Properties

Label 572.2.e.a.131.7
Level $572$
Weight $2$
Character 572.131
Analytic conductor $4.567$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [572,2,Mod(131,572)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(572, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("572.131");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 572.e (of order \(2\), degree \(1\), 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: \(4.56744299562\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: 8.0.342102016.5
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} + x^{6} + 4x^{4} + 4x^{2} + 16 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 131.7
Root \(1.17915 + 0.780776i\) of defining polynomial
Character \(\chi\) \(=\) 572.131
Dual form 572.2.e.a.131.8

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.17915 - 0.780776i) q^{2} +(0.780776 - 1.84130i) q^{4} -3.56155 q^{5} +4.05444 q^{7} +(-0.516994 - 2.78078i) q^{8} +3.00000 q^{9} +O(q^{10})\) \(q+(1.17915 - 0.780776i) q^{2} +(0.780776 - 1.84130i) q^{4} -3.56155 q^{5} +4.05444 q^{7} +(-0.516994 - 2.78078i) q^{8} +3.00000 q^{9} +(-4.19960 + 2.78078i) q^{10} +(-0.848071 - 3.20636i) q^{11} +1.00000i q^{13} +(4.78078 - 3.16561i) q^{14} +(-2.78078 - 2.87529i) q^{16} -5.12311i q^{17} +(3.53744 - 2.34233i) q^{18} -4.34475 q^{19} +(-2.78078 + 6.55789i) q^{20} +(-3.50345 - 3.11862i) q^{22} +2.35829i q^{23} +7.68466 q^{25} +(0.780776 + 1.17915i) q^{26} +(3.16561 - 7.46543i) q^{28} -6.68466i q^{29} -0.371834i q^{31} +(-5.52390 - 1.21922i) q^{32} +(-4.00000 - 6.04090i) q^{34} -14.4401 q^{35} +(2.34233 - 5.52390i) q^{36} +8.24621 q^{37} +(-5.12311 + 3.39228i) q^{38} +(1.84130 + 9.90388i) q^{40} +4.43845i q^{41} -1.03399 q^{43} +(-6.56604 - 0.941901i) q^{44} -10.6847 q^{45} +(1.84130 + 2.78078i) q^{46} +6.41273i q^{47} +9.43845 q^{49} +(9.06134 - 6.00000i) q^{50} +(1.84130 + 0.780776i) q^{52} +12.2462 q^{53} +(3.02045 + 11.4196i) q^{55} +(-2.09612 - 11.2745i) q^{56} +(-5.21922 - 7.88220i) q^{58} -4.05444i q^{59} +12.6847i q^{61} +(-0.290319 - 0.438447i) q^{62} +12.1633 q^{63} +(-7.46543 + 2.87529i) q^{64} -3.56155i q^{65} +14.0683i q^{67} +(-9.43318 - 4.00000i) q^{68} +(-17.0270 + 11.2745i) q^{70} +13.7779i q^{71} +(-1.55098 - 8.34233i) q^{72} +5.80776i q^{73} +(9.72350 - 6.43845i) q^{74} +(-3.39228 + 8.00000i) q^{76} +(-3.43845 - 13.0000i) q^{77} -1.32431 q^{79} +(9.90388 + 10.2405i) q^{80} +9.00000 q^{81} +(3.46543 + 5.23358i) q^{82} -1.69614 q^{83} +18.2462i q^{85} +(-1.21922 + 0.807313i) q^{86} +(-8.47774 + 4.01597i) q^{88} -2.00000 q^{89} +(-12.5988 + 8.34233i) q^{90} +4.05444i q^{91} +(4.34233 + 1.84130i) q^{92} +(5.00691 + 7.56155i) q^{94} +15.4741 q^{95} -4.24621 q^{97} +(11.1293 - 7.36932i) q^{98} +(-2.54421 - 9.61909i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 2 q^{4} - 12 q^{5} + 24 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 2 q^{4} - 12 q^{5} + 24 q^{9} + 30 q^{14} - 14 q^{16} - 14 q^{20} - 8 q^{22} + 12 q^{25} - 2 q^{26} - 32 q^{34} - 6 q^{36} - 8 q^{38} - 6 q^{44} - 36 q^{45} + 92 q^{49} + 32 q^{53} - 58 q^{56} - 50 q^{58} - 2 q^{64} - 62 q^{70} - 44 q^{77} + 38 q^{80} + 72 q^{81} - 30 q^{82} - 18 q^{86} + 20 q^{88} - 16 q^{89} + 10 q^{92} + 32 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/572\mathbb{Z}\right)^\times\).

\(n\) \(287\) \(353\) \(365\)
\(\chi(n)\) \(-1\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.17915 0.780776i 0.833783 0.552092i
\(3\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(4\) 0.780776 1.84130i 0.390388 0.920650i
\(5\) −3.56155 −1.59277 −0.796387 0.604787i \(-0.793258\pi\)
−0.796387 + 0.604787i \(0.793258\pi\)
\(6\) 0 0
\(7\) 4.05444 1.53243 0.766216 0.642583i \(-0.222137\pi\)
0.766216 + 0.642583i \(0.222137\pi\)
\(8\) −0.516994 2.78078i −0.182785 0.983153i
\(9\) 3.00000 1.00000
\(10\) −4.19960 + 2.78078i −1.32803 + 0.879359i
\(11\) −0.848071 3.20636i −0.255703 0.966755i
\(12\) 0 0
\(13\) 1.00000i 0.277350i
\(14\) 4.78078 3.16561i 1.27772 0.846044i
\(15\) 0 0
\(16\) −2.78078 2.87529i −0.695194 0.718822i
\(17\) 5.12311i 1.24254i −0.783598 0.621268i \(-0.786618\pi\)
0.783598 0.621268i \(-0.213382\pi\)
\(18\) 3.53744 2.34233i 0.833783 0.552092i
\(19\) −4.34475 −0.996755 −0.498378 0.866960i \(-0.666071\pi\)
−0.498378 + 0.866960i \(0.666071\pi\)
\(20\) −2.78078 + 6.55789i −0.621801 + 1.46639i
\(21\) 0 0
\(22\) −3.50345 3.11862i −0.746939 0.664893i
\(23\) 2.35829i 0.491738i 0.969303 + 0.245869i \(0.0790734\pi\)
−0.969303 + 0.245869i \(0.920927\pi\)
\(24\) 0 0
\(25\) 7.68466 1.53693
\(26\) 0.780776 + 1.17915i 0.153123 + 0.231250i
\(27\) 0 0
\(28\) 3.16561 7.46543i 0.598244 1.41083i
\(29\) 6.68466i 1.24131i −0.784084 0.620655i \(-0.786867\pi\)
0.784084 0.620655i \(-0.213133\pi\)
\(30\) 0 0
\(31\) 0.371834i 0.0667834i −0.999442 0.0333917i \(-0.989369\pi\)
0.999442 0.0333917i \(-0.0106309\pi\)
\(32\) −5.52390 1.21922i −0.976497 0.215530i
\(33\) 0 0
\(34\) −4.00000 6.04090i −0.685994 1.03601i
\(35\) −14.4401 −2.44082
\(36\) 2.34233 5.52390i 0.390388 0.920650i
\(37\) 8.24621 1.35567 0.677834 0.735215i \(-0.262919\pi\)
0.677834 + 0.735215i \(0.262919\pi\)
\(38\) −5.12311 + 3.39228i −0.831077 + 0.550301i
\(39\) 0 0
\(40\) 1.84130 + 9.90388i 0.291135 + 1.56594i
\(41\) 4.43845i 0.693169i 0.938019 + 0.346584i \(0.112659\pi\)
−0.938019 + 0.346584i \(0.887341\pi\)
\(42\) 0 0
\(43\) −1.03399 −0.157682 −0.0788408 0.996887i \(-0.525122\pi\)
−0.0788408 + 0.996887i \(0.525122\pi\)
\(44\) −6.56604 0.941901i −0.989867 0.141997i
\(45\) −10.6847 −1.59277
\(46\) 1.84130 + 2.78078i 0.271485 + 0.410003i
\(47\) 6.41273i 0.935393i 0.883889 + 0.467696i \(0.154916\pi\)
−0.883889 + 0.467696i \(0.845084\pi\)
\(48\) 0 0
\(49\) 9.43845 1.34835
\(50\) 9.06134 6.00000i 1.28147 0.848528i
\(51\) 0 0
\(52\) 1.84130 + 0.780776i 0.255342 + 0.108274i
\(53\) 12.2462 1.68215 0.841073 0.540921i \(-0.181924\pi\)
0.841073 + 0.540921i \(0.181924\pi\)
\(54\) 0 0
\(55\) 3.02045 + 11.4196i 0.407277 + 1.53982i
\(56\) −2.09612 11.2745i −0.280106 1.50662i
\(57\) 0 0
\(58\) −5.21922 7.88220i −0.685318 1.03498i
\(59\) 4.05444i 0.527843i −0.964544 0.263921i \(-0.914984\pi\)
0.964544 0.263921i \(-0.0850159\pi\)
\(60\) 0 0
\(61\) 12.6847i 1.62410i 0.583585 + 0.812052i \(0.301649\pi\)
−0.583585 + 0.812052i \(0.698351\pi\)
\(62\) −0.290319 0.438447i −0.0368706 0.0556828i
\(63\) 12.1633 1.53243
\(64\) −7.46543 + 2.87529i −0.933179 + 0.359411i
\(65\) 3.56155i 0.441756i
\(66\) 0 0
\(67\) 14.0683i 1.71871i 0.511379 + 0.859355i \(0.329135\pi\)
−0.511379 + 0.859355i \(0.670865\pi\)
\(68\) −9.43318 4.00000i −1.14394 0.485071i
\(69\) 0 0
\(70\) −17.0270 + 11.2745i −2.03511 + 1.34756i
\(71\) 13.7779i 1.63514i 0.575829 + 0.817570i \(0.304679\pi\)
−0.575829 + 0.817570i \(0.695321\pi\)
\(72\) −1.55098 8.34233i −0.182785 0.983153i
\(73\) 5.80776i 0.679747i 0.940471 + 0.339874i \(0.110384\pi\)
−0.940471 + 0.339874i \(0.889616\pi\)
\(74\) 9.72350 6.43845i 1.13033 0.748454i
\(75\) 0 0
\(76\) −3.39228 + 8.00000i −0.389121 + 0.917663i
\(77\) −3.43845 13.0000i −0.391847 1.48149i
\(78\) 0 0
\(79\) −1.32431 −0.148996 −0.0744981 0.997221i \(-0.523735\pi\)
−0.0744981 + 0.997221i \(0.523735\pi\)
\(80\) 9.90388 + 10.2405i 1.10729 + 1.14492i
\(81\) 9.00000 1.00000
\(82\) 3.46543 + 5.23358i 0.382693 + 0.577953i
\(83\) −1.69614 −0.186176 −0.0930878 0.995658i \(-0.529674\pi\)
−0.0930878 + 0.995658i \(0.529674\pi\)
\(84\) 0 0
\(85\) 18.2462i 1.97908i
\(86\) −1.21922 + 0.807313i −0.131472 + 0.0870548i
\(87\) 0 0
\(88\) −8.47774 + 4.01597i −0.903730 + 0.428103i
\(89\) −2.00000 −0.212000 −0.106000 0.994366i \(-0.533804\pi\)
−0.106000 + 0.994366i \(0.533804\pi\)
\(90\) −12.5988 + 8.34233i −1.32803 + 0.879359i
\(91\) 4.05444i 0.425020i
\(92\) 4.34233 + 1.84130i 0.452719 + 0.191969i
\(93\) 0 0
\(94\) 5.00691 + 7.56155i 0.516423 + 0.779915i
\(95\) 15.4741 1.58761
\(96\) 0 0
\(97\) −4.24621 −0.431137 −0.215569 0.976489i \(-0.569161\pi\)
−0.215569 + 0.976489i \(0.569161\pi\)
\(98\) 11.1293 7.36932i 1.12423 0.744413i
\(99\) −2.54421 9.61909i −0.255703 0.966755i
\(100\) 6.00000 14.1498i 0.600000 1.41498i
\(101\) 4.87689i 0.485269i −0.970118 0.242635i \(-0.921988\pi\)
0.970118 0.242635i \(-0.0780116\pi\)
\(102\) 0 0
\(103\) 16.5081i 1.62659i −0.581853 0.813294i \(-0.697672\pi\)
0.581853 0.813294i \(-0.302328\pi\)
\(104\) 2.78078 0.516994i 0.272678 0.0506954i
\(105\) 0 0
\(106\) 14.4401 9.56155i 1.40255 0.928700i
\(107\) −14.4401 −1.39598 −0.697988 0.716110i \(-0.745921\pi\)
−0.697988 + 0.716110i \(0.745921\pi\)
\(108\) 0 0
\(109\) 2.00000i 0.191565i −0.995402 0.0957826i \(-0.969465\pi\)
0.995402 0.0957826i \(-0.0305354\pi\)
\(110\) 12.4777 + 11.1071i 1.18971 + 1.05902i
\(111\) 0 0
\(112\) −11.2745 11.6577i −1.06534 1.10155i
\(113\) −4.68466 −0.440696 −0.220348 0.975421i \(-0.570719\pi\)
−0.220348 + 0.975421i \(0.570719\pi\)
\(114\) 0 0
\(115\) 8.39919i 0.783229i
\(116\) −12.3085 5.21922i −1.14281 0.484593i
\(117\) 3.00000i 0.277350i
\(118\) −3.16561 4.78078i −0.291418 0.440106i
\(119\) 20.7713i 1.90410i
\(120\) 0 0
\(121\) −9.56155 + 5.43845i −0.869232 + 0.494404i
\(122\) 9.90388 + 14.9571i 0.896655 + 1.35415i
\(123\) 0 0
\(124\) −0.684658 0.290319i −0.0614841 0.0260714i
\(125\) −9.56155 −0.855211
\(126\) 14.3423 9.49682i 1.27772 0.846044i
\(127\) 19.4470 1.72564 0.862821 0.505510i \(-0.168696\pi\)
0.862821 + 0.505510i \(0.168696\pi\)
\(128\) −6.55789 + 9.21922i −0.579641 + 0.814872i
\(129\) 0 0
\(130\) −2.78078 4.19960i −0.243890 0.368329i
\(131\) 7.65552 0.668866 0.334433 0.942420i \(-0.391455\pi\)
0.334433 + 0.942420i \(0.391455\pi\)
\(132\) 0 0
\(133\) −17.6155 −1.52746
\(134\) 10.9842 + 16.5885i 0.948887 + 1.43303i
\(135\) 0 0
\(136\) −14.2462 + 2.64861i −1.22160 + 0.227117i
\(137\) 3.36932 0.287860 0.143930 0.989588i \(-0.454026\pi\)
0.143930 + 0.989588i \(0.454026\pi\)
\(138\) 0 0
\(139\) −5.46026 −0.463133 −0.231566 0.972819i \(-0.574385\pi\)
−0.231566 + 0.972819i \(0.574385\pi\)
\(140\) −11.2745 + 26.5885i −0.952867 + 2.24714i
\(141\) 0 0
\(142\) 10.7575 + 16.2462i 0.902748 + 1.36335i
\(143\) 3.20636 0.848071i 0.268130 0.0709192i
\(144\) −8.34233 8.62586i −0.695194 0.718822i
\(145\) 23.8078i 1.97713i
\(146\) 4.53457 + 6.84821i 0.375283 + 0.566762i
\(147\) 0 0
\(148\) 6.43845 15.1838i 0.529237 1.24810i
\(149\) 14.4924i 1.18727i −0.804736 0.593633i \(-0.797693\pi\)
0.804736 0.593633i \(-0.202307\pi\)
\(150\) 0 0
\(151\) −21.1431 −1.72060 −0.860302 0.509785i \(-0.829725\pi\)
−0.860302 + 0.509785i \(0.829725\pi\)
\(152\) 2.24621 + 12.0818i 0.182192 + 0.979963i
\(153\) 15.3693i 1.24254i
\(154\) −14.2045 12.6443i −1.14463 1.01890i
\(155\) 1.32431i 0.106371i
\(156\) 0 0
\(157\) 8.00000 0.638470 0.319235 0.947676i \(-0.396574\pi\)
0.319235 + 0.947676i \(0.396574\pi\)
\(158\) −1.56155 + 1.03399i −0.124230 + 0.0822596i
\(159\) 0 0
\(160\) 19.6737 + 4.34233i 1.55534 + 0.343291i
\(161\) 9.56155i 0.753556i
\(162\) 10.6123 7.02699i 0.833783 0.552092i
\(163\) 1.98646i 0.155592i −0.996969 0.0777958i \(-0.975212\pi\)
0.996969 0.0777958i \(-0.0247882\pi\)
\(164\) 8.17252 + 3.46543i 0.638166 + 0.270605i
\(165\) 0 0
\(166\) −2.00000 + 1.32431i −0.155230 + 0.102786i
\(167\) −5.37874 −0.416220 −0.208110 0.978105i \(-0.566731\pi\)
−0.208110 + 0.978105i \(0.566731\pi\)
\(168\) 0 0
\(169\) −1.00000 −0.0769231
\(170\) 14.2462 + 21.5150i 1.09263 + 1.65012i
\(171\) −13.0343 −0.996755
\(172\) −0.807313 + 1.90388i −0.0615570 + 0.145170i
\(173\) 3.80776i 0.289499i 0.989468 + 0.144749i \(0.0462376\pi\)
−0.989468 + 0.144749i \(0.953762\pi\)
\(174\) 0 0
\(175\) 31.1570 2.35524
\(176\) −6.86093 + 11.3546i −0.517162 + 0.855888i
\(177\) 0 0
\(178\) −2.35829 + 1.56155i −0.176762 + 0.117043i
\(179\) 20.7713i 1.55252i 0.630413 + 0.776260i \(0.282886\pi\)
−0.630413 + 0.776260i \(0.717114\pi\)
\(180\) −8.34233 + 19.6737i −0.621801 + 1.46639i
\(181\) 18.2462 1.35623 0.678115 0.734956i \(-0.262797\pi\)
0.678115 + 0.734956i \(0.262797\pi\)
\(182\) 3.16561 + 4.78078i 0.234650 + 0.354375i
\(183\) 0 0
\(184\) 6.55789 1.21922i 0.483454 0.0898824i
\(185\) −29.3693 −2.15928
\(186\) 0 0
\(187\) −16.4265 + 4.34475i −1.20123 + 0.317720i
\(188\) 11.8078 + 5.00691i 0.861170 + 0.365166i
\(189\) 0 0
\(190\) 18.2462 12.0818i 1.32372 0.876505i
\(191\) 13.1158i 0.949024i −0.880249 0.474512i \(-0.842624\pi\)
0.880249 0.474512i \(-0.157376\pi\)
\(192\) 0 0
\(193\) 12.2462i 0.881502i −0.897630 0.440751i \(-0.854712\pi\)
0.897630 0.440751i \(-0.145288\pi\)
\(194\) −5.00691 + 3.31534i −0.359475 + 0.238028i
\(195\) 0 0
\(196\) 7.36932 17.3790i 0.526380 1.24136i
\(197\) 19.3693i 1.38001i 0.723806 + 0.690003i \(0.242391\pi\)
−0.723806 + 0.690003i \(0.757609\pi\)
\(198\) −10.5104 9.35587i −0.746939 0.664893i
\(199\) 11.7915i 0.835875i 0.908476 + 0.417938i \(0.137247\pi\)
−0.908476 + 0.417938i \(0.862753\pi\)
\(200\) −3.97292 21.3693i −0.280928 1.51104i
\(201\) 0 0
\(202\) −3.80776 5.75058i −0.267913 0.404609i
\(203\) 27.1025i 1.90222i
\(204\) 0 0
\(205\) 15.8078i 1.10406i
\(206\) −12.8891 19.4654i −0.898026 1.35622i
\(207\) 7.07488i 0.491738i
\(208\) 2.87529 2.78078i 0.199365 0.192812i
\(209\) 3.68466 + 13.9309i 0.254873 + 0.963618i
\(210\) 0 0
\(211\) 5.46026 0.375900 0.187950 0.982179i \(-0.439816\pi\)
0.187950 + 0.982179i \(0.439816\pi\)
\(212\) 9.56155 22.5490i 0.656690 1.54867i
\(213\) 0 0
\(214\) −17.0270 + 11.2745i −1.16394 + 0.770707i
\(215\) 3.68260 0.251151
\(216\) 0 0
\(217\) 1.50758i 0.102341i
\(218\) −1.56155 2.35829i −0.105762 0.159724i
\(219\) 0 0
\(220\) 23.3853 + 3.35463i 1.57664 + 0.226169i
\(221\) 5.12311 0.344617
\(222\) 0 0
\(223\) 11.8730i 0.795074i 0.917586 + 0.397537i \(0.130135\pi\)
−0.917586 + 0.397537i \(0.869865\pi\)
\(224\) −22.3963 4.94326i −1.49642 0.330286i
\(225\) 23.0540 1.53693
\(226\) −5.52390 + 3.65767i −0.367444 + 0.243305i
\(227\) 13.0343 0.865115 0.432557 0.901606i \(-0.357611\pi\)
0.432557 + 0.901606i \(0.357611\pi\)
\(228\) 0 0
\(229\) 25.8078 1.70543 0.852713 0.522380i \(-0.174956\pi\)
0.852713 + 0.522380i \(0.174956\pi\)
\(230\) −6.55789 9.90388i −0.432414 0.653043i
\(231\) 0 0
\(232\) −18.5885 + 3.45593i −1.22040 + 0.226893i
\(233\) 0.876894i 0.0574473i −0.999587 0.0287236i \(-0.990856\pi\)
0.999587 0.0287236i \(-0.00914427\pi\)
\(234\) 2.34233 + 3.53744i 0.153123 + 0.231250i
\(235\) 22.8393i 1.48987i
\(236\) −7.46543 3.16561i −0.485958 0.206064i
\(237\) 0 0
\(238\) −16.2177 24.4924i −1.05124 1.58761i
\(239\) 0.662153 0.0428311 0.0214156 0.999771i \(-0.493183\pi\)
0.0214156 + 0.999771i \(0.493183\pi\)
\(240\) 0 0
\(241\) 30.4924i 1.96419i −0.188387 0.982095i \(-0.560326\pi\)
0.188387 0.982095i \(-0.439674\pi\)
\(242\) −7.02827 + 13.8782i −0.451794 + 0.892122i
\(243\) 0 0
\(244\) 23.3563 + 9.90388i 1.49523 + 0.634031i
\(245\) −33.6155 −2.14762
\(246\) 0 0
\(247\) 4.34475i 0.276450i
\(248\) −1.03399 + 0.192236i −0.0656583 + 0.0122070i
\(249\) 0 0
\(250\) −11.2745 + 7.46543i −0.713061 + 0.472156i
\(251\) 14.8934i 0.940065i 0.882649 + 0.470033i \(0.155758\pi\)
−0.882649 + 0.470033i \(0.844242\pi\)
\(252\) 9.49682 22.3963i 0.598244 1.41083i
\(253\) 7.56155 2.00000i 0.475391 0.125739i
\(254\) 22.9309 15.1838i 1.43881 0.952713i
\(255\) 0 0
\(256\) −0.534565 + 15.9911i −0.0334103 + 0.999442i
\(257\) −10.1922 −0.635774 −0.317887 0.948129i \(-0.602973\pi\)
−0.317887 + 0.948129i \(0.602973\pi\)
\(258\) 0 0
\(259\) 33.4337 2.07747
\(260\) −6.55789 2.78078i −0.406703 0.172456i
\(261\) 20.0540i 1.24131i
\(262\) 9.02699 5.97725i 0.557689 0.369276i
\(263\) 2.81164 0.173373 0.0866867 0.996236i \(-0.472372\pi\)
0.0866867 + 0.996236i \(0.472372\pi\)
\(264\) 0 0
\(265\) −43.6155 −2.67928
\(266\) −20.7713 + 13.7538i −1.27357 + 0.843299i
\(267\) 0 0
\(268\) 25.9039 + 10.9842i 1.58233 + 0.670964i
\(269\) −11.1231 −0.678188 −0.339094 0.940753i \(-0.610120\pi\)
−0.339094 + 0.940753i \(0.610120\pi\)
\(270\) 0 0
\(271\) −17.7509 −1.07829 −0.539144 0.842214i \(-0.681252\pi\)
−0.539144 + 0.842214i \(0.681252\pi\)
\(272\) −14.7304 + 14.2462i −0.893162 + 0.863803i
\(273\) 0 0
\(274\) 3.97292 2.63068i 0.240013 0.158925i
\(275\) −6.51713 24.6398i −0.392998 1.48584i
\(276\) 0 0
\(277\) 5.56155i 0.334161i −0.985943 0.167081i \(-0.946566\pi\)
0.985943 0.167081i \(-0.0534340\pi\)
\(278\) −6.43845 + 4.26324i −0.386152 + 0.255692i
\(279\) 1.11550i 0.0667834i
\(280\) 7.46543 + 40.1547i 0.446145 + 2.39970i
\(281\) 0.438447i 0.0261556i −0.999914 0.0130778i \(-0.995837\pi\)
0.999914 0.0130778i \(-0.00416291\pi\)
\(282\) 0 0
\(283\) −5.16994 −0.307321 −0.153660 0.988124i \(-0.549106\pi\)
−0.153660 + 0.988124i \(0.549106\pi\)
\(284\) 25.3693 + 10.7575i 1.50539 + 0.638339i
\(285\) 0 0
\(286\) 3.11862 3.50345i 0.184408 0.207164i
\(287\) 17.9954i 1.06223i
\(288\) −16.5717 3.65767i −0.976497 0.215530i
\(289\) −9.24621 −0.543895
\(290\) 18.5885 + 28.0729i 1.09156 + 1.64850i
\(291\) 0 0
\(292\) 10.6938 + 4.53457i 0.625810 + 0.265365i
\(293\) 10.8769i 0.635435i 0.948185 + 0.317717i \(0.102916\pi\)
−0.948185 + 0.317717i \(0.897084\pi\)
\(294\) 0 0
\(295\) 14.4401i 0.840734i
\(296\) −4.26324 22.9309i −0.247796 1.33283i
\(297\) 0 0
\(298\) −11.3153 17.0887i −0.655480 0.989922i
\(299\) −2.35829 −0.136384
\(300\) 0 0
\(301\) −4.19224 −0.241636
\(302\) −24.9309 + 16.5081i −1.43461 + 0.949932i
\(303\) 0 0
\(304\) 12.0818 + 12.4924i 0.692938 + 0.716490i
\(305\) 45.1771i 2.58683i
\(306\) −12.0000 18.1227i −0.685994 1.03601i
\(307\) −15.1022 −0.861930 −0.430965 0.902369i \(-0.641827\pi\)
−0.430965 + 0.902369i \(0.641827\pi\)
\(308\) −26.6216 3.81888i −1.51690 0.217601i
\(309\) 0 0
\(310\) 1.03399 + 1.56155i 0.0587265 + 0.0886902i
\(311\) 2.81164i 0.159434i 0.996818 + 0.0797168i \(0.0254016\pi\)
−0.996818 + 0.0797168i \(0.974598\pi\)
\(312\) 0 0
\(313\) −19.3153 −1.09177 −0.545884 0.837861i \(-0.683806\pi\)
−0.545884 + 0.837861i \(0.683806\pi\)
\(314\) 9.43318 6.24621i 0.532345 0.352494i
\(315\) −43.3203 −2.44082
\(316\) −1.03399 + 2.43845i −0.0581663 + 0.137173i
\(317\) −11.1771 −0.627767 −0.313884 0.949461i \(-0.601630\pi\)
−0.313884 + 0.949461i \(0.601630\pi\)
\(318\) 0 0
\(319\) −21.4335 + 5.66906i −1.20004 + 0.317407i
\(320\) 26.5885 10.2405i 1.48634 0.572461i
\(321\) 0 0
\(322\) 7.46543 + 11.2745i 0.416032 + 0.628302i
\(323\) 22.2586i 1.23850i
\(324\) 7.02699 16.5717i 0.390388 0.920650i
\(325\) 7.68466i 0.426268i
\(326\) −1.55098 2.34233i −0.0859009 0.129730i
\(327\) 0 0
\(328\) 12.3423 2.29465i 0.681491 0.126701i
\(329\) 26.0000i 1.43343i
\(330\) 0 0
\(331\) 0.825183i 0.0453562i −0.999743 0.0226781i \(-0.992781\pi\)
0.999743 0.0226781i \(-0.00721928\pi\)
\(332\) −1.32431 + 3.12311i −0.0726808 + 0.171403i
\(333\) 24.7386 1.35567
\(334\) −6.34233 + 4.19960i −0.347037 + 0.229792i
\(335\) 50.1048i 2.73752i
\(336\) 0 0
\(337\) 20.2462i 1.10288i −0.834214 0.551441i \(-0.814078\pi\)
0.834214 0.551441i \(-0.185922\pi\)
\(338\) −1.17915 + 0.780776i −0.0641372 + 0.0424686i
\(339\) 0 0
\(340\) 33.5968 + 14.2462i 1.82204 + 0.772609i
\(341\) −1.19224 + 0.315342i −0.0645632 + 0.0170767i
\(342\) −15.3693 + 10.1768i −0.831077 + 0.550301i
\(343\) 9.88653 0.533822
\(344\) 0.534565 + 2.87529i 0.0288218 + 0.155025i
\(345\) 0 0
\(346\) 2.97301 + 4.48991i 0.159830 + 0.241379i
\(347\) 6.62153 0.355463 0.177731 0.984079i \(-0.443124\pi\)
0.177731 + 0.984079i \(0.443124\pi\)
\(348\) 0 0
\(349\) 18.0000i 0.963518i 0.876304 + 0.481759i \(0.160002\pi\)
−0.876304 + 0.481759i \(0.839998\pi\)
\(350\) 36.7386 24.3266i 1.96376 1.30031i
\(351\) 0 0
\(352\) 0.775383 + 18.7456i 0.0413280 + 0.999146i
\(353\) 5.12311 0.272675 0.136338 0.990662i \(-0.456467\pi\)
0.136338 + 0.990662i \(0.456467\pi\)
\(354\) 0 0
\(355\) 49.0708i 2.60441i
\(356\) −1.56155 + 3.68260i −0.0827621 + 0.195177i
\(357\) 0 0
\(358\) 16.2177 + 24.4924i 0.857134 + 1.29446i
\(359\) −8.77102 −0.462917 −0.231458 0.972845i \(-0.574350\pi\)
−0.231458 + 0.972845i \(0.574350\pi\)
\(360\) 5.52390 + 29.7116i 0.291135 + 1.56594i
\(361\) −0.123106 −0.00647924
\(362\) 21.5150 14.2462i 1.13080 0.748764i
\(363\) 0 0
\(364\) 7.46543 + 3.16561i 0.391295 + 0.165923i
\(365\) 20.6847i 1.08268i
\(366\) 0 0
\(367\) 11.5012i 0.600355i −0.953883 0.300178i \(-0.902954\pi\)
0.953883 0.300178i \(-0.0970460\pi\)
\(368\) 6.78078 6.55789i 0.353472 0.341854i
\(369\) 13.3153i 0.693169i
\(370\) −34.6307 + 22.9309i −1.80037 + 1.19212i
\(371\) 49.6515 2.57778
\(372\) 0 0
\(373\) 16.0540i 0.831243i −0.909538 0.415622i \(-0.863564\pi\)
0.909538 0.415622i \(-0.136436\pi\)
\(374\) −15.9770 + 17.9486i −0.826153 + 0.928098i
\(375\) 0 0
\(376\) 17.8324 3.31534i 0.919634 0.170976i
\(377\) 6.68466 0.344277
\(378\) 0 0
\(379\) 13.6149i 0.699351i 0.936871 + 0.349675i \(0.113708\pi\)
−0.936871 + 0.349675i \(0.886292\pi\)
\(380\) 12.0818 28.4924i 0.619783 1.46163i
\(381\) 0 0
\(382\) −10.2405 15.4654i −0.523949 0.791280i
\(383\) 10.3857i 0.530682i 0.964155 + 0.265341i \(0.0854845\pi\)
−0.964155 + 0.265341i \(0.914515\pi\)
\(384\) 0 0
\(385\) 12.2462 + 46.3002i 0.624125 + 2.35968i
\(386\) −9.56155 14.4401i −0.486670 0.734981i
\(387\) −3.10196 −0.157682
\(388\) −3.31534 + 7.81855i −0.168311 + 0.396927i
\(389\) 12.0000 0.608424 0.304212 0.952604i \(-0.401607\pi\)
0.304212 + 0.952604i \(0.401607\pi\)
\(390\) 0 0
\(391\) 12.0818 0.611002
\(392\) −4.87962 26.2462i −0.246458 1.32563i
\(393\) 0 0
\(394\) 15.1231 + 22.8393i 0.761891 + 1.15063i
\(395\) 4.71659 0.237317
\(396\) −19.6981 2.82570i −0.989867 0.141997i
\(397\) −20.0540 −1.00648 −0.503240 0.864147i \(-0.667859\pi\)
−0.503240 + 0.864147i \(0.667859\pi\)
\(398\) 9.20650 + 13.9039i 0.461480 + 0.696939i
\(399\) 0 0
\(400\) −21.3693 22.0956i −1.06847 1.10478i
\(401\) −9.61553 −0.480177 −0.240088 0.970751i \(-0.577176\pi\)
−0.240088 + 0.970751i \(0.577176\pi\)
\(402\) 0 0
\(403\) 0.371834 0.0185224
\(404\) −8.97983 3.80776i −0.446763 0.189443i
\(405\) −32.0540 −1.59277
\(406\) −21.1610 31.9579i −1.05020 1.58604i
\(407\) −6.99337 26.4404i −0.346648 1.31060i
\(408\) 0 0
\(409\) 17.3153i 0.856189i −0.903734 0.428094i \(-0.859185\pi\)
0.903734 0.428094i \(-0.140815\pi\)
\(410\) −12.3423 18.6397i −0.609544 0.920548i
\(411\) 0 0
\(412\) −30.3963 12.8891i −1.49752 0.635001i
\(413\) 16.4384i 0.808883i
\(414\) 5.52390 + 8.34233i 0.271485 + 0.410003i
\(415\) 6.04090 0.296536
\(416\) 1.21922 5.52390i 0.0597774 0.270832i
\(417\) 0 0
\(418\) 15.2216 + 13.5497i 0.744515 + 0.662735i
\(419\) 14.7304i 0.719627i −0.933024 0.359814i \(-0.882840\pi\)
0.933024 0.359814i \(-0.117160\pi\)
\(420\) 0 0
\(421\) 30.6847 1.49548 0.747739 0.663992i \(-0.231139\pi\)
0.747739 + 0.663992i \(0.231139\pi\)
\(422\) 6.43845 4.26324i 0.313419 0.207531i
\(423\) 19.2382i 0.935393i
\(424\) −6.33122 34.0540i −0.307471 1.65381i
\(425\) 39.3693i 1.90969i
\(426\) 0 0
\(427\) 51.4291i 2.48883i
\(428\) −11.2745 + 26.5885i −0.544972 + 1.28521i
\(429\) 0 0
\(430\) 4.34233 2.87529i 0.209406 0.138659i
\(431\) −26.4404 −1.27359 −0.636794 0.771034i \(-0.719740\pi\)
−0.636794 + 0.771034i \(0.719740\pi\)
\(432\) 0 0
\(433\) 24.0540 1.15596 0.577980 0.816051i \(-0.303841\pi\)
0.577980 + 0.816051i \(0.303841\pi\)
\(434\) −1.17708 1.77766i −0.0565017 0.0853302i
\(435\) 0 0
\(436\) −3.68260 1.56155i −0.176365 0.0747848i
\(437\) 10.2462i 0.490143i
\(438\) 0 0
\(439\) 18.8664 0.900442 0.450221 0.892917i \(-0.351345\pi\)
0.450221 + 0.892917i \(0.351345\pi\)
\(440\) 30.1939 14.3031i 1.43944 0.681872i
\(441\) 28.3153 1.34835
\(442\) 6.04090 4.00000i 0.287336 0.190261i
\(443\) 27.7189i 1.31696i −0.752596 0.658482i \(-0.771199\pi\)
0.752596 0.658482i \(-0.228801\pi\)
\(444\) 0 0
\(445\) 7.12311 0.337668
\(446\) 9.27015 + 14.0000i 0.438954 + 0.662919i
\(447\) 0 0
\(448\) −30.2681 + 11.6577i −1.43003 + 0.550773i
\(449\) −9.61553 −0.453785 −0.226892 0.973920i \(-0.572857\pi\)
−0.226892 + 0.973920i \(0.572857\pi\)
\(450\) 27.1840 18.0000i 1.28147 0.848528i
\(451\) 14.2313 3.76412i 0.670125 0.177245i
\(452\) −3.65767 + 8.62586i −0.172042 + 0.405727i
\(453\) 0 0
\(454\) 15.3693 10.1768i 0.721318 0.477623i
\(455\) 14.4401i 0.676962i
\(456\) 0 0
\(457\) 26.3002i 1.23027i −0.788421 0.615135i \(-0.789101\pi\)
0.788421 0.615135i \(-0.210899\pi\)
\(458\) 30.4312 20.1501i 1.42195 0.941552i
\(459\) 0 0
\(460\) −15.4654 6.55789i −0.721080 0.305763i
\(461\) 17.6155i 0.820437i 0.911987 + 0.410218i \(0.134548\pi\)
−0.911987 + 0.410218i \(0.865452\pi\)
\(462\) 0 0
\(463\) 17.0072i 0.790391i −0.918597 0.395195i \(-0.870677\pi\)
0.918597 0.395195i \(-0.129323\pi\)
\(464\) −19.2203 + 18.5885i −0.892281 + 0.862951i
\(465\) 0 0
\(466\) −0.684658 1.03399i −0.0317162 0.0478985i
\(467\) 23.4199i 1.08374i 0.840461 + 0.541872i \(0.182284\pi\)
−0.840461 + 0.541872i \(0.817716\pi\)
\(468\) 5.52390 + 2.34233i 0.255342 + 0.108274i
\(469\) 57.0388i 2.63381i
\(470\) −17.8324 26.9309i −0.822546 1.24223i
\(471\) 0 0
\(472\) −11.2745 + 2.09612i −0.518950 + 0.0964816i
\(473\) 0.876894 + 3.31534i 0.0403196 + 0.152440i
\(474\) 0 0
\(475\) −33.3880 −1.53194
\(476\) −38.2462 16.2177i −1.75301 0.743339i
\(477\) 36.7386 1.68215
\(478\) 0.780776 0.516994i 0.0357119 0.0236467i
\(479\) 14.0683 0.642795 0.321397 0.946944i \(-0.395847\pi\)
0.321397 + 0.946944i \(0.395847\pi\)
\(480\) 0 0
\(481\) 8.24621i 0.375995i
\(482\) −23.8078 35.9551i −1.08441 1.63771i
\(483\) 0 0
\(484\) 2.54838 + 21.8519i 0.115836 + 0.993268i
\(485\) 15.1231 0.686705
\(486\) 0 0
\(487\) 19.2382i 0.871766i 0.900003 + 0.435883i \(0.143564\pi\)
−0.900003 + 0.435883i \(0.856436\pi\)
\(488\) 35.2732 6.55789i 1.59674 0.296862i
\(489\) 0 0
\(490\) −39.6377 + 26.2462i −1.79065 + 1.18568i
\(491\) −3.68260 −0.166193 −0.0830967 0.996541i \(-0.526481\pi\)
−0.0830967 + 0.996541i \(0.526481\pi\)
\(492\) 0 0
\(493\) −34.2462 −1.54237
\(494\) −3.39228 5.12311i −0.152626 0.230499i
\(495\) 9.06134 + 34.2589i 0.407277 + 1.53982i
\(496\) −1.06913 + 1.03399i −0.0480054 + 0.0464274i
\(497\) 55.8617i 2.50574i
\(498\) 0 0
\(499\) 3.31077i 0.148210i −0.997250 0.0741051i \(-0.976390\pi\)
0.997250 0.0741051i \(-0.0236100\pi\)
\(500\) −7.46543 + 17.6057i −0.333864 + 0.787351i
\(501\) 0 0
\(502\) 11.6284 + 17.5616i 0.519003 + 0.783810i
\(503\) 13.9867 0.623638 0.311819 0.950142i \(-0.399062\pi\)
0.311819 + 0.950142i \(0.399062\pi\)
\(504\) −6.28835 33.8234i −0.280106 1.50662i
\(505\) 17.3693i 0.772924i
\(506\) 7.35463 8.26218i 0.326953 0.367299i
\(507\) 0 0
\(508\) 15.1838 35.8078i 0.673670 1.58871i
\(509\) −14.0000 −0.620539 −0.310270 0.950649i \(-0.600419\pi\)
−0.310270 + 0.950649i \(0.600419\pi\)
\(510\) 0 0
\(511\) 23.5472i 1.04167i
\(512\) 11.8551 + 19.2732i 0.523927 + 0.851763i
\(513\) 0 0
\(514\) −12.0181 + 7.95786i −0.530098 + 0.351006i
\(515\) 58.7943i 2.59079i
\(516\) 0 0
\(517\) 20.5616 5.43845i 0.904296 0.239183i
\(518\) 39.4233 26.1043i 1.73216 1.14696i
\(519\) 0 0
\(520\) −9.90388 + 1.84130i −0.434314 + 0.0807464i
\(521\) 25.1771 1.10303 0.551514 0.834166i \(-0.314050\pi\)
0.551514 + 0.834166i \(0.314050\pi\)
\(522\) −15.6577 23.6466i −0.685318 1.03498i
\(523\) 13.4061 0.586208 0.293104 0.956081i \(-0.405312\pi\)
0.293104 + 0.956081i \(0.405312\pi\)
\(524\) 5.97725 14.0961i 0.261117 0.615792i
\(525\) 0 0
\(526\) 3.31534 2.19526i 0.144556 0.0957181i
\(527\) −1.90495 −0.0829807
\(528\) 0 0
\(529\) 17.4384 0.758193
\(530\) −51.4291 + 34.0540i −2.23394 + 1.47921i
\(531\) 12.1633i 0.527843i
\(532\) −13.7538 + 32.4355i −0.596302 + 1.40626i
\(533\) −4.43845 −0.192250
\(534\) 0 0
\(535\) 51.4291 2.22348
\(536\) 39.1207 7.27320i 1.68976 0.314154i
\(537\) 0 0
\(538\) −13.1158 + 8.68466i −0.565461 + 0.374422i
\(539\) −8.00447 30.2631i −0.344777 1.30352i
\(540\) 0 0
\(541\) 40.2462i 1.73032i 0.501496 + 0.865160i \(0.332783\pi\)
−0.501496 + 0.865160i \(0.667217\pi\)
\(542\) −20.9309 + 13.8594i −0.899058 + 0.595314i
\(543\) 0 0
\(544\) −6.24621 + 28.2995i −0.267804 + 1.21333i
\(545\) 7.12311i 0.305120i
\(546\) 0 0
\(547\) −36.5357 −1.56215 −0.781077 0.624435i \(-0.785329\pi\)
−0.781077 + 0.624435i \(0.785329\pi\)
\(548\) 2.63068 6.20393i 0.112377 0.265019i
\(549\) 38.0540i 1.62410i
\(550\) −26.9228 23.9656i −1.14799 1.02189i
\(551\) 29.0432i 1.23728i
\(552\) 0 0
\(553\) −5.36932 −0.228327
\(554\) −4.34233 6.55789i −0.184488 0.278618i
\(555\) 0 0
\(556\) −4.26324 + 10.0540i −0.180802 + 0.426384i
\(557\) 19.7538i 0.836995i 0.908218 + 0.418497i \(0.137443\pi\)
−0.908218 + 0.418497i \(0.862557\pi\)
\(558\) −0.870958 1.31534i −0.0368706 0.0556828i
\(559\) 1.03399i 0.0437330i
\(560\) 40.1547 + 41.5194i 1.69684 + 1.75452i
\(561\) 0 0
\(562\) −0.342329 0.516994i −0.0144403 0.0218081i
\(563\) −26.2316 −1.10553 −0.552764 0.833338i \(-0.686427\pi\)
−0.552764 + 0.833338i \(0.686427\pi\)
\(564\) 0 0
\(565\) 16.6847 0.701929
\(566\) −6.09612 + 4.03657i −0.256239 + 0.169670i
\(567\) 36.4899 1.53243
\(568\) 38.3134 7.12311i 1.60759 0.298879i
\(569\) 20.9848i 0.879730i 0.898064 + 0.439865i \(0.144974\pi\)
−0.898064 + 0.439865i \(0.855026\pi\)
\(570\) 0 0
\(571\) −36.1181 −1.51149 −0.755747 0.654863i \(-0.772726\pi\)
−0.755747 + 0.654863i \(0.772726\pi\)
\(572\) 0.941901 6.56604i 0.0393829 0.274540i
\(573\) 0 0
\(574\) 14.0504 + 21.2192i 0.586452 + 0.885673i
\(575\) 18.1227i 0.755768i
\(576\) −22.3963 + 8.62586i −0.933179 + 0.359411i
\(577\) −26.0000 −1.08239 −0.541197 0.840896i \(-0.682029\pi\)
−0.541197 + 0.840896i \(0.682029\pi\)
\(578\) −10.9026 + 7.21922i −0.453490 + 0.300280i
\(579\) 0 0
\(580\) 43.8373 + 18.5885i 1.82024 + 0.771847i
\(581\) −6.87689 −0.285302
\(582\) 0 0
\(583\) −10.3857 39.2658i −0.430130 1.62622i
\(584\) 16.1501 3.00258i 0.668296 0.124248i
\(585\) 10.6847i 0.441756i
\(586\) 8.49242 + 12.8255i 0.350819 + 0.529815i
\(587\) 26.8937i 1.11002i −0.831843 0.555011i \(-0.812714\pi\)
0.831843 0.555011i \(-0.187286\pi\)
\(588\) 0 0
\(589\) 1.61553i 0.0665667i
\(590\) 11.2745 + 17.0270i 0.464163 + 0.700990i
\(591\) 0 0
\(592\) −22.9309 23.7102i −0.942453 0.974485i
\(593\) 28.7386i 1.18015i −0.807347 0.590077i \(-0.799097\pi\)
0.807347 0.590077i \(-0.200903\pi\)
\(594\) 0 0
\(595\) 73.9781i 3.03281i
\(596\) −26.6849 11.3153i −1.09306 0.463494i
\(597\) 0 0
\(598\) −2.78078 + 1.84130i −0.113714 + 0.0752964i
\(599\) 23.1296i 0.945050i −0.881317 0.472525i \(-0.843343\pi\)
0.881317 0.472525i \(-0.156657\pi\)
\(600\) 0 0
\(601\) 8.73863i 0.356456i −0.983989 0.178228i \(-0.942963\pi\)
0.983989 0.178228i \(-0.0570365\pi\)
\(602\) −4.94326 + 3.27320i −0.201472 + 0.133406i
\(603\) 42.2048i 1.71871i
\(604\) −16.5081 + 38.9309i −0.671703 + 1.58407i
\(605\) 34.0540 19.3693i 1.38449 0.787475i
\(606\) 0 0
\(607\) 34.3404 1.39384 0.696918 0.717151i \(-0.254554\pi\)
0.696918 + 0.717151i \(0.254554\pi\)
\(608\) 24.0000 + 5.29723i 0.973329 + 0.214831i
\(609\) 0 0
\(610\) −35.2732 53.2704i −1.42817 2.15686i
\(611\) −6.41273 −0.259431
\(612\) −28.2995 12.0000i −1.14394 0.485071i
\(613\) 7.36932i 0.297644i −0.988864 0.148822i \(-0.952452\pi\)
0.988864 0.148822i \(-0.0475481\pi\)
\(614\) −17.8078 + 11.7915i −0.718663 + 0.475865i
\(615\) 0 0
\(616\) −34.3724 + 16.2825i −1.38490 + 0.656039i
\(617\) 16.6307 0.669526 0.334763 0.942302i \(-0.391344\pi\)
0.334763 + 0.942302i \(0.391344\pi\)
\(618\) 0 0
\(619\) 13.4876i 0.542113i −0.962563 0.271056i \(-0.912627\pi\)
0.962563 0.271056i \(-0.0873730\pi\)
\(620\) 2.43845 + 1.03399i 0.0979304 + 0.0415259i
\(621\) 0 0
\(622\) 2.19526 + 3.31534i 0.0880221 + 0.132933i
\(623\) −8.10887 −0.324875
\(624\) 0 0
\(625\) −4.36932 −0.174773
\(626\) −22.7756 + 15.0810i −0.910297 + 0.602757i
\(627\) 0 0
\(628\) 6.24621 14.7304i 0.249251 0.587807i
\(629\) 42.2462i 1.68447i
\(630\) −51.0810 + 33.8234i −2.03511 + 1.34756i
\(631\) 19.6558i 0.782485i 0.920288 + 0.391242i \(0.127955\pi\)
−0.920288 + 0.391242i \(0.872045\pi\)
\(632\) 0.684658 + 3.68260i 0.0272343 + 0.146486i
\(633\) 0 0
\(634\) −13.1794 + 8.72680i −0.523422 + 0.346586i
\(635\) −69.2615 −2.74856
\(636\) 0 0
\(637\) 9.43845i 0.373965i
\(638\) −20.8469 + 23.4194i −0.825338 + 0.927183i
\(639\) 41.3338i 1.63514i
\(640\) 23.3563 32.8348i 0.923238 1.29791i
\(641\) −5.56155 −0.219668 −0.109834 0.993950i \(-0.535032\pi\)
−0.109834 + 0.993950i \(0.535032\pi\)
\(642\) 0 0
\(643\) 15.1022i 0.595574i −0.954632 0.297787i \(-0.903751\pi\)
0.954632 0.297787i \(-0.0962486\pi\)
\(644\) 17.6057 + 7.46543i 0.693762 + 0.294179i
\(645\) 0 0
\(646\) 17.3790 + 26.2462i 0.683768 + 1.03264i
\(647\) 31.1112i 1.22311i −0.791203 0.611553i \(-0.790545\pi\)
0.791203 0.611553i \(-0.209455\pi\)
\(648\) −4.65294 25.0270i −0.182785 0.983153i
\(649\) −13.0000 + 3.43845i −0.510295 + 0.134971i
\(650\) 6.00000 + 9.06134i 0.235339 + 0.355415i
\(651\) 0 0
\(652\) −3.65767 1.55098i −0.143245 0.0607411i
\(653\) −46.2462 −1.80975 −0.904877 0.425673i \(-0.860037\pi\)
−0.904877 + 0.425673i \(0.860037\pi\)
\(654\) 0 0
\(655\) −27.2655 −1.06535
\(656\) 12.7618 12.3423i 0.498265 0.481887i
\(657\) 17.4233i 0.679747i
\(658\) 20.3002 + 30.6578i 0.791384 + 1.19517i
\(659\) 20.1907 0.786517 0.393258 0.919428i \(-0.371348\pi\)
0.393258 + 0.919428i \(0.371348\pi\)
\(660\) 0 0
\(661\) 14.0000 0.544537 0.272268 0.962221i \(-0.412226\pi\)
0.272268 + 0.962221i \(0.412226\pi\)
\(662\) −0.644283 0.973012i −0.0250408 0.0378172i
\(663\) 0 0
\(664\) 0.876894 + 4.71659i 0.0340301 + 0.183039i
\(665\) 62.7386 2.43290
\(666\) 29.1705 19.3153i 1.13033 0.748454i
\(667\) 15.7644 0.610400
\(668\) −4.19960 + 9.90388i −0.162487 + 0.383193i
\(669\) 0 0
\(670\) −39.1207 59.0810i −1.51136 2.28250i
\(671\) 40.6716 10.7575i 1.57011 0.415288i
\(672\) 0 0
\(673\) 27.7538i 1.06983i 0.844906 + 0.534915i \(0.179656\pi\)
−0.844906 + 0.534915i \(0.820344\pi\)
\(674\) −15.8078 23.8733i −0.608892 0.919564i
\(675\) 0 0
\(676\) −0.780776 + 1.84130i −0.0300299 + 0.0708193i
\(677\) 2.63068i 0.101105i 0.998721 + 0.0505527i \(0.0160983\pi\)
−0.998721 + 0.0505527i \(0.983902\pi\)
\(678\) 0 0
\(679\) −17.2160 −0.660689
\(680\) 50.7386 9.43318i 1.94574 0.361746i
\(681\) 0 0
\(682\) −1.15961 + 1.30270i −0.0444038 + 0.0498831i
\(683\) 20.6898i 0.791673i −0.918321 0.395836i \(-0.870455\pi\)
0.918321 0.395836i \(-0.129545\pi\)
\(684\) −10.1768 + 24.0000i −0.389121 + 0.917663i
\(685\) −12.0000 −0.458496
\(686\) 11.6577 7.71917i 0.445092 0.294719i
\(687\) 0 0
\(688\) 2.87529 + 2.97301i 0.109619 + 0.113345i
\(689\) 12.2462i 0.466543i
\(690\) 0 0
\(691\) 28.3453i 1.07831i −0.842208 0.539153i \(-0.818744\pi\)
0.842208 0.539153i \(-0.181256\pi\)
\(692\) 7.01124 + 2.97301i 0.266527 + 0.113017i
\(693\) −10.3153 39.0000i −0.391847 1.48149i
\(694\) 7.80776 5.16994i 0.296379 0.196248i
\(695\) 19.4470 0.737667
\(696\) 0 0
\(697\) 22.7386 0.861287
\(698\) 14.0540 + 21.2247i 0.531951 + 0.803365i
\(699\) 0 0
\(700\) 24.3266 57.3693i 0.919460 2.16836i
\(701\) 13.8078i 0.521512i −0.965405 0.260756i \(-0.916028\pi\)
0.965405 0.260756i \(-0.0839718\pi\)
\(702\) 0 0
\(703\) −35.8278 −1.35127
\(704\) 15.5504 + 21.4985i 0.586079 + 0.810254i
\(705\) 0 0
\(706\) 6.04090 4.00000i 0.227352 0.150542i
\(707\) 19.7731i 0.743642i
\(708\) 0 0
\(709\) −28.9309 −1.08652 −0.543261 0.839564i \(-0.682811\pi\)
−0.543261 + 0.839564i \(0.682811\pi\)
\(710\) −38.3134 57.8617i −1.43787 2.17151i
\(711\) −3.97292 −0.148996
\(712\) 1.03399 + 5.56155i 0.0387503 + 0.208428i
\(713\) 0.876894 0.0328400
\(714\) 0 0
\(715\) −11.4196 + 3.02045i −0.427070 + 0.112958i
\(716\) 38.2462 + 16.2177i 1.42933 + 0.606085i
\(717\) 0 0
\(718\) −10.3423 + 6.84821i −0.385972 + 0.255573i
\(719\) 38.0230i 1.41802i 0.705199 + 0.709010i \(0.250858\pi\)
−0.705199 + 0.709010i \(0.749142\pi\)
\(720\) 29.7116 + 30.7215i 1.10729 + 1.14492i
\(721\) 66.9309i 2.49264i
\(722\) −0.145160 + 0.0961180i −0.00540228 + 0.00357714i
\(723\) 0 0
\(724\) 14.2462 33.5968i 0.529456 1.24861i
\(725\) 51.3693i 1.90781i
\(726\) 0 0
\(727\) 24.0006i 0.890131i 0.895498 + 0.445066i \(0.146820\pi\)
−0.895498 + 0.445066i \(0.853180\pi\)
\(728\) 11.2745 2.09612i 0.417860 0.0776873i
\(729\) 27.0000 1.00000
\(730\) −16.1501 24.3903i −0.597742 0.902724i
\(731\) 5.29723i 0.195925i
\(732\) 0 0
\(733\) 43.8617i 1.62007i −0.586381 0.810035i \(-0.699448\pi\)
0.586381 0.810035i \(-0.300552\pi\)
\(734\) −8.97983 13.5616i −0.331452 0.500566i
\(735\) 0 0
\(736\) 2.87529 13.0270i 0.105985 0.480181i
\(737\) 45.1080 11.9309i 1.66157 0.439479i
\(738\) 10.3963 + 15.7007i 0.382693 + 0.577953i
\(739\) 22.6305 0.832475 0.416238 0.909256i \(-0.363348\pi\)
0.416238 + 0.909256i \(0.363348\pi\)
\(740\) −22.9309 + 54.0777i −0.842956 + 1.98794i
\(741\) 0 0
\(742\) 58.5464 38.7667i 2.14931 1.42317i
\(743\) −32.7716 −1.20227 −0.601136 0.799147i \(-0.705285\pi\)
−0.601136 + 0.799147i \(0.705285\pi\)
\(744\) 0 0
\(745\) 51.6155i 1.89105i
\(746\) −12.5346 18.9300i −0.458923 0.693077i
\(747\) −5.08842 −0.186176
\(748\) −4.82546 + 33.6385i −0.176436 + 1.22995i
\(749\) −58.5464 −2.13924
\(750\) 0 0
\(751\) 5.58755i 0.203892i 0.994790 + 0.101946i \(0.0325070\pi\)
−0.994790 + 0.101946i \(0.967493\pi\)
\(752\) 18.4384 17.8324i 0.672381 0.650280i
\(753\) 0 0
\(754\) 7.88220 5.21922i 0.287053 0.190073i
\(755\) 75.3024 2.74053
\(756\) 0 0
\(757\) −0.246211 −0.00894870 −0.00447435 0.999990i \(-0.501424\pi\)
−0.00447435 + 0.999990i \(0.501424\pi\)
\(758\) 10.6302 + 16.0540i 0.386106 + 0.583107i
\(759\) 0 0
\(760\) −8.00000 43.0299i −0.290191 1.56086i
\(761\) 1.31534i 0.0476811i 0.999716 + 0.0238405i \(0.00758940\pi\)
−0.999716 + 0.0238405i \(0.992411\pi\)
\(762\) 0 0
\(763\) 8.10887i 0.293561i
\(764\) −24.1501 10.2405i −0.873720 0.370488i
\(765\) 54.7386i 1.97908i
\(766\) 8.10887 + 12.2462i 0.292985 + 0.442474i
\(767\) 4.05444 0.146397
\(768\) 0 0
\(769\) 28.0540i 1.01165i 0.862635 + 0.505826i \(0.168812\pi\)
−0.862635 + 0.505826i \(0.831188\pi\)
\(770\) 50.5902 + 45.0332i 1.82314 + 1.62288i
\(771\) 0 0
\(772\) −22.5490 9.56155i −0.811555 0.344128i
\(773\) −40.7386 −1.46527 −0.732633 0.680623i \(-0.761709\pi\)
−0.732633 + 0.680623i \(0.761709\pi\)
\(774\) −3.65767 + 2.42194i −0.131472 + 0.0870548i
\(775\) 2.85742i 0.102641i
\(776\) 2.19526 + 11.8078i 0.0788054 + 0.423874i
\(777\) 0 0
\(778\) 14.1498 9.36932i 0.507294 0.335906i
\(779\) 19.2840i 0.690920i
\(780\) 0 0
\(781\) 44.1771 11.6847i 1.58078 0.418110i
\(782\) 14.2462 9.43318i 0.509443 0.337330i
\(783\) 0 0
\(784\) −26.2462 27.1383i −0.937365 0.969223i
\(785\) −28.4924 −1.01694
\(786\) 0 0
\(787\) −38.5222 −1.37317 −0.686583 0.727051i \(-0.740890\pi\)
−0.686583 + 0.727051i \(0.740890\pi\)
\(788\) 35.6647 + 15.1231i 1.27050 + 0.538738i
\(789\) 0 0
\(790\) 5.56155 3.68260i 0.197871 0.131021i
\(791\) −18.9936 −0.675336
\(792\) −25.4332 + 12.0479i −0.903730 + 0.428103i
\(793\) −12.6847 −0.450445
\(794\) −23.6466 + 15.6577i −0.839186 + 0.555670i
\(795\) 0 0
\(796\) 21.7116 + 9.20650i 0.769549 + 0.326316i
\(797\) 28.0000 0.991811 0.495905 0.868377i \(-0.334836\pi\)
0.495905 + 0.868377i \(0.334836\pi\)
\(798\) 0 0
\(799\) 32.8531 1.16226
\(800\) −42.4493 9.36932i −1.50081 0.331255i
\(801\) −6.00000 −0.212000
\(802\) −11.3381 + 7.50758i −0.400363 + 0.265102i
\(803\) 18.6218 4.92539i 0.657149 0.173813i
\(804\) 0 0
\(805\) 34.0540i 1.20024i
\(806\) 0.438447 0.290319i 0.0154436 0.0102261i
\(807\) 0 0
\(808\) −13.5616 + 2.52132i −0.477094 + 0.0886999i
\(809\) 26.8769i 0.944941i 0.881346 + 0.472471i \(0.156638\pi\)
−0.881346 + 0.472471i \(0.843362\pi\)
\(810\) −37.7964 + 25.0270i −1.32803 + 0.879359i
\(811\) 27.3471 0.960285 0.480143 0.877190i \(-0.340585\pi\)
0.480143 + 0.877190i \(0.340585\pi\)
\(812\) −49.9039 21.1610i −1.75128 0.742606i
\(813\) 0 0
\(814\) −28.8902 25.7168i −1.01260 0.901374i
\(815\) 7.07488i 0.247822i
\(816\) 0 0
\(817\) 4.49242 0.157170
\(818\) −13.5194 20.4173i −0.472695 0.713875i
\(819\) 12.1633i 0.425020i
\(820\) −29.1068 12.3423i −1.01646 0.431013i
\(821\) 45.2311i 1.57857i 0.614024 + 0.789287i \(0.289550\pi\)
−0.614024 + 0.789287i \(0.710450\pi\)
\(822\) 0 0
\(823\) 10.8848i 0.379419i −0.981840 0.189710i \(-0.939245\pi\)
0.981840 0.189710i \(-0.0607547\pi\)
\(824\) −45.9052 + 8.53457i −1.59918 + 0.297316i
\(825\) 0 0
\(826\) −12.8348 19.3833i −0.446578 0.674433i
\(827\) −13.1973 −0.458915 −0.229457 0.973319i \(-0.573695\pi\)
−0.229457 + 0.973319i \(0.573695\pi\)
\(828\) 13.0270 + 5.52390i 0.452719 + 0.191969i
\(829\) −10.9848 −0.381519 −0.190760 0.981637i \(-0.561095\pi\)
−0.190760 + 0.981637i \(0.561095\pi\)
\(830\) 7.12311 4.71659i 0.247247 0.163715i
\(831\) 0 0
\(832\) −2.87529 7.46543i −0.0996827 0.258817i
\(833\) 48.3542i 1.67537i
\(834\) 0 0
\(835\) 19.1567 0.662944
\(836\) 28.5278 + 4.09233i 0.986655 + 0.141536i
\(837\) 0 0
\(838\) −11.5012 17.3693i −0.397301 0.600013i
\(839\) 33.3880i 1.15268i 0.817210 + 0.576340i \(0.195520\pi\)
−0.817210 + 0.576340i \(0.804480\pi\)
\(840\) 0 0
\(841\) −15.6847 −0.540850
\(842\) 36.1817 23.9579i 1.24690 0.825642i
\(843\) 0 0
\(844\) 4.26324 10.0540i 0.146747 0.346072i
\(845\) 3.56155 0.122521
\(846\) 15.0207 + 22.6847i 0.516423 + 0.779915i
\(847\) −38.7667 + 22.0498i −1.33204 + 0.757641i
\(848\) −34.0540 35.2114i −1.16942 1.20916i
\(849\) 0 0
\(850\) −30.7386 46.4222i −1.05433 1.59227i
\(851\) 19.4470i 0.666634i
\(852\) 0 0
\(853\) 32.2462i 1.10409i 0.833815 + 0.552045i \(0.186152\pi\)
−0.833815 + 0.552045i \(0.813848\pi\)
\(854\) 40.1547 + 60.6425i 1.37406 + 2.07514i
\(855\) 46.4222 1.58761
\(856\) 7.46543 + 40.1547i 0.255163 + 1.37246i
\(857\) 12.0000i 0.409912i 0.978771 + 0.204956i \(0.0657052\pi\)
−0.978771 + 0.204956i \(0.934295\pi\)
\(858\) 0 0
\(859\) 56.2730i 1.92001i −0.279982 0.960005i \(-0.590329\pi\)
0.279982 0.960005i \(-0.409671\pi\)
\(860\) 2.87529 6.78078i 0.0980465 0.231223i
\(861\) 0 0
\(862\) −31.1771 + 20.6440i −1.06190 + 0.703138i
\(863\) 55.3205i 1.88313i −0.336827 0.941566i \(-0.609354\pi\)
0.336827 0.941566i \(-0.390646\pi\)
\(864\) 0 0
\(865\) 13.5616i 0.461107i
\(866\) 28.3632 18.7808i 0.963820 0.638197i
\(867\) 0 0
\(868\) −2.77590 1.17708i −0.0942203 0.0399527i
\(869\) 1.12311 + 4.24621i 0.0380987 + 0.144043i
\(870\) 0 0
\(871\) −14.0683 −0.476685
\(872\) −5.56155 + 1.03399i −0.188338 + 0.0350152i
\(873\) −12.7386 −0.431137
\(874\) −8.00000 12.0818i −0.270604 0.408673i
\(875\) −38.7667 −1.31055
\(876\) 0 0
\(877\) 14.3845i 0.485729i 0.970060 + 0.242865i \(0.0780871\pi\)
−0.970060 + 0.242865i \(0.921913\pi\)
\(878\) 22.2462 14.7304i 0.750773 0.497127i
\(879\) 0 0
\(880\) 24.4356 40.4401i 0.823723 1.36324i
\(881\) 11.5616 0.389519 0.194759 0.980851i \(-0.437607\pi\)
0.194759 + 0.980851i \(0.437607\pi\)
\(882\) 33.3880 22.1080i 1.12423 0.744413i
\(883\) 12.8255i 0.431611i −0.976436 0.215806i \(-0.930762\pi\)
0.976436 0.215806i \(-0.0692377\pi\)
\(884\) 4.00000 9.43318i 0.134535 0.317272i
\(885\) 0 0
\(886\) −21.6423 32.6847i −0.727086 1.09806i
\(887\) −42.8669 −1.43933 −0.719665 0.694321i \(-0.755705\pi\)
−0.719665 + 0.694321i \(0.755705\pi\)
\(888\) 0 0
\(889\) 78.8466 2.64443
\(890\) 8.39919 5.56155i 0.281541 0.186424i
\(891\) −7.63263 28.8573i −0.255703 0.966755i
\(892\) 21.8617 + 9.27015i 0.731985 + 0.310388i
\(893\) 27.8617i 0.932358i
\(894\) 0 0
\(895\) 73.9781i 2.47281i
\(896\) −26.5885 + 37.3787i −0.888261 + 1.24874i
\(897\) 0 0
\(898\) −11.3381 + 7.50758i −0.378358 + 0.250531i
\(899\) −2.48558 −0.0828989
\(900\) 18.0000 42.4493i 0.600000 1.41498i
\(901\) 62.7386i 2.09013i
\(902\) 13.8418 15.5499i 0.460883 0.517755i
\(903\) 0 0
\(904\) 2.42194 + 13.0270i 0.0805525 + 0.433271i
\(905\) −64.9848 −2.16017
\(906\) 0 0
\(907\) 23.4199i 0.777646i 0.921313 + 0.388823i \(0.127118\pi\)
−0.921313 + 0.388823i \(0.872882\pi\)
\(908\) 10.1768 24.0000i 0.337731 0.796468i
\(909\) 14.6307i 0.485269i
\(910\) −11.2745 17.0270i −0.373745 0.564439i
\(911\) 1.74192i 0.0577122i 0.999584 + 0.0288561i \(0.00918646\pi\)
−0.999584 + 0.0288561i \(0.990814\pi\)
\(912\) 0 0
\(913\) 1.43845 + 5.43845i 0.0476057 + 0.179986i
\(914\) −20.5346 31.0118i −0.679223 1.02578i
\(915\) 0 0
\(916\) 20.1501 47.5199i 0.665778 1.57010i
\(917\) 31.0388 1.02499
\(918\) 0 0
\(919\) 47.0029 1.55048 0.775241 0.631666i \(-0.217629\pi\)
0.775241 + 0.631666i \(0.217629\pi\)
\(920\) −23.3563 + 4.34233i −0.770033 + 0.143162i
\(921\) 0 0
\(922\) 13.7538 + 20.7713i 0.452957 + 0.684066i
\(923\) −13.7779 −0.453506
\(924\) 0 0
\(925\) 63.3693 2.08357
\(926\) −13.2788 20.0540i −0.436369 0.659015i
\(927\) 49.5242i 1.62659i
\(928\) −8.15009 + 36.9254i −0.267540 + 1.21214i
\(929\) −14.8769 −0.488095 −0.244048 0.969763i \(-0.578475\pi\)
−0.244048 + 0.969763i \(0.578475\pi\)
\(930\) 0 0
\(931\) −41.0077 −1.34397
\(932\) −1.61463 0.684658i −0.0528888 0.0224267i
\(933\) 0 0
\(934\) 18.2857 + 27.6155i 0.598327 + 0.903608i
\(935\) 58.5040 15.4741i 1.91329 0.506056i
\(936\) 8.34233 1.55098i 0.272678 0.0506954i
\(937\) 3.12311i 0.102027i 0.998698 + 0.0510137i \(0.0162452\pi\)
−0.998698 + 0.0510137i \(0.983755\pi\)
\(938\) 44.5346 + 67.2572i 1.45411 + 2.19602i
\(939\) 0 0
\(940\) −42.0540 17.8324i −1.37165 0.581628i
\(941\) 30.4924i 0.994025i 0.867744 + 0.497012i \(0.165570\pi\)
−0.867744 + 0.497012i \(0.834430\pi\)
\(942\) 0 0
\(943\) −10.4672 −0.340858
\(944\) −11.6577 + 11.2745i −0.379425 + 0.366953i
\(945\) 0 0
\(946\) 3.62253 + 3.22462i 0.117779 + 0.104841i
\(947\) 30.5763i 0.993597i 0.867866 + 0.496798i \(0.165491\pi\)
−0.867866 + 0.496798i \(0.834509\pi\)
\(948\) 0 0
\(949\) −5.80776 −0.188528
\(950\) −39.3693 + 26.0685i −1.27731 + 0.845775i
\(951\) 0 0
\(952\) −57.7603 + 10.7386i −1.87202 + 0.348041i
\(953\) 5.75379i 0.186383i 0.995648 + 0.0931917i \(0.0297070\pi\)
−0.995648 + 0.0931917i \(0.970293\pi\)
\(954\) 43.3203 28.6847i 1.40255 0.928700i
\(955\) 46.7125i 1.51158i
\(956\) 0.516994 1.21922i 0.0167208 0.0394325i
\(957\) 0 0
\(958\) 16.5885 10.9842i 0.535951 0.354882i
\(959\) 13.6607 0.441126
\(960\) 0 0
\(961\) 30.8617 0.995540
\(962\) 6.43845 + 9.72350i 0.207584 + 0.313498i
\(963\) −43.3203 −1.39598
\(964\) −56.1457 23.8078i −1.80833 0.766796i
\(965\) 43.6155i 1.40403i
\(966\) 0 0
\(967\) 46.9213 1.50889 0.754444 0.656364i \(-0.227906\pi\)
0.754444 + 0.656364i \(0.227906\pi\)
\(968\) 20.0664 + 23.7769i 0.644958 + 0.764218i
\(969\) 0 0
\(970\) 17.8324 11.8078i 0.572563 0.379124i
\(971\) 25.6509i 0.823177i 0.911370 + 0.411589i \(0.135026\pi\)
−0.911370 + 0.411589i \(0.864974\pi\)
\(972\) 0 0
\(973\) −22.1383 −0.709720
\(974\) 15.0207 + 22.6847i 0.481295 + 0.726863i
\(975\) 0 0
\(976\) 36.4720 35.2732i 1.16744 1.12907i
\(977\) −57.1231 −1.82753 −0.913765 0.406243i \(-0.866839\pi\)
−0.913765 + 0.406243i \(0.866839\pi\)
\(978\) 0 0
\(979\) 1.69614 + 6.41273i 0.0542089 + 0.204952i
\(980\) −26.2462 + 61.8963i −0.838404 + 1.97720i
\(981\) 6.00000i 0.191565i
\(982\) −4.34233 + 2.87529i −0.138569 + 0.0917541i
\(983\) 20.5625i 0.655842i 0.944705 + 0.327921i \(0.106348\pi\)
−0.944705 + 0.327921i \(0.893652\pi\)
\(984\) 0 0
\(985\) 68.9848i 2.19804i
\(986\) −40.3813 + 26.7386i −1.28600 + 0.851532i
\(987\) 0 0
\(988\) −8.00000 3.39228i −0.254514 0.107923i
\(989\) 2.43845i 0.0775381i
\(990\) 37.4332 + 33.3214i 1.18971 + 1.05902i
\(991\) 40.8347i 1.29716i 0.761148 + 0.648578i \(0.224636\pi\)
−0.761148 + 0.648578i \(0.775364\pi\)
\(992\) −0.453349 + 2.05398i −0.0143938 + 0.0652138i
\(993\) 0 0
\(994\) 43.6155 + 65.8692i 1.38340 + 2.08924i
\(995\) 41.9960i 1.33136i
\(996\) 0 0
\(997\) 23.4233i 0.741823i −0.928668 0.370912i \(-0.879045\pi\)
0.928668 0.370912i \(-0.120955\pi\)
\(998\) −2.58497 3.90388i −0.0818258 0.123575i
\(999\) 0 0
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 572.2.e.a.131.7 yes 8
4.3 odd 2 inner 572.2.e.a.131.1 8
11.10 odd 2 inner 572.2.e.a.131.2 yes 8
44.43 even 2 inner 572.2.e.a.131.8 yes 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
572.2.e.a.131.1 8 4.3 odd 2 inner
572.2.e.a.131.2 yes 8 11.10 odd 2 inner
572.2.e.a.131.7 yes 8 1.1 even 1 trivial
572.2.e.a.131.8 yes 8 44.43 even 2 inner