Properties

Label 405.2.e.j.136.2
Level $405$
Weight $2$
Character 405.136
Analytic conductor $3.234$
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] = [405,2,Mod(136,405)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(405, 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("405.136");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 405 = 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 405.e (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: \(3.23394128186\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{13})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{3} + 4x^{2} + 3x + 9 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 135)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 136.2
Root \(-0.651388 + 1.12824i\) of defining polynomial
Character \(\chi\) \(=\) 405.136
Dual form 405.2.e.j.271.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.651388 - 1.12824i) q^{2} +(0.151388 + 0.262211i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-2.30278 + 3.98852i) q^{7} +3.00000 q^{8} +O(q^{10})\) \(q+(0.651388 - 1.12824i) q^{2} +(0.151388 + 0.262211i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-2.30278 + 3.98852i) q^{7} +3.00000 q^{8} +1.30278 q^{10} +(-1.30278 + 2.25647i) q^{11} +(0.302776 + 0.524423i) q^{13} +(3.00000 + 5.19615i) q^{14} +(1.65139 - 2.86029i) q^{16} +5.60555 q^{17} -3.60555 q^{19} +(-0.151388 + 0.262211i) q^{20} +(1.69722 + 2.93968i) q^{22} +(-1.50000 - 2.59808i) q^{23} +(-0.500000 + 0.866025i) q^{25} +0.788897 q^{26} -1.39445 q^{28} +(4.30278 - 7.45263i) q^{29} +(-0.802776 - 1.39045i) q^{31} +(0.848612 + 1.46984i) q^{32} +(3.65139 - 6.32439i) q^{34} -4.60555 q^{35} +2.00000 q^{37} +(-2.34861 + 4.06792i) q^{38} +(1.50000 + 2.59808i) q^{40} +(1.30278 + 2.25647i) q^{41} +(3.30278 - 5.72058i) q^{43} -0.788897 q^{44} -3.90833 q^{46} +(2.60555 - 4.51295i) q^{47} +(-7.10555 - 12.3072i) q^{49} +(0.651388 + 1.12824i) q^{50} +(-0.0916731 + 0.158782i) q^{52} +5.60555 q^{53} -2.60555 q^{55} +(-6.90833 + 11.9656i) q^{56} +(-5.60555 - 9.70910i) q^{58} +(-4.30278 - 7.45263i) q^{59} +(-5.10555 + 8.84307i) q^{61} -2.09167 q^{62} +8.81665 q^{64} +(-0.302776 + 0.524423i) q^{65} +(7.60555 + 13.1732i) q^{67} +(0.848612 + 1.46984i) q^{68} +(-3.00000 + 5.19615i) q^{70} -14.6056 q^{71} +5.39445 q^{73} +(1.30278 - 2.25647i) q^{74} +(-0.545837 - 0.945417i) q^{76} +(-6.00000 - 10.3923i) q^{77} +(2.19722 - 3.80570i) q^{79} +3.30278 q^{80} +3.39445 q^{82} +(1.50000 - 2.59808i) q^{83} +(2.80278 + 4.85455i) q^{85} +(-4.30278 - 7.45263i) q^{86} +(-3.90833 + 6.76942i) q^{88} -7.81665 q^{89} -2.78890 q^{91} +(0.454163 - 0.786634i) q^{92} +(-3.39445 - 5.87936i) q^{94} +(-1.80278 - 3.12250i) q^{95} +(-4.00000 + 6.92820i) q^{97} -18.5139 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - q^{2} - 3 q^{4} + 2 q^{5} - 2 q^{7} + 12 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - q^{2} - 3 q^{4} + 2 q^{5} - 2 q^{7} + 12 q^{8} - 2 q^{10} + 2 q^{11} - 6 q^{13} + 12 q^{14} + 3 q^{16} + 8 q^{17} + 3 q^{20} + 14 q^{22} - 6 q^{23} - 2 q^{25} + 32 q^{26} - 20 q^{28} + 10 q^{29} + 4 q^{31} + 7 q^{32} + 11 q^{34} - 4 q^{35} + 8 q^{37} - 13 q^{38} + 6 q^{40} - 2 q^{41} + 6 q^{43} - 32 q^{44} + 6 q^{46} - 4 q^{47} - 14 q^{49} - q^{50} - 22 q^{52} + 8 q^{53} + 4 q^{55} - 6 q^{56} - 8 q^{58} - 10 q^{59} - 6 q^{61} - 30 q^{62} - 8 q^{64} + 6 q^{65} + 16 q^{67} + 7 q^{68} - 12 q^{70} - 44 q^{71} + 36 q^{73} - 2 q^{74} - 13 q^{76} - 24 q^{77} + 16 q^{79} + 6 q^{80} + 28 q^{82} + 6 q^{83} + 4 q^{85} - 10 q^{86} + 6 q^{88} + 12 q^{89} - 40 q^{91} - 9 q^{92} - 28 q^{94} - 16 q^{97} - 38 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/405\mathbb{Z}\right)^\times\).

\(n\) \(82\) \(326\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.651388 1.12824i 0.460601 0.797784i −0.538390 0.842696i \(-0.680967\pi\)
0.998991 + 0.0449118i \(0.0143007\pi\)
\(3\) 0 0
\(4\) 0.151388 + 0.262211i 0.0756939 + 0.131106i
\(5\) 0.500000 + 0.866025i 0.223607 + 0.387298i
\(6\) 0 0
\(7\) −2.30278 + 3.98852i −0.870367 + 1.50752i −0.00875026 + 0.999962i \(0.502785\pi\)
−0.861617 + 0.507559i \(0.830548\pi\)
\(8\) 3.00000 1.06066
\(9\) 0 0
\(10\) 1.30278 0.411974
\(11\) −1.30278 + 2.25647i −0.392802 + 0.680352i −0.992818 0.119635i \(-0.961827\pi\)
0.600016 + 0.799988i \(0.295161\pi\)
\(12\) 0 0
\(13\) 0.302776 + 0.524423i 0.0839749 + 0.145449i 0.904954 0.425510i \(-0.139905\pi\)
−0.820979 + 0.570958i \(0.806572\pi\)
\(14\) 3.00000 + 5.19615i 0.801784 + 1.38873i
\(15\) 0 0
\(16\) 1.65139 2.86029i 0.412847 0.715072i
\(17\) 5.60555 1.35955 0.679773 0.733423i \(-0.262078\pi\)
0.679773 + 0.733423i \(0.262078\pi\)
\(18\) 0 0
\(19\) −3.60555 −0.827170 −0.413585 0.910465i \(-0.635724\pi\)
−0.413585 + 0.910465i \(0.635724\pi\)
\(20\) −0.151388 + 0.262211i −0.0338513 + 0.0586323i
\(21\) 0 0
\(22\) 1.69722 + 2.93968i 0.361849 + 0.626742i
\(23\) −1.50000 2.59808i −0.312772 0.541736i 0.666190 0.745782i \(-0.267924\pi\)
−0.978961 + 0.204046i \(0.934591\pi\)
\(24\) 0 0
\(25\) −0.500000 + 0.866025i −0.100000 + 0.173205i
\(26\) 0.788897 0.154716
\(27\) 0 0
\(28\) −1.39445 −0.263526
\(29\) 4.30278 7.45263i 0.799005 1.38392i −0.121259 0.992621i \(-0.538693\pi\)
0.920264 0.391297i \(-0.127973\pi\)
\(30\) 0 0
\(31\) −0.802776 1.39045i −0.144183 0.249732i 0.784885 0.619641i \(-0.212722\pi\)
−0.929068 + 0.369910i \(0.879389\pi\)
\(32\) 0.848612 + 1.46984i 0.150015 + 0.259833i
\(33\) 0 0
\(34\) 3.65139 6.32439i 0.626208 1.08462i
\(35\) −4.60555 −0.778480
\(36\) 0 0
\(37\) 2.00000 0.328798 0.164399 0.986394i \(-0.447432\pi\)
0.164399 + 0.986394i \(0.447432\pi\)
\(38\) −2.34861 + 4.06792i −0.380995 + 0.659903i
\(39\) 0 0
\(40\) 1.50000 + 2.59808i 0.237171 + 0.410792i
\(41\) 1.30278 + 2.25647i 0.203459 + 0.352402i 0.949641 0.313341i \(-0.101448\pi\)
−0.746181 + 0.665743i \(0.768115\pi\)
\(42\) 0 0
\(43\) 3.30278 5.72058i 0.503669 0.872380i −0.496322 0.868138i \(-0.665317\pi\)
0.999991 0.00424128i \(-0.00135005\pi\)
\(44\) −0.788897 −0.118931
\(45\) 0 0
\(46\) −3.90833 −0.576251
\(47\) 2.60555 4.51295i 0.380059 0.658281i −0.611012 0.791622i \(-0.709237\pi\)
0.991070 + 0.133341i \(0.0425704\pi\)
\(48\) 0 0
\(49\) −7.10555 12.3072i −1.01508 1.75817i
\(50\) 0.651388 + 1.12824i 0.0921201 + 0.159557i
\(51\) 0 0
\(52\) −0.0916731 + 0.158782i −0.0127128 + 0.0220192i
\(53\) 5.60555 0.769982 0.384991 0.922920i \(-0.374205\pi\)
0.384991 + 0.922920i \(0.374205\pi\)
\(54\) 0 0
\(55\) −2.60555 −0.351332
\(56\) −6.90833 + 11.9656i −0.923164 + 1.59897i
\(57\) 0 0
\(58\) −5.60555 9.70910i −0.736045 1.27487i
\(59\) −4.30278 7.45263i −0.560174 0.970249i −0.997481 0.0709370i \(-0.977401\pi\)
0.437307 0.899312i \(-0.355932\pi\)
\(60\) 0 0
\(61\) −5.10555 + 8.84307i −0.653699 + 1.13224i 0.328519 + 0.944497i \(0.393450\pi\)
−0.982218 + 0.187742i \(0.939883\pi\)
\(62\) −2.09167 −0.265643
\(63\) 0 0
\(64\) 8.81665 1.10208
\(65\) −0.302776 + 0.524423i −0.0375547 + 0.0650466i
\(66\) 0 0
\(67\) 7.60555 + 13.1732i 0.929166 + 1.60936i 0.784720 + 0.619850i \(0.212807\pi\)
0.144446 + 0.989513i \(0.453860\pi\)
\(68\) 0.848612 + 1.46984i 0.102909 + 0.178244i
\(69\) 0 0
\(70\) −3.00000 + 5.19615i −0.358569 + 0.621059i
\(71\) −14.6056 −1.73336 −0.866680 0.498864i \(-0.833751\pi\)
−0.866680 + 0.498864i \(0.833751\pi\)
\(72\) 0 0
\(73\) 5.39445 0.631372 0.315686 0.948864i \(-0.397765\pi\)
0.315686 + 0.948864i \(0.397765\pi\)
\(74\) 1.30278 2.25647i 0.151445 0.262310i
\(75\) 0 0
\(76\) −0.545837 0.945417i −0.0626117 0.108447i
\(77\) −6.00000 10.3923i −0.683763 1.18431i
\(78\) 0 0
\(79\) 2.19722 3.80570i 0.247207 0.428175i −0.715543 0.698569i \(-0.753821\pi\)
0.962750 + 0.270394i \(0.0871539\pi\)
\(80\) 3.30278 0.369262
\(81\) 0 0
\(82\) 3.39445 0.374854
\(83\) 1.50000 2.59808i 0.164646 0.285176i −0.771883 0.635764i \(-0.780685\pi\)
0.936530 + 0.350588i \(0.114018\pi\)
\(84\) 0 0
\(85\) 2.80278 + 4.85455i 0.304004 + 0.526550i
\(86\) −4.30278 7.45263i −0.463980 0.803637i
\(87\) 0 0
\(88\) −3.90833 + 6.76942i −0.416629 + 0.721623i
\(89\) −7.81665 −0.828564 −0.414282 0.910149i \(-0.635967\pi\)
−0.414282 + 0.910149i \(0.635967\pi\)
\(90\) 0 0
\(91\) −2.78890 −0.292356
\(92\) 0.454163 0.786634i 0.0473498 0.0820123i
\(93\) 0 0
\(94\) −3.39445 5.87936i −0.350111 0.606409i
\(95\) −1.80278 3.12250i −0.184961 0.320362i
\(96\) 0 0
\(97\) −4.00000 + 6.92820i −0.406138 + 0.703452i −0.994453 0.105180i \(-0.966458\pi\)
0.588315 + 0.808632i \(0.299792\pi\)
\(98\) −18.5139 −1.87018
\(99\) 0 0
\(100\) −0.302776 −0.0302776
\(101\) 6.00000 10.3923i 0.597022 1.03407i −0.396236 0.918149i \(-0.629684\pi\)
0.993258 0.115924i \(-0.0369830\pi\)
\(102\) 0 0
\(103\) 2.00000 + 3.46410i 0.197066 + 0.341328i 0.947576 0.319531i \(-0.103525\pi\)
−0.750510 + 0.660859i \(0.770192\pi\)
\(104\) 0.908327 + 1.57327i 0.0890688 + 0.154272i
\(105\) 0 0
\(106\) 3.65139 6.32439i 0.354654 0.614279i
\(107\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(108\) 0 0
\(109\) −7.00000 −0.670478 −0.335239 0.942133i \(-0.608817\pi\)
−0.335239 + 0.942133i \(0.608817\pi\)
\(110\) −1.69722 + 2.93968i −0.161824 + 0.280287i
\(111\) 0 0
\(112\) 7.60555 + 13.1732i 0.718657 + 1.24475i
\(113\) −0.394449 0.683205i −0.0371066 0.0642705i 0.846876 0.531791i \(-0.178481\pi\)
−0.883982 + 0.467520i \(0.845147\pi\)
\(114\) 0 0
\(115\) 1.50000 2.59808i 0.139876 0.242272i
\(116\) 2.60555 0.241919
\(117\) 0 0
\(118\) −11.2111 −1.03207
\(119\) −12.9083 + 22.3579i −1.18330 + 2.04954i
\(120\) 0 0
\(121\) 2.10555 + 3.64692i 0.191414 + 0.331538i
\(122\) 6.65139 + 11.5205i 0.602188 + 1.04302i
\(123\) 0 0
\(124\) 0.243061 0.420994i 0.0218275 0.0378064i
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) −4.78890 −0.424946 −0.212473 0.977167i \(-0.568152\pi\)
−0.212473 + 0.977167i \(0.568152\pi\)
\(128\) 4.04584 7.00759i 0.357605 0.619390i
\(129\) 0 0
\(130\) 0.394449 + 0.683205i 0.0345954 + 0.0599211i
\(131\) 3.00000 + 5.19615i 0.262111 + 0.453990i 0.966803 0.255524i \(-0.0822479\pi\)
−0.704692 + 0.709514i \(0.748915\pi\)
\(132\) 0 0
\(133\) 8.30278 14.3808i 0.719942 1.24698i
\(134\) 19.8167 1.71190
\(135\) 0 0
\(136\) 16.8167 1.44202
\(137\) −2.40833 + 4.17134i −0.205757 + 0.356382i −0.950374 0.311111i \(-0.899299\pi\)
0.744616 + 0.667493i \(0.232632\pi\)
\(138\) 0 0
\(139\) 2.00000 + 3.46410i 0.169638 + 0.293821i 0.938293 0.345843i \(-0.112407\pi\)
−0.768655 + 0.639664i \(0.779074\pi\)
\(140\) −0.697224 1.20763i −0.0589262 0.102063i
\(141\) 0 0
\(142\) −9.51388 + 16.4785i −0.798387 + 1.38285i
\(143\) −1.57779 −0.131942
\(144\) 0 0
\(145\) 8.60555 0.714652
\(146\) 3.51388 6.08622i 0.290811 0.503699i
\(147\) 0 0
\(148\) 0.302776 + 0.524423i 0.0248880 + 0.0431073i
\(149\) −6.51388 11.2824i −0.533638 0.924288i −0.999228 0.0392872i \(-0.987491\pi\)
0.465590 0.885000i \(-0.345842\pi\)
\(150\) 0 0
\(151\) 7.21110 12.4900i 0.586831 1.01642i −0.407813 0.913065i \(-0.633709\pi\)
0.994644 0.103356i \(-0.0329581\pi\)
\(152\) −10.8167 −0.877346
\(153\) 0 0
\(154\) −15.6333 −1.25977
\(155\) 0.802776 1.39045i 0.0644805 0.111683i
\(156\) 0 0
\(157\) −1.90833 3.30532i −0.152301 0.263793i 0.779772 0.626064i \(-0.215335\pi\)
−0.932073 + 0.362270i \(0.882002\pi\)
\(158\) −2.86249 4.95798i −0.227728 0.394436i
\(159\) 0 0
\(160\) −0.848612 + 1.46984i −0.0670887 + 0.116201i
\(161\) 13.8167 1.08890
\(162\) 0 0
\(163\) 2.00000 0.156652 0.0783260 0.996928i \(-0.475042\pi\)
0.0783260 + 0.996928i \(0.475042\pi\)
\(164\) −0.394449 + 0.683205i −0.0308013 + 0.0533494i
\(165\) 0 0
\(166\) −1.95416 3.38471i −0.151672 0.262704i
\(167\) −1.50000 2.59808i −0.116073 0.201045i 0.802135 0.597143i \(-0.203697\pi\)
−0.918208 + 0.396098i \(0.870364\pi\)
\(168\) 0 0
\(169\) 6.31665 10.9408i 0.485896 0.841597i
\(170\) 7.30278 0.560097
\(171\) 0 0
\(172\) 2.00000 0.152499
\(173\) 5.40833 9.36750i 0.411187 0.712198i −0.583832 0.811874i \(-0.698447\pi\)
0.995020 + 0.0996766i \(0.0317808\pi\)
\(174\) 0 0
\(175\) −2.30278 3.98852i −0.174073 0.301504i
\(176\) 4.30278 + 7.45263i 0.324334 + 0.561763i
\(177\) 0 0
\(178\) −5.09167 + 8.81904i −0.381637 + 0.661015i
\(179\) 6.78890 0.507426 0.253713 0.967280i \(-0.418348\pi\)
0.253713 + 0.967280i \(0.418348\pi\)
\(180\) 0 0
\(181\) −7.00000 −0.520306 −0.260153 0.965567i \(-0.583773\pi\)
−0.260153 + 0.965567i \(0.583773\pi\)
\(182\) −1.81665 + 3.14654i −0.134659 + 0.233237i
\(183\) 0 0
\(184\) −4.50000 7.79423i −0.331744 0.574598i
\(185\) 1.00000 + 1.73205i 0.0735215 + 0.127343i
\(186\) 0 0
\(187\) −7.30278 + 12.6488i −0.534032 + 0.924970i
\(188\) 1.57779 0.115073
\(189\) 0 0
\(190\) −4.69722 −0.340772
\(191\) 8.21110 14.2220i 0.594135 1.02907i −0.399534 0.916718i \(-0.630828\pi\)
0.993668 0.112353i \(-0.0358387\pi\)
\(192\) 0 0
\(193\) −10.9083 18.8938i −0.785199 1.36000i −0.928880 0.370380i \(-0.879228\pi\)
0.143682 0.989624i \(-0.454106\pi\)
\(194\) 5.21110 + 9.02589i 0.374135 + 0.648021i
\(195\) 0 0
\(196\) 2.15139 3.72631i 0.153671 0.266165i
\(197\) 1.18335 0.0843099 0.0421550 0.999111i \(-0.486578\pi\)
0.0421550 + 0.999111i \(0.486578\pi\)
\(198\) 0 0
\(199\) 13.2111 0.936510 0.468255 0.883593i \(-0.344883\pi\)
0.468255 + 0.883593i \(0.344883\pi\)
\(200\) −1.50000 + 2.59808i −0.106066 + 0.183712i
\(201\) 0 0
\(202\) −7.81665 13.5388i −0.549978 0.952590i
\(203\) 19.8167 + 34.3235i 1.39086 + 2.40903i
\(204\) 0 0
\(205\) −1.30278 + 2.25647i −0.0909898 + 0.157599i
\(206\) 5.21110 0.363075
\(207\) 0 0
\(208\) 2.00000 0.138675
\(209\) 4.69722 8.13583i 0.324914 0.562767i
\(210\) 0 0
\(211\) −6.40833 11.0995i −0.441167 0.764124i 0.556609 0.830775i \(-0.312102\pi\)
−0.997776 + 0.0666502i \(0.978769\pi\)
\(212\) 0.848612 + 1.46984i 0.0582829 + 0.100949i
\(213\) 0 0
\(214\) 0 0
\(215\) 6.60555 0.450495
\(216\) 0 0
\(217\) 7.39445 0.501968
\(218\) −4.55971 + 7.89766i −0.308823 + 0.534897i
\(219\) 0 0
\(220\) −0.394449 0.683205i −0.0265937 0.0460617i
\(221\) 1.69722 + 2.93968i 0.114168 + 0.197744i
\(222\) 0 0
\(223\) 5.00000 8.66025i 0.334825 0.579934i −0.648626 0.761107i \(-0.724656\pi\)
0.983451 + 0.181173i \(0.0579895\pi\)
\(224\) −7.81665 −0.522272
\(225\) 0 0
\(226\) −1.02776 −0.0683653
\(227\) −13.1056 + 22.6995i −0.869846 + 1.50662i −0.00769242 + 0.999970i \(0.502449\pi\)
−0.862154 + 0.506647i \(0.830885\pi\)
\(228\) 0 0
\(229\) 3.10555 + 5.37897i 0.205221 + 0.355453i 0.950203 0.311632i \(-0.100875\pi\)
−0.744982 + 0.667084i \(0.767542\pi\)
\(230\) −1.95416 3.38471i −0.128854 0.223181i
\(231\) 0 0
\(232\) 12.9083 22.3579i 0.847473 1.46787i
\(233\) 18.0000 1.17922 0.589610 0.807688i \(-0.299282\pi\)
0.589610 + 0.807688i \(0.299282\pi\)
\(234\) 0 0
\(235\) 5.21110 0.339935
\(236\) 1.30278 2.25647i 0.0848035 0.146884i
\(237\) 0 0
\(238\) 16.8167 + 29.1273i 1.09006 + 1.88804i
\(239\) −0.394449 0.683205i −0.0255148 0.0441929i 0.852986 0.521934i \(-0.174789\pi\)
−0.878501 + 0.477741i \(0.841456\pi\)
\(240\) 0 0
\(241\) −14.1056 + 24.4315i −0.908618 + 1.57377i −0.0926334 + 0.995700i \(0.529528\pi\)
−0.815985 + 0.578073i \(0.803805\pi\)
\(242\) 5.48612 0.352661
\(243\) 0 0
\(244\) −3.09167 −0.197924
\(245\) 7.10555 12.3072i 0.453957 0.786277i
\(246\) 0 0
\(247\) −1.09167 1.89083i −0.0694615 0.120311i
\(248\) −2.40833 4.17134i −0.152929 0.264881i
\(249\) 0 0
\(250\) −0.651388 + 1.12824i −0.0411974 + 0.0713560i
\(251\) 15.6333 0.986766 0.493383 0.869812i \(-0.335760\pi\)
0.493383 + 0.869812i \(0.335760\pi\)
\(252\) 0 0
\(253\) 7.81665 0.491429
\(254\) −3.11943 + 5.40301i −0.195730 + 0.339015i
\(255\) 0 0
\(256\) 3.54584 + 6.14157i 0.221615 + 0.383848i
\(257\) 11.4083 + 19.7598i 0.711632 + 1.23258i 0.964244 + 0.265015i \(0.0853769\pi\)
−0.252612 + 0.967568i \(0.581290\pi\)
\(258\) 0 0
\(259\) −4.60555 + 7.97705i −0.286175 + 0.495670i
\(260\) −0.183346 −0.0113706
\(261\) 0 0
\(262\) 7.81665 0.482914
\(263\) −8.60555 + 14.9053i −0.530641 + 0.919097i 0.468720 + 0.883347i \(0.344715\pi\)
−0.999361 + 0.0357503i \(0.988618\pi\)
\(264\) 0 0
\(265\) 2.80278 + 4.85455i 0.172173 + 0.298213i
\(266\) −10.8167 18.7350i −0.663212 1.14872i
\(267\) 0 0
\(268\) −2.30278 + 3.98852i −0.140664 + 0.243638i
\(269\) −11.2111 −0.683553 −0.341776 0.939781i \(-0.611029\pi\)
−0.341776 + 0.939781i \(0.611029\pi\)
\(270\) 0 0
\(271\) −19.2389 −1.16868 −0.584339 0.811510i \(-0.698646\pi\)
−0.584339 + 0.811510i \(0.698646\pi\)
\(272\) 9.25694 16.0335i 0.561284 0.972173i
\(273\) 0 0
\(274\) 3.13751 + 5.43433i 0.189544 + 0.328300i
\(275\) −1.30278 2.25647i −0.0785603 0.136070i
\(276\) 0 0
\(277\) 14.5139 25.1388i 0.872054 1.51044i 0.0121867 0.999926i \(-0.496121\pi\)
0.859868 0.510517i \(-0.170546\pi\)
\(278\) 5.21110 0.312541
\(279\) 0 0
\(280\) −13.8167 −0.825703
\(281\) 0.908327 1.57327i 0.0541862 0.0938533i −0.837660 0.546192i \(-0.816077\pi\)
0.891846 + 0.452339i \(0.149410\pi\)
\(282\) 0 0
\(283\) −5.30278 9.18468i −0.315217 0.545972i 0.664266 0.747496i \(-0.268744\pi\)
−0.979484 + 0.201524i \(0.935411\pi\)
\(284\) −2.21110 3.82974i −0.131205 0.227253i
\(285\) 0 0
\(286\) −1.02776 + 1.78013i −0.0607725 + 0.105261i
\(287\) −12.0000 −0.708338
\(288\) 0 0
\(289\) 14.4222 0.848365
\(290\) 5.60555 9.70910i 0.329169 0.570138i
\(291\) 0 0
\(292\) 0.816654 + 1.41449i 0.0477911 + 0.0827765i
\(293\) −14.4083 24.9560i −0.841743 1.45794i −0.888420 0.459032i \(-0.848196\pi\)
0.0466761 0.998910i \(-0.485137\pi\)
\(294\) 0 0
\(295\) 4.30278 7.45263i 0.250517 0.433909i
\(296\) 6.00000 0.348743
\(297\) 0 0
\(298\) −16.9722 −0.983176
\(299\) 0.908327 1.57327i 0.0525299 0.0909845i
\(300\) 0 0
\(301\) 15.2111 + 26.3464i 0.876753 + 1.51858i
\(302\) −9.39445 16.2717i −0.540590 0.936329i
\(303\) 0 0
\(304\) −5.95416 + 10.3129i −0.341495 + 0.591486i
\(305\) −10.2111 −0.584686
\(306\) 0 0
\(307\) −20.4222 −1.16556 −0.582778 0.812631i \(-0.698034\pi\)
−0.582778 + 0.812631i \(0.698034\pi\)
\(308\) 1.81665 3.14654i 0.103513 0.179291i
\(309\) 0 0
\(310\) −1.04584 1.81144i −0.0593995 0.102883i
\(311\) 6.90833 + 11.9656i 0.391735 + 0.678505i 0.992679 0.120786i \(-0.0385416\pi\)
−0.600943 + 0.799292i \(0.705208\pi\)
\(312\) 0 0
\(313\) −11.8167 + 20.4670i −0.667917 + 1.15687i 0.310569 + 0.950551i \(0.399480\pi\)
−0.978486 + 0.206315i \(0.933853\pi\)
\(314\) −4.97224 −0.280600
\(315\) 0 0
\(316\) 1.33053 0.0748483
\(317\) −0.197224 + 0.341603i −0.0110772 + 0.0191863i −0.871511 0.490376i \(-0.836859\pi\)
0.860434 + 0.509562i \(0.170193\pi\)
\(318\) 0 0
\(319\) 11.2111 + 19.4182i 0.627701 + 1.08721i
\(320\) 4.40833 + 7.63545i 0.246433 + 0.426834i
\(321\) 0 0
\(322\) 9.00000 15.5885i 0.501550 0.868711i
\(323\) −20.2111 −1.12458
\(324\) 0 0
\(325\) −0.605551 −0.0335899
\(326\) 1.30278 2.25647i 0.0721541 0.124975i
\(327\) 0 0
\(328\) 3.90833 + 6.76942i 0.215801 + 0.373779i
\(329\) 12.0000 + 20.7846i 0.661581 + 1.14589i
\(330\) 0 0
\(331\) −7.39445 + 12.8076i −0.406436 + 0.703967i −0.994487 0.104856i \(-0.966562\pi\)
0.588052 + 0.808823i \(0.299895\pi\)
\(332\) 0.908327 0.0498509
\(333\) 0 0
\(334\) −3.90833 −0.213854
\(335\) −7.60555 + 13.1732i −0.415536 + 0.719729i
\(336\) 0 0
\(337\) 0.302776 + 0.524423i 0.0164932 + 0.0285671i 0.874154 0.485648i \(-0.161416\pi\)
−0.857661 + 0.514216i \(0.828083\pi\)
\(338\) −8.22918 14.2534i −0.447609 0.775281i
\(339\) 0 0
\(340\) −0.848612 + 1.46984i −0.0460225 + 0.0797132i
\(341\) 4.18335 0.226541
\(342\) 0 0
\(343\) 33.2111 1.79323
\(344\) 9.90833 17.1617i 0.534221 0.925298i
\(345\) 0 0
\(346\) −7.04584 12.2037i −0.378787 0.656077i
\(347\) 0.788897 + 1.36641i 0.0423502 + 0.0733528i 0.886424 0.462875i \(-0.153182\pi\)
−0.844073 + 0.536228i \(0.819849\pi\)
\(348\) 0 0
\(349\) −12.9222 + 22.3819i −0.691710 + 1.19808i 0.279568 + 0.960126i \(0.409809\pi\)
−0.971277 + 0.237950i \(0.923524\pi\)
\(350\) −6.00000 −0.320713
\(351\) 0 0
\(352\) −4.42221 −0.235704
\(353\) −10.8167 + 18.7350i −0.575712 + 0.997163i 0.420251 + 0.907408i \(0.361942\pi\)
−0.995964 + 0.0897554i \(0.971391\pi\)
\(354\) 0 0
\(355\) −7.30278 12.6488i −0.387591 0.671327i
\(356\) −1.18335 2.04962i −0.0627172 0.108629i
\(357\) 0 0
\(358\) 4.42221 7.65948i 0.233721 0.404816i
\(359\) −33.6333 −1.77510 −0.887549 0.460713i \(-0.847594\pi\)
−0.887549 + 0.460713i \(0.847594\pi\)
\(360\) 0 0
\(361\) −6.00000 −0.315789
\(362\) −4.55971 + 7.89766i −0.239653 + 0.415092i
\(363\) 0 0
\(364\) −0.422205 0.731281i −0.0221296 0.0383295i
\(365\) 2.69722 + 4.67173i 0.141179 + 0.244530i
\(366\) 0 0
\(367\) −2.30278 + 3.98852i −0.120204 + 0.208199i −0.919848 0.392275i \(-0.871688\pi\)
0.799644 + 0.600474i \(0.205022\pi\)
\(368\) −9.90833 −0.516507
\(369\) 0 0
\(370\) 2.60555 0.135456
\(371\) −12.9083 + 22.3579i −0.670167 + 1.16076i
\(372\) 0 0
\(373\) 5.39445 + 9.34346i 0.279314 + 0.483786i 0.971214 0.238207i \(-0.0765596\pi\)
−0.691900 + 0.721993i \(0.743226\pi\)
\(374\) 9.51388 + 16.4785i 0.491951 + 0.852084i
\(375\) 0 0
\(376\) 7.81665 13.5388i 0.403113 0.698212i
\(377\) 5.21110 0.268385
\(378\) 0 0
\(379\) 14.3944 0.739393 0.369697 0.929153i \(-0.379462\pi\)
0.369697 + 0.929153i \(0.379462\pi\)
\(380\) 0.545837 0.945417i 0.0280008 0.0484988i
\(381\) 0 0
\(382\) −10.6972 18.5281i −0.547318 0.947982i
\(383\) −9.31665 16.1369i −0.476059 0.824558i 0.523565 0.851986i \(-0.324602\pi\)
−0.999624 + 0.0274277i \(0.991268\pi\)
\(384\) 0 0
\(385\) 6.00000 10.3923i 0.305788 0.529641i
\(386\) −28.4222 −1.44665
\(387\) 0 0
\(388\) −2.42221 −0.122969
\(389\) 2.09167 3.62288i 0.106052 0.183688i −0.808116 0.589024i \(-0.799512\pi\)
0.914168 + 0.405337i \(0.132846\pi\)
\(390\) 0 0
\(391\) −8.40833 14.5636i −0.425227 0.736515i
\(392\) −21.3167 36.9215i −1.07665 1.86482i
\(393\) 0 0
\(394\) 0.770817 1.33509i 0.0388332 0.0672611i
\(395\) 4.39445 0.221109
\(396\) 0 0
\(397\) −12.6056 −0.632654 −0.316327 0.948650i \(-0.602450\pi\)
−0.316327 + 0.948650i \(0.602450\pi\)
\(398\) 8.60555 14.9053i 0.431357 0.747133i
\(399\) 0 0
\(400\) 1.65139 + 2.86029i 0.0825694 + 0.143014i
\(401\) −15.0000 25.9808i −0.749064 1.29742i −0.948272 0.317460i \(-0.897170\pi\)
0.199207 0.979957i \(-0.436163\pi\)
\(402\) 0 0
\(403\) 0.486122 0.841988i 0.0242155 0.0419424i
\(404\) 3.63331 0.180764
\(405\) 0 0
\(406\) 51.6333 2.56252
\(407\) −2.60555 + 4.51295i −0.129152 + 0.223698i
\(408\) 0 0
\(409\) −2.50000 4.33013i −0.123617 0.214111i 0.797574 0.603220i \(-0.206116\pi\)
−0.921192 + 0.389109i \(0.872783\pi\)
\(410\) 1.69722 + 2.93968i 0.0838199 + 0.145180i
\(411\) 0 0
\(412\) −0.605551 + 1.04885i −0.0298334 + 0.0516729i
\(413\) 39.6333 1.95023
\(414\) 0 0
\(415\) 3.00000 0.147264
\(416\) −0.513878 + 0.890063i −0.0251950 + 0.0436389i
\(417\) 0 0
\(418\) −6.11943 10.5992i −0.299311 0.518422i
\(419\) −6.51388 11.2824i −0.318224 0.551180i 0.661894 0.749598i \(-0.269753\pi\)
−0.980118 + 0.198418i \(0.936420\pi\)
\(420\) 0 0
\(421\) 11.7111 20.2842i 0.570764 0.988593i −0.425723 0.904853i \(-0.639980\pi\)
0.996488 0.0837393i \(-0.0266863\pi\)
\(422\) −16.6972 −0.812808
\(423\) 0 0
\(424\) 16.8167 0.816689
\(425\) −2.80278 + 4.85455i −0.135955 + 0.235480i
\(426\) 0 0
\(427\) −23.5139 40.7272i −1.13792 1.97093i
\(428\) 0 0
\(429\) 0 0
\(430\) 4.30278 7.45263i 0.207498 0.359398i
\(431\) −25.8167 −1.24354 −0.621772 0.783198i \(-0.713587\pi\)
−0.621772 + 0.783198i \(0.713587\pi\)
\(432\) 0 0
\(433\) −28.2389 −1.35707 −0.678536 0.734567i \(-0.737385\pi\)
−0.678536 + 0.734567i \(0.737385\pi\)
\(434\) 4.81665 8.34269i 0.231207 0.400462i
\(435\) 0 0
\(436\) −1.05971 1.83548i −0.0507511 0.0879035i
\(437\) 5.40833 + 9.36750i 0.258715 + 0.448108i
\(438\) 0 0
\(439\) −10.1972 + 17.6621i −0.486687 + 0.842967i −0.999883 0.0153049i \(-0.995128\pi\)
0.513196 + 0.858271i \(0.328461\pi\)
\(440\) −7.81665 −0.372644
\(441\) 0 0
\(442\) 4.42221 0.210343
\(443\) 9.31665 16.1369i 0.442648 0.766688i −0.555237 0.831692i \(-0.687373\pi\)
0.997885 + 0.0650038i \(0.0207059\pi\)
\(444\) 0 0
\(445\) −3.90833 6.76942i −0.185272 0.320901i
\(446\) −6.51388 11.2824i −0.308441 0.534236i
\(447\) 0 0
\(448\) −20.3028 + 35.1654i −0.959216 + 1.66141i
\(449\) 12.2389 0.577587 0.288794 0.957391i \(-0.406746\pi\)
0.288794 + 0.957391i \(0.406746\pi\)
\(450\) 0 0
\(451\) −6.78890 −0.319677
\(452\) 0.119429 0.206858i 0.00561749 0.00972978i
\(453\) 0 0
\(454\) 17.0736 + 29.5723i 0.801303 + 1.38790i
\(455\) −1.39445 2.41526i −0.0653728 0.113229i
\(456\) 0 0
\(457\) −0.605551 + 1.04885i −0.0283265 + 0.0490629i −0.879841 0.475268i \(-0.842351\pi\)
0.851515 + 0.524331i \(0.175684\pi\)
\(458\) 8.09167 0.378099
\(459\) 0 0
\(460\) 0.908327 0.0423510
\(461\) −10.8167 + 18.7350i −0.503782 + 0.872576i 0.496209 + 0.868203i \(0.334725\pi\)
−0.999990 + 0.00437236i \(0.998608\pi\)
\(462\) 0 0
\(463\) 7.60555 + 13.1732i 0.353460 + 0.612211i 0.986853 0.161620i \(-0.0516717\pi\)
−0.633393 + 0.773830i \(0.718338\pi\)
\(464\) −14.2111 24.6144i −0.659734 1.14269i
\(465\) 0 0
\(466\) 11.7250 20.3083i 0.543149 0.940762i
\(467\) 2.21110 0.102318 0.0511588 0.998691i \(-0.483709\pi\)
0.0511588 + 0.998691i \(0.483709\pi\)
\(468\) 0 0
\(469\) −70.0555 −3.23486
\(470\) 3.39445 5.87936i 0.156574 0.271195i
\(471\) 0 0
\(472\) −12.9083 22.3579i −0.594154 1.02910i
\(473\) 8.60555 + 14.9053i 0.395684 + 0.685344i
\(474\) 0 0
\(475\) 1.80278 3.12250i 0.0827170 0.143270i
\(476\) −7.81665 −0.358276
\(477\) 0 0
\(478\) −1.02776 −0.0470085
\(479\) −8.09167 + 14.0152i −0.369718 + 0.640370i −0.989521 0.144387i \(-0.953879\pi\)
0.619803 + 0.784757i \(0.287212\pi\)
\(480\) 0 0
\(481\) 0.605551 + 1.04885i 0.0276108 + 0.0478232i
\(482\) 18.3764 + 31.8288i 0.837021 + 1.44976i
\(483\) 0 0
\(484\) −0.637510 + 1.10420i −0.0289777 + 0.0501909i
\(485\) −8.00000 −0.363261
\(486\) 0 0
\(487\) −8.18335 −0.370823 −0.185411 0.982661i \(-0.559362\pi\)
−0.185411 + 0.982661i \(0.559362\pi\)
\(488\) −15.3167 + 26.5292i −0.693352 + 1.20092i
\(489\) 0 0
\(490\) −9.25694 16.0335i −0.418186 0.724319i
\(491\) 6.39445 + 11.0755i 0.288577 + 0.499831i 0.973470 0.228813i \(-0.0734844\pi\)
−0.684893 + 0.728644i \(0.740151\pi\)
\(492\) 0 0
\(493\) 24.1194 41.7761i 1.08628 1.88150i
\(494\) −2.84441 −0.127976
\(495\) 0 0
\(496\) −5.30278 −0.238102
\(497\) 33.6333 58.2546i 1.50866 2.61308i
\(498\) 0 0
\(499\) 13.8028 + 23.9071i 0.617897 + 1.07023i 0.989869 + 0.141985i \(0.0453485\pi\)
−0.371972 + 0.928244i \(0.621318\pi\)
\(500\) −0.151388 0.262211i −0.00677027 0.0117265i
\(501\) 0 0
\(502\) 10.1833 17.6381i 0.454505 0.787226i
\(503\) −31.4222 −1.40105 −0.700523 0.713629i \(-0.747050\pi\)
−0.700523 + 0.713629i \(0.747050\pi\)
\(504\) 0 0
\(505\) 12.0000 0.533993
\(506\) 5.09167 8.81904i 0.226352 0.392054i
\(507\) 0 0
\(508\) −0.724981 1.25570i −0.0321658 0.0557128i
\(509\) 16.4222 + 28.4441i 0.727901 + 1.26076i 0.957769 + 0.287540i \(0.0928375\pi\)
−0.229867 + 0.973222i \(0.573829\pi\)
\(510\) 0 0
\(511\) −12.4222 + 21.5159i −0.549526 + 0.951807i
\(512\) 25.4222 1.12351
\(513\) 0 0
\(514\) 29.7250 1.31111
\(515\) −2.00000 + 3.46410i −0.0881305 + 0.152647i
\(516\) 0 0
\(517\) 6.78890 + 11.7587i 0.298575 + 0.517148i
\(518\) 6.00000 + 10.3923i 0.263625 + 0.456612i
\(519\) 0 0
\(520\) −0.908327 + 1.57327i −0.0398328 + 0.0689924i
\(521\) 21.3944 0.937308 0.468654 0.883382i \(-0.344739\pi\)
0.468654 + 0.883382i \(0.344739\pi\)
\(522\) 0 0
\(523\) 23.3944 1.02297 0.511484 0.859293i \(-0.329096\pi\)
0.511484 + 0.859293i \(0.329096\pi\)
\(524\) −0.908327 + 1.57327i −0.0396804 + 0.0687285i
\(525\) 0 0
\(526\) 11.2111 + 19.4182i 0.488827 + 0.846674i
\(527\) −4.50000 7.79423i −0.196023 0.339522i
\(528\) 0 0
\(529\) 7.00000 12.1244i 0.304348 0.527146i
\(530\) 7.30278 0.317212
\(531\) 0 0
\(532\) 5.02776 0.217981
\(533\) −0.788897 + 1.36641i −0.0341709 + 0.0591858i
\(534\) 0 0
\(535\) 0 0
\(536\) 22.8167 + 39.5196i 0.985529 + 1.70699i
\(537\) 0 0
\(538\) −7.30278 + 12.6488i −0.314845 + 0.545328i
\(539\) 37.0278 1.59490
\(540\) 0 0
\(541\) −11.5778 −0.497768 −0.248884 0.968533i \(-0.580064\pi\)
−0.248884 + 0.968533i \(0.580064\pi\)
\(542\) −12.5320 + 21.7060i −0.538294 + 0.932352i
\(543\) 0 0
\(544\) 4.75694 + 8.23926i 0.203952 + 0.353255i
\(545\) −3.50000 6.06218i −0.149924 0.259675i
\(546\) 0 0
\(547\) 3.30278 5.72058i 0.141216 0.244594i −0.786738 0.617286i \(-0.788232\pi\)
0.927955 + 0.372692i \(0.121565\pi\)
\(548\) −1.45837 −0.0622983
\(549\) 0 0
\(550\) −3.39445 −0.144740
\(551\) −15.5139 + 26.8708i −0.660913 + 1.14474i
\(552\) 0 0
\(553\) 10.1194 + 17.5274i 0.430322 + 0.745339i
\(554\) −18.9083 32.7502i −0.803338 1.39142i
\(555\) 0 0
\(556\) −0.605551 + 1.04885i −0.0256811 + 0.0444810i
\(557\) 33.6333 1.42509 0.712544 0.701627i \(-0.247543\pi\)
0.712544 + 0.701627i \(0.247543\pi\)
\(558\) 0 0
\(559\) 4.00000 0.169182
\(560\) −7.60555 + 13.1732i −0.321393 + 0.556669i
\(561\) 0 0
\(562\) −1.18335 2.04962i −0.0499164 0.0864578i
\(563\) 12.0000 + 20.7846i 0.505740 + 0.875967i 0.999978 + 0.00664037i \(0.00211371\pi\)
−0.494238 + 0.869326i \(0.664553\pi\)
\(564\) 0 0
\(565\) 0.394449 0.683205i 0.0165946 0.0287427i
\(566\) −13.8167 −0.580757
\(567\) 0 0
\(568\) −43.8167 −1.83851
\(569\) 18.9083 32.7502i 0.792678 1.37296i −0.131625 0.991300i \(-0.542019\pi\)
0.924303 0.381659i \(-0.124647\pi\)
\(570\) 0 0
\(571\) 18.2250 + 31.5666i 0.762692 + 1.32102i 0.941458 + 0.337129i \(0.109456\pi\)
−0.178767 + 0.983891i \(0.557211\pi\)
\(572\) −0.238859 0.413716i −0.00998719 0.0172983i
\(573\) 0 0
\(574\) −7.81665 + 13.5388i −0.326261 + 0.565100i
\(575\) 3.00000 0.125109
\(576\) 0 0
\(577\) 27.8167 1.15802 0.579011 0.815320i \(-0.303439\pi\)
0.579011 + 0.815320i \(0.303439\pi\)
\(578\) 9.39445 16.2717i 0.390758 0.676812i
\(579\) 0 0
\(580\) 1.30278 + 2.25647i 0.0540948 + 0.0936950i
\(581\) 6.90833 + 11.9656i 0.286606 + 0.496416i
\(582\) 0 0
\(583\) −7.30278 + 12.6488i −0.302450 + 0.523859i
\(584\) 16.1833 0.669672
\(585\) 0 0
\(586\) −37.5416 −1.55083
\(587\) 10.5000 18.1865i 0.433381 0.750639i −0.563781 0.825925i \(-0.690654\pi\)
0.997162 + 0.0752860i \(0.0239870\pi\)
\(588\) 0 0
\(589\) 2.89445 + 5.01333i 0.119264 + 0.206571i
\(590\) −5.60555 9.70910i −0.230777 0.399717i
\(591\) 0 0
\(592\) 3.30278 5.72058i 0.135743 0.235114i
\(593\) −21.2389 −0.872175 −0.436088 0.899904i \(-0.643636\pi\)
−0.436088 + 0.899904i \(0.643636\pi\)
\(594\) 0 0
\(595\) −25.8167 −1.05838
\(596\) 1.97224 3.41603i 0.0807862 0.139926i
\(597\) 0 0
\(598\) −1.18335 2.04962i −0.0483906 0.0838150i
\(599\) −7.69722 13.3320i −0.314500 0.544730i 0.664831 0.746994i \(-0.268504\pi\)
−0.979331 + 0.202264i \(0.935170\pi\)
\(600\) 0 0
\(601\) −16.3167 + 28.2613i −0.665570 + 1.15280i 0.313560 + 0.949568i \(0.398478\pi\)
−0.979130 + 0.203233i \(0.934855\pi\)
\(602\) 39.6333 1.61533
\(603\) 0 0
\(604\) 4.36669 0.177678
\(605\) −2.10555 + 3.64692i −0.0856028 + 0.148268i
\(606\) 0 0
\(607\) −8.69722 15.0640i −0.353009 0.611430i 0.633766 0.773525i \(-0.281508\pi\)
−0.986775 + 0.162095i \(0.948175\pi\)
\(608\) −3.05971 5.29958i −0.124088 0.214926i
\(609\) 0 0
\(610\) −6.65139 + 11.5205i −0.269307 + 0.466453i
\(611\) 3.15559 0.127661
\(612\) 0 0
\(613\) 28.8444 1.16501 0.582507 0.812825i \(-0.302072\pi\)
0.582507 + 0.812825i \(0.302072\pi\)
\(614\) −13.3028 + 23.0411i −0.536856 + 0.929862i
\(615\) 0 0
\(616\) −18.0000 31.1769i −0.725241 1.25615i
\(617\) −13.2250 22.9063i −0.532418 0.922174i −0.999284 0.0378463i \(-0.987950\pi\)
0.466866 0.884328i \(-0.345383\pi\)
\(618\) 0 0
\(619\) 3.81665 6.61064i 0.153404 0.265704i −0.779073 0.626934i \(-0.784310\pi\)
0.932477 + 0.361230i \(0.117643\pi\)
\(620\) 0.486122 0.0195231
\(621\) 0 0
\(622\) 18.0000 0.721734
\(623\) 18.0000 31.1769i 0.721155 1.24908i
\(624\) 0 0
\(625\) −0.500000 0.866025i −0.0200000 0.0346410i
\(626\) 15.3944 + 26.6640i 0.615286 + 1.06571i
\(627\) 0 0
\(628\) 0.577795 1.00077i 0.0230565 0.0399351i
\(629\) 11.2111 0.447016
\(630\) 0 0
\(631\) 30.0278 1.19539 0.597693 0.801725i \(-0.296084\pi\)
0.597693 + 0.801725i \(0.296084\pi\)
\(632\) 6.59167 11.4171i 0.262203 0.454148i
\(633\) 0 0
\(634\) 0.256939 + 0.445032i 0.0102044 + 0.0176745i
\(635\) −2.39445 4.14731i −0.0950208 0.164581i
\(636\) 0 0
\(637\) 4.30278 7.45263i 0.170482 0.295284i
\(638\) 29.2111 1.15648
\(639\) 0 0
\(640\) 8.09167 0.319851
\(641\) −12.0000 + 20.7846i −0.473972 + 0.820943i −0.999556 0.0297987i \(-0.990513\pi\)
0.525584 + 0.850741i \(0.323847\pi\)
\(642\) 0 0
\(643\) 11.5139 + 19.9426i 0.454063 + 0.786460i 0.998634 0.0522547i \(-0.0166408\pi\)
−0.544571 + 0.838715i \(0.683307\pi\)
\(644\) 2.09167 + 3.62288i 0.0824235 + 0.142762i
\(645\) 0 0
\(646\) −13.1653 + 22.8029i −0.517980 + 0.897168i
\(647\) −38.2111 −1.50223 −0.751117 0.660169i \(-0.770484\pi\)
−0.751117 + 0.660169i \(0.770484\pi\)
\(648\) 0 0
\(649\) 22.4222 0.880149
\(650\) −0.394449 + 0.683205i −0.0154716 + 0.0267975i
\(651\) 0 0
\(652\) 0.302776 + 0.524423i 0.0118576 + 0.0205380i
\(653\) 13.6194 + 23.5895i 0.532969 + 0.923130i 0.999259 + 0.0384979i \(0.0122573\pi\)
−0.466289 + 0.884632i \(0.654409\pi\)
\(654\) 0 0
\(655\) −3.00000 + 5.19615i −0.117220 + 0.203030i
\(656\) 8.60555 0.335990
\(657\) 0 0
\(658\) 31.2666 1.21890
\(659\) −10.3028 + 17.8449i −0.401339 + 0.695140i −0.993888 0.110395i \(-0.964788\pi\)
0.592549 + 0.805535i \(0.298122\pi\)
\(660\) 0 0
\(661\) −11.4222 19.7838i −0.444272 0.769502i 0.553729 0.832697i \(-0.313204\pi\)
−0.998001 + 0.0631948i \(0.979871\pi\)
\(662\) 9.63331 + 16.6854i 0.374409 + 0.648496i
\(663\) 0 0
\(664\) 4.50000 7.79423i 0.174634 0.302475i
\(665\) 16.6056 0.643936
\(666\) 0 0
\(667\) −25.8167 −0.999625
\(668\) 0.454163 0.786634i 0.0175721 0.0304358i
\(669\) 0 0
\(670\) 9.90833 + 17.1617i 0.382792 + 0.663015i
\(671\) −13.3028 23.0411i −0.513548 0.889491i
\(672\) 0 0
\(673\) 5.51388 9.55032i 0.212544 0.368138i −0.739966 0.672645i \(-0.765158\pi\)
0.952510 + 0.304507i \(0.0984917\pi\)
\(674\) 0.788897 0.0303872
\(675\) 0 0
\(676\) 3.82506 0.147118
\(677\) −10.8167 + 18.7350i −0.415718 + 0.720044i −0.995504 0.0947247i \(-0.969803\pi\)
0.579786 + 0.814769i \(0.303136\pi\)
\(678\) 0 0
\(679\) −18.4222 31.9082i −0.706979 1.22452i
\(680\) 8.40833 + 14.5636i 0.322445 + 0.558490i
\(681\) 0 0
\(682\) 2.72498 4.71981i 0.104345 0.180731i
\(683\) 9.00000 0.344375 0.172188 0.985064i \(-0.444916\pi\)
0.172188 + 0.985064i \(0.444916\pi\)
\(684\) 0 0
\(685\) −4.81665 −0.184035
\(686\) 21.6333 37.4700i 0.825964 1.43061i
\(687\) 0 0
\(688\) −10.9083 18.8938i −0.415876 0.720318i
\(689\) 1.69722 + 2.93968i 0.0646591 + 0.111993i
\(690\) 0 0
\(691\) −1.19722 + 2.07365i −0.0455446 + 0.0788855i −0.887899 0.460038i \(-0.847836\pi\)
0.842354 + 0.538924i \(0.181169\pi\)
\(692\) 3.27502 0.124498
\(693\) 0 0
\(694\) 2.05551 0.0780262
\(695\) −2.00000 + 3.46410i −0.0758643 + 0.131401i
\(696\) 0 0
\(697\) 7.30278 + 12.6488i 0.276612 + 0.479107i
\(698\) 16.8347 + 29.1586i 0.637204 + 1.10367i
\(699\) 0 0
\(700\) 0.697224 1.20763i 0.0263526 0.0456440i
\(701\) −40.4222 −1.52673 −0.763363 0.645970i \(-0.776453\pi\)
−0.763363 + 0.645970i \(0.776453\pi\)
\(702\) 0 0
\(703\) −7.21110 −0.271972
\(704\) −11.4861 + 19.8945i −0.432900 + 0.749804i
\(705\) 0 0
\(706\) 14.0917 + 24.4075i 0.530347 + 0.918588i
\(707\) 27.6333 + 47.8623i 1.03926 + 1.80005i
\(708\) 0 0
\(709\) −17.4222 + 30.1761i −0.654305 + 1.13329i 0.327763 + 0.944760i \(0.393705\pi\)
−0.982068 + 0.188529i \(0.939628\pi\)
\(710\) −19.0278 −0.714099
\(711\) 0 0
\(712\) −23.4500 −0.878824
\(713\) −2.40833 + 4.17134i −0.0901926 + 0.156218i
\(714\) 0 0
\(715\) −0.788897 1.36641i −0.0295031 0.0511009i
\(716\) 1.02776 + 1.78013i 0.0384091 + 0.0665264i
\(717\) 0 0
\(718\) −21.9083 + 37.9463i −0.817611 + 1.41614i
\(719\) 49.2666 1.83733 0.918667 0.395032i \(-0.129267\pi\)
0.918667 + 0.395032i \(0.129267\pi\)
\(720\) 0 0
\(721\) −18.4222 −0.686079
\(722\) −3.90833 + 6.76942i −0.145453 + 0.251932i
\(723\) 0 0
\(724\) −1.05971 1.83548i −0.0393840 0.0682151i
\(725\) 4.30278 + 7.45263i 0.159801 + 0.276784i
\(726\) 0 0
\(727\) 3.81665 6.61064i 0.141552 0.245175i −0.786529 0.617553i \(-0.788124\pi\)
0.928081 + 0.372378i \(0.121457\pi\)
\(728\) −8.36669 −0.310090
\(729\) 0 0
\(730\) 7.02776 0.260109
\(731\) 18.5139 32.0670i 0.684761 1.18604i
\(732\) 0 0
\(733\) −16.0000 27.7128i −0.590973 1.02360i −0.994102 0.108453i \(-0.965410\pi\)
0.403128 0.915144i \(-0.367923\pi\)
\(734\) 3.00000 + 5.19615i 0.110732 + 0.191793i
\(735\) 0 0
\(736\) 2.54584 4.40952i 0.0938408 0.162537i
\(737\) −39.6333 −1.45991
\(738\) 0 0
\(739\) 30.0278 1.10459 0.552294 0.833649i \(-0.313752\pi\)
0.552294 + 0.833649i \(0.313752\pi\)
\(740\) −0.302776 + 0.524423i −0.0111303 + 0.0192782i
\(741\) 0 0
\(742\) 16.8167 + 29.1273i 0.617359 + 1.06930i
\(743\) −17.2111 29.8105i −0.631414 1.09364i −0.987263 0.159098i \(-0.949141\pi\)
0.355849 0.934544i \(-0.384192\pi\)
\(744\) 0 0
\(745\) 6.51388 11.2824i 0.238650 0.413354i
\(746\) 14.0555 0.514609
\(747\) 0 0
\(748\) −4.42221 −0.161692
\(749\) 0 0
\(750\) 0 0
\(751\) −3.01388 5.22019i −0.109978 0.190487i 0.805783 0.592211i \(-0.201745\pi\)
−0.915761 + 0.401723i \(0.868411\pi\)
\(752\) −8.60555 14.9053i −0.313812 0.543539i
\(753\) 0 0
\(754\) 3.39445 5.87936i 0.123619 0.214114i
\(755\) 14.4222 0.524878
\(756\) 0 0
\(757\) 31.2111 1.13439 0.567193 0.823585i \(-0.308029\pi\)
0.567193 + 0.823585i \(0.308029\pi\)
\(758\) 9.37637 16.2403i 0.340565 0.589876i
\(759\) 0 0
\(760\) −5.40833 9.36750i −0.196181 0.339795i
\(761\) −26.7250 46.2890i −0.968780 1.67798i −0.699097 0.715027i \(-0.746415\pi\)
−0.269682 0.962949i \(-0.586919\pi\)
\(762\) 0 0
\(763\) 16.1194 27.9197i 0.583563 1.01076i
\(764\) 4.97224 0.179889
\(765\) 0 0
\(766\) −24.2750 −0.877092
\(767\) 2.60555 4.51295i 0.0940810 0.162953i
\(768\) 0 0
\(769\) −20.5000 35.5070i −0.739249 1.28042i −0.952834 0.303492i \(-0.901847\pi\)
0.213585 0.976924i \(-0.431486\pi\)
\(770\) −7.81665 13.5388i −0.281693 0.487906i
\(771\) 0 0
\(772\) 3.30278 5.72058i 0.118869 0.205888i
\(773\) −16.8167 −0.604853 −0.302426 0.953173i \(-0.597797\pi\)
−0.302426 + 0.953173i \(0.597797\pi\)
\(774\) 0 0
\(775\) 1.60555 0.0576731
\(776\) −12.0000 + 20.7846i −0.430775 + 0.746124i
\(777\) 0 0
\(778\) −2.72498 4.71981i −0.0976953 0.169213i
\(779\) −4.69722 8.13583i −0.168296 0.291496i
\(780\) 0 0
\(781\) 19.0278 32.9570i 0.680867 1.17930i
\(782\) −21.9083 −0.783440
\(783\) 0 0
\(784\) −46.9361 −1.67629
\(785\) 1.90833 3.30532i 0.0681111 0.117972i
\(786\) 0 0
\(787\) 1.48612 + 2.57404i 0.0529745 + 0.0917546i 0.891297 0.453421i \(-0.149796\pi\)
−0.838322 + 0.545175i \(0.816463\pi\)
\(788\) 0.179144 + 0.310287i 0.00638175 + 0.0110535i
\(789\) 0 0
\(790\) 2.86249 4.95798i 0.101843 0.176397i
\(791\) 3.63331 0.129186
\(792\) 0 0
\(793\) −6.18335 −0.219577
\(794\) −8.21110 + 14.2220i −0.291401 + 0.504722i
\(795\) 0 0
\(796\) 2.00000 + 3.46410i 0.0708881 + 0.122782i
\(797\) −18.8305 32.6154i −0.667012 1.15530i −0.978736 0.205125i \(-0.934240\pi\)
0.311724 0.950173i \(-0.399094\pi\)
\(798\) 0 0
\(799\) 14.6056 25.2976i 0.516707 0.894963i
\(800\) −1.69722 −0.0600059
\(801\) 0 0
\(802\) −39.0833 −1.38008
\(803\) −7.02776 + 12.1724i −0.248004 + 0.429556i
\(804\) 0 0
\(805\) 6.90833 + 11.9656i 0.243487 + 0.421731i
\(806\) −0.633308 1.09692i −0.0223073 0.0386374i
\(807\) 0 0
\(808\) 18.0000 31.1769i 0.633238 1.09680i
\(809\) −50.6056 −1.77920 −0.889598 0.456744i \(-0.849016\pi\)
−0.889598 + 0.456744i \(0.849016\pi\)
\(810\) 0 0
\(811\) 42.4222 1.48965 0.744823 0.667263i \(-0.232534\pi\)
0.744823 + 0.667263i \(0.232534\pi\)
\(812\) −6.00000 + 10.3923i −0.210559 + 0.364698i
\(813\) 0 0
\(814\) 3.39445 + 5.87936i 0.118975 + 0.206071i
\(815\) 1.00000 + 1.73205i 0.0350285 + 0.0606711i
\(816\) 0 0
\(817\) −11.9083 + 20.6258i −0.416620 + 0.721606i
\(818\) −6.51388 −0.227752
\(819\) 0 0
\(820\) −0.788897 −0.0275495
\(821\) 15.0000 25.9808i 0.523504 0.906735i −0.476122 0.879379i \(-0.657958\pi\)
0.999626 0.0273557i \(-0.00870868\pi\)
\(822\) 0 0
\(823\) −1.90833 3.30532i −0.0665201 0.115216i 0.830847 0.556501i \(-0.187856\pi\)
−0.897367 + 0.441284i \(0.854523\pi\)
\(824\) 6.00000 + 10.3923i 0.209020 + 0.362033i
\(825\) 0 0
\(826\) 25.8167 44.7158i 0.898276 1.55586i
\(827\) 33.7889 1.17496 0.587478 0.809240i \(-0.300121\pi\)
0.587478 + 0.809240i \(0.300121\pi\)
\(828\) 0 0
\(829\) −27.2111 −0.945081 −0.472540 0.881309i \(-0.656663\pi\)
−0.472540 + 0.881309i \(0.656663\pi\)
\(830\) 1.95416 3.38471i 0.0678300 0.117485i
\(831\) 0 0
\(832\) 2.66947 + 4.62365i 0.0925472 + 0.160296i
\(833\) −39.8305 68.9885i −1.38005 2.39031i
\(834\) 0 0
\(835\) 1.50000 2.59808i 0.0519096 0.0899101i
\(836\) 2.84441 0.0983760
\(837\) 0 0
\(838\) −16.9722 −0.586296
\(839\) 9.39445 16.2717i 0.324332 0.561760i −0.657045 0.753852i \(-0.728194\pi\)
0.981377 + 0.192092i \(0.0615270\pi\)
\(840\) 0 0
\(841\) −22.5278 39.0192i −0.776819 1.34549i
\(842\) −15.2569 26.4258i −0.525789 0.910693i
\(843\) 0 0
\(844\) 1.94029 3.36067i 0.0667874 0.115679i
\(845\) 12.6333 0.434599
\(846\) 0 0
\(847\) −19.3944 −0.666401
\(848\) 9.25694 16.0335i 0.317885 0.550592i
\(849\) 0 0
\(850\) 3.65139 + 6.32439i 0.125242 + 0.216925i
\(851\) −3.00000 5.19615i −0.102839 0.178122i
\(852\) 0 0
\(853\) −7.39445 + 12.8076i −0.253181 + 0.438523i −0.964400 0.264448i \(-0.914810\pi\)
0.711219 + 0.702971i \(0.248144\pi\)
\(854\) −61.2666 −2.09650
\(855\) 0 0
\(856\) 0 0
\(857\) −22.6194 + 39.1780i −0.772665 + 1.33830i 0.163433 + 0.986555i \(0.447743\pi\)
−0.936098 + 0.351741i \(0.885590\pi\)
\(858\) 0 0
\(859\) −3.01388 5.22019i −0.102832 0.178111i 0.810018 0.586405i \(-0.199457\pi\)
−0.912850 + 0.408294i \(0.866124\pi\)
\(860\) 1.00000 + 1.73205i 0.0340997 + 0.0590624i
\(861\) 0 0
\(862\) −16.8167 + 29.1273i −0.572778 + 0.992080i
\(863\) −15.7889 −0.537460 −0.268730 0.963216i \(-0.586604\pi\)
−0.268730 + 0.963216i \(0.586604\pi\)
\(864\) 0 0
\(865\) 10.8167 0.367777
\(866\) −18.3944 + 31.8601i −0.625069 + 1.08265i
\(867\) 0 0
\(868\) 1.11943 + 1.93891i 0.0379959 + 0.0658108i
\(869\) 5.72498 + 9.91596i 0.194207 + 0.336376i
\(870\) 0 0
\(871\) −4.60555 + 7.97705i −0.156053 + 0.270292i
\(872\) −21.0000 −0.711150
\(873\) 0 0
\(874\) 14.0917 0.476658
\(875\) 2.30278 3.98852i 0.0778480 0.134837i
\(876\) 0 0
\(877\) 28.3305 + 49.0699i 0.956654 + 1.65697i 0.730537 + 0.682873i \(0.239270\pi\)
0.226117 + 0.974100i \(0.427397\pi\)
\(878\) 13.2847 + 23.0098i 0.448337 + 0.776542i
\(879\) 0 0
\(880\) −4.30278 + 7.45263i −0.145047 + 0.251228i
\(881\) 32.6056 1.09851 0.549254 0.835655i \(-0.314912\pi\)
0.549254 + 0.835655i \(0.314912\pi\)
\(882\) 0 0
\(883\) −5.81665 −0.195746 −0.0978730 0.995199i \(-0.531204\pi\)
−0.0978730 + 0.995199i \(0.531204\pi\)
\(884\) −0.513878 + 0.890063i −0.0172836 + 0.0299361i
\(885\) 0 0
\(886\) −12.1375 21.0228i −0.407768 0.706274i
\(887\) 6.31665 + 10.9408i 0.212092 + 0.367355i 0.952369 0.304947i \(-0.0986389\pi\)
−0.740277 + 0.672302i \(0.765306\pi\)
\(888\) 0 0
\(889\) 11.0278 19.1006i 0.369859 0.640615i
\(890\) −10.1833 −0.341347
\(891\) 0 0
\(892\) 3.02776 0.101377
\(893\) −9.39445 + 16.2717i −0.314373 + 0.544510i
\(894\) 0 0
\(895\) 3.39445 + 5.87936i 0.113464 + 0.196525i
\(896\) 18.6333 + 32.2738i 0.622495 + 1.07819i
\(897\) 0 0
\(898\) 7.97224 13.8083i 0.266037 0.460790i
\(899\) −13.8167 −0.460811
\(900\) 0 0
\(901\) 31.4222 1.04683
\(902\) −4.42221 + 7.65948i −0.147243 + 0.255033i
\(903\) 0 0
\(904\) −1.18335 2.04962i −0.0393575 0.0681692i
\(905\) −3.50000 6.06218i −0.116344 0.201514i
\(906\) 0 0
\(907\) −15.2111 + 26.3464i −0.505076 + 0.874818i 0.494906 + 0.868946i \(0.335202\pi\)
−0.999983 + 0.00587164i \(0.998131\pi\)
\(908\) −7.93608 −0.263368
\(909\) 0 0
\(910\) −3.63331 −0.120443
\(911\) 15.5139 26.8708i 0.513998 0.890270i −0.485870 0.874031i \(-0.661497\pi\)
0.999868 0.0162393i \(-0.00516936\pi\)
\(912\) 0 0
\(913\) 3.90833 + 6.76942i 0.129347 + 0.224035i
\(914\) 0.788897 + 1.36641i 0.0260944 + 0.0451968i
\(915\) 0 0
\(916\) −0.940285 + 1.62862i −0.0310679 + 0.0538112i
\(917\) −27.6333 −0.912532
\(918\) 0 0
\(919\) −2.42221 −0.0799012 −0.0399506 0.999202i \(-0.512720\pi\)
−0.0399506 + 0.999202i \(0.512720\pi\)
\(920\) 4.50000 7.79423i 0.148361 0.256968i
\(921\) 0 0
\(922\) 14.0917 + 24.4075i 0.464085 + 0.803818i
\(923\) −4.42221 7.65948i −0.145559 0.252115i
\(924\) 0 0
\(925\) −1.00000 + 1.73205i −0.0328798 + 0.0569495i
\(926\) 19.8167 0.651216
\(927\) 0 0
\(928\) 14.6056 0.479451
\(929\) 13.3028 23.0411i 0.436450 0.755953i −0.560963 0.827841i \(-0.689569\pi\)
0.997413 + 0.0718876i \(0.0229023\pi\)
\(930\) 0 0
\(931\) 25.6194 + 44.3742i 0.839643 + 1.45430i
\(932\) 2.72498 + 4.71981i 0.0892597 + 0.154602i
\(933\) 0 0
\(934\) 1.44029 2.49465i 0.0471276 0.0816274i
\(935\) −14.6056 −0.477653
\(936\) 0 0
\(937\) 26.7889 0.875155 0.437578 0.899181i \(-0.355837\pi\)
0.437578 + 0.899181i \(0.355837\pi\)
\(938\) −45.6333 + 79.0392i −1.48998 + 2.58072i
\(939\) 0 0
\(940\) 0.788897 + 1.36641i 0.0257310 + 0.0445674i
\(941\) 14.2111 + 24.6144i 0.463269 + 0.802405i 0.999122 0.0419065i \(-0.0133432\pi\)
−0.535853 + 0.844311i \(0.680010\pi\)
\(942\) 0 0
\(943\) 3.90833 6.76942i 0.127273 0.220443i
\(944\) −28.4222 −0.925064
\(945\) 0 0
\(946\) 22.4222 0.729009
\(947\) 19.5000 33.7750i 0.633665 1.09754i −0.353131 0.935574i \(-0.614883\pi\)
0.986796 0.161966i \(-0.0517835\pi\)
\(948\) 0 0
\(949\) 1.63331 + 2.82897i 0.0530194 + 0.0918323i
\(950\) −2.34861 4.06792i −0.0761990 0.131981i
\(951\) 0 0
\(952\) −38.7250 + 67.0736i −1.25508 + 2.17387i
\(953\) −26.8444 −0.869576 −0.434788 0.900533i \(-0.643177\pi\)
−0.434788 + 0.900533i \(0.643177\pi\)
\(954\) 0 0
\(955\) 16.4222 0.531410
\(956\) 0.119429 0.206858i 0.00386262 0.00669026i
\(957\) 0 0
\(958\) 10.5416 + 18.2586i 0.340585 + 0.589910i
\(959\) −11.0917 19.2113i −0.358169 0.620367i
\(960\) 0 0
\(961\) 14.2111 24.6144i 0.458423 0.794011i
\(962\) 1.57779 0.0508701
\(963\) 0 0
\(964\) −8.54163 −0.275108
\(965\) 10.9083 18.8938i 0.351151 0.608212i
\(966\) 0 0
\(967\) −25.0000 43.3013i −0.803946 1.39247i −0.917000 0.398886i \(-0.869397\pi\)
0.113055 0.993589i \(-0.463936\pi\)
\(968\) 6.31665 + 10.9408i 0.203025 + 0.351650i
\(969\) 0 0
\(970\) −5.21110 + 9.02589i −0.167318 + 0.289804i
\(971\) 18.0000 0.577647 0.288824 0.957382i \(-0.406736\pi\)
0.288824 + 0.957382i \(0.406736\pi\)
\(972\) 0 0
\(973\) −18.4222 −0.590589
\(974\) −5.33053 + 9.23275i −0.170801 + 0.295836i
\(975\) 0 0
\(976\) 16.8625 + 29.2067i 0.539755 + 0.934883i
\(977\) −0.394449 0.683205i −0.0126195 0.0218577i 0.859647 0.510889i \(-0.170684\pi\)
−0.872266 + 0.489031i \(0.837350\pi\)
\(978\) 0 0
\(979\) 10.1833 17.6381i 0.325461 0.563715i
\(980\) 4.30278 0.137447
\(981\) 0 0
\(982\) 16.6611 0.531676
\(983\) 0.316654 0.548461i 0.0100997 0.0174932i −0.860931 0.508721i \(-0.830118\pi\)
0.871031 + 0.491228i \(0.163452\pi\)
\(984\) 0 0
\(985\) 0.591673 + 1.02481i 0.0188523 + 0.0326531i
\(986\) −31.4222 54.4249i −1.00069 1.73324i
\(987\) 0 0
\(988\) 0.330532 0.572498i 0.0105156 0.0182136i
\(989\) −19.8167 −0.630133
\(990\) 0 0
\(991\) −50.8167 −1.61424 −0.807122 0.590385i \(-0.798976\pi\)
−0.807122 + 0.590385i \(0.798976\pi\)
\(992\) 1.36249 2.35990i 0.0432591 0.0749270i
\(993\) 0 0
\(994\) −43.8167 75.8927i −1.38978 2.40717i
\(995\) 6.60555 + 11.4412i 0.209410 + 0.362709i
\(996\) 0 0
\(997\) −26.9361 + 46.6547i −0.853074 + 1.47757i 0.0253457 + 0.999679i \(0.491931\pi\)
−0.878420 + 0.477889i \(0.841402\pi\)
\(998\) 35.9638 1.13842
\(999\) 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 405.2.e.j.136.2 4
3.2 odd 2 405.2.e.k.136.1 4
9.2 odd 6 135.2.a.c.1.2 2
9.4 even 3 inner 405.2.e.j.271.2 4
9.5 odd 6 405.2.e.k.271.1 4
9.7 even 3 135.2.a.d.1.1 yes 2
36.7 odd 6 2160.2.a.y.1.1 2
36.11 even 6 2160.2.a.ba.1.1 2
45.2 even 12 675.2.b.i.649.3 4
45.7 odd 12 675.2.b.h.649.2 4
45.29 odd 6 675.2.a.p.1.1 2
45.34 even 6 675.2.a.k.1.2 2
45.38 even 12 675.2.b.i.649.2 4
45.43 odd 12 675.2.b.h.649.3 4
63.20 even 6 6615.2.a.p.1.2 2
63.34 odd 6 6615.2.a.v.1.1 2
72.11 even 6 8640.2.a.ck.1.1 2
72.29 odd 6 8640.2.a.cr.1.2 2
72.43 odd 6 8640.2.a.cy.1.1 2
72.61 even 6 8640.2.a.df.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
135.2.a.c.1.2 2 9.2 odd 6
135.2.a.d.1.1 yes 2 9.7 even 3
405.2.e.j.136.2 4 1.1 even 1 trivial
405.2.e.j.271.2 4 9.4 even 3 inner
405.2.e.k.136.1 4 3.2 odd 2
405.2.e.k.271.1 4 9.5 odd 6
675.2.a.k.1.2 2 45.34 even 6
675.2.a.p.1.1 2 45.29 odd 6
675.2.b.h.649.2 4 45.7 odd 12
675.2.b.h.649.3 4 45.43 odd 12
675.2.b.i.649.2 4 45.38 even 12
675.2.b.i.649.3 4 45.2 even 12
2160.2.a.y.1.1 2 36.7 odd 6
2160.2.a.ba.1.1 2 36.11 even 6
6615.2.a.p.1.2 2 63.20 even 6
6615.2.a.v.1.1 2 63.34 odd 6
8640.2.a.ck.1.1 2 72.11 even 6
8640.2.a.cr.1.2 2 72.29 odd 6
8640.2.a.cy.1.1 2 72.43 odd 6
8640.2.a.df.1.2 2 72.61 even 6