i −0.541687 + 0.312743i −0.745762 0.666212i \(-0.767915\pi\)
0.204075 + 0.978955i \(0.434581\pi\)
\(770\) −2.24069 3.88098i −0.0807487 0.139861i
\(771\) 0 0
\(772\) 22.0730i 0.794426i
\(773\) 12.1659 + 7.02398i 0.437576 + 0.252635i 0.702569 0.711616i \(-0.252036\pi\)
−0.264993 + 0.964250i \(0.585370\pi\)
\(774\) 0 0
\(775\) 1.52797i 0.0548862i
\(776\) −2.44414 + 4.23338i −0.0877396 + 0.151970i
\(777\) 0 0
\(778\) 10.6178 6.13022i 0.380668 0.219779i
\(779\) −57.5603 −2.06231
\(780\) 0 0
\(781\) 6.57682 0.235337
\(782\)