Properties

Label 405.2.e.j.271.2
Level $405$
Weight $2$
Character 405.271
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 271.2
Root \(-0.651388 - 1.12824i\) of defining polynomial
Character \(\chi\) \(=\) 405.271
Dual form 405.2.e.j.136.2

$q$-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 \(\left(\mathbb{Z}/405\mathbb{Z}\right)^\times\).

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

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.651388 + 1.12824i 0.460601 + 0.797784i 0.998991 0.0449118i \(-0.0143007\pi\)
−0.538390 + 0.842696i \(0.680967\pi\)
\(3\) 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 −0.861617 0.507559i \(-0.830548\pi\)
−0.00875026 0.999962i \(-0.502785\pi\)
\(8\) 3.00000 1.06066
\(9\) 0 0
\(10\) 1.30278 0.411974
\(11\) −1.30278 2.25647i −0.392802 0.680352i 0.600016 0.799988i \(-0.295161\pi\)
−0.992818 + 0.119635i \(0.961827\pi\)
\(12\) 0 0
\(13\) 0.302776 0.524423i 0.0839749 0.145449i −0.820979 0.570958i \(-0.806572\pi\)
0.904954 + 0.425510i \(0.139905\pi\)
\(14\) 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 −0.978961 0.204046i \(-0.934591\pi\)
0.666190 + 0.745782i \(0.267924\pi\)
\(24\) 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 0.920264 + 0.391297i \(0.127973\pi\)
−0.121259 + 0.992621i \(0.538693\pi\)
\(30\) 0 0
\(31\) −0.802776 + 1.39045i −0.144183 + 0.249732i −0.929068 0.369910i \(-0.879389\pi\)
0.784885 + 0.619641i \(0.212722\pi\)
\(32\) 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 −0.746181 0.665743i \(-0.768115\pi\)
0.949641 + 0.313341i \(0.101448\pi\)
\(42\) 0 0
\(43\) 3.30278 + 5.72058i 0.503669 + 0.872380i 0.999991 + 0.00424128i \(0.00135005\pi\)
−0.496322 + 0.868138i \(0.665317\pi\)
\(44\) −0.788897 −0.118931
\(45\) 0 0
\(46\) −3.90833 −0.576251
\(47\) 2.60555 + 4.51295i 0.380059 + 0.658281i 0.991070 0.133341i \(-0.0425704\pi\)
−0.611012 + 0.791622i \(0.709237\pi\)
\(48\) 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 0.437307 + 0.899312i \(0.355932\pi\)
−0.997481 + 0.0709370i \(0.977401\pi\)
\(60\) 0 0
\(61\) −5.10555 8.84307i −0.653699 1.13224i −0.982218 0.187742i \(-0.939883\pi\)
0.328519 0.944497i \(-0.393450\pi\)
\(62\) −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 0.144446 0.989513i \(-0.453860\pi\)
0.784720 0.619850i \(-0.212807\pi\)
\(68\) 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 0.962750 0.270394i \(-0.0871539\pi\)
−0.715543 + 0.698569i \(0.753821\pi\)
\(80\) 3.30278 0.369262
\(81\) 0 0
\(82\) 3.39445 0.374854
\(83\) 1.50000 + 2.59808i 0.164646 + 0.285176i 0.936530 0.350588i \(-0.114018\pi\)
−0.771883 + 0.635764i \(0.780685\pi\)
\(84\) 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 0.588315 0.808632i \(-0.299792\pi\)
−0.994453 + 0.105180i \(0.966458\pi\)
\(98\) −18.5139 −1.87018
\(99\) 0 0
\(100\) −0.302776 −0.0302776
\(101\) 6.00000 + 10.3923i 0.597022 + 1.03407i 0.993258 + 0.115924i \(0.0369830\pi\)
−0.396236 + 0.918149i \(0.629684\pi\)
\(102\) 0 0
\(103\) 2.00000 3.46410i 0.197066 0.341328i −0.750510 0.660859i \(-0.770192\pi\)
0.947576 + 0.319531i \(0.103525\pi\)
\(104\) 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 −0.883982 0.467520i \(-0.845147\pi\)
0.846876 + 0.531791i \(0.178481\pi\)
\(114\) 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 −0.704692 0.709514i \(-0.748915\pi\)
0.966803 + 0.255524i \(0.0822479\pi\)
\(132\) 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 0.744616 0.667493i \(-0.232632\pi\)
−0.950374 + 0.311111i \(0.899299\pi\)
\(138\) 0 0
\(139\) 2.00000 3.46410i 0.169638 0.293821i −0.768655 0.639664i \(-0.779074\pi\)
0.938293 + 0.345843i \(0.112407\pi\)
\(140\) −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 0.465590 + 0.885000i \(0.345842\pi\)
−0.999228 + 0.0392872i \(0.987491\pi\)
\(150\) 0 0
\(151\) 7.21110 + 12.4900i 0.586831 + 1.01642i 0.994644 + 0.103356i \(0.0329581\pi\)
−0.407813 + 0.913065i \(0.633709\pi\)
\(152\) −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 −0.932073 0.362270i \(-0.882002\pi\)
0.779772 + 0.626064i \(0.215335\pi\)
\(158\) −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 −0.918208 0.396098i \(-0.870364\pi\)
0.802135 + 0.597143i \(0.203697\pi\)
\(168\) 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 0.995020 0.0996766i \(-0.0317808\pi\)
−0.583832 + 0.811874i \(0.698447\pi\)
\(174\) 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 0.993668 + 0.112353i \(0.0358387\pi\)
−0.399534 + 0.916718i \(0.630828\pi\)
\(192\) 0 0
\(193\) −10.9083 + 18.8938i −0.785199 + 1.36000i 0.143682 + 0.989624i \(0.454106\pi\)
−0.928880 + 0.370380i \(0.879228\pi\)
\(194\) 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 −0.997776 0.0666502i \(-0.978769\pi\)
0.556609 + 0.830775i \(0.312102\pi\)
\(212\) 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 0.983451 0.181173i \(-0.0579895\pi\)
−0.648626 + 0.761107i \(0.724656\pi\)
\(224\) −7.81665 −0.522272
\(225\) 0 0
\(226\) −1.02776 −0.0683653
\(227\) −13.1056 22.6995i −0.869846 1.50662i −0.862154 0.506647i \(-0.830885\pi\)
−0.00769242 0.999970i \(-0.502449\pi\)
\(228\) 0 0
\(229\) 3.10555 5.37897i 0.205221 0.355453i −0.744982 0.667084i \(-0.767542\pi\)
0.950203 + 0.311632i \(0.100875\pi\)
\(230\) −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 −0.878501 0.477741i \(-0.841456\pi\)
0.852986 + 0.521934i \(0.174789\pi\)
\(240\) 0 0
\(241\) −14.1056 24.4315i −0.908618 1.57377i −0.815985 0.578073i \(-0.803805\pi\)
−0.0926334 0.995700i \(-0.529528\pi\)
\(242\) 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 −0.252612 0.967568i \(-0.581290\pi\)
0.964244 0.265015i \(-0.0853769\pi\)
\(258\) 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 −0.999361 0.0357503i \(-0.988618\pi\)
0.468720 0.883347i \(-0.344715\pi\)
\(264\) 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 0.859868 + 0.510517i \(0.170546\pi\)
0.0121867 + 0.999926i \(0.496121\pi\)
\(278\) 5.21110 0.312541
\(279\) 0 0
\(280\) −13.8167 −0.825703
\(281\) 0.908327 + 1.57327i 0.0541862 + 0.0938533i 0.891846 0.452339i \(-0.149410\pi\)
−0.837660 + 0.546192i \(0.816077\pi\)
\(282\) 0 0
\(283\) −5.30278 + 9.18468i −0.315217 + 0.545972i −0.979484 0.201524i \(-0.935411\pi\)
0.664266 + 0.747496i \(0.268744\pi\)
\(284\) −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 0.0466761 + 0.998910i \(0.485137\pi\)
−0.888420 + 0.459032i \(0.848196\pi\)
\(294\) 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 −0.600943 0.799292i \(-0.705208\pi\)
0.992679 + 0.120786i \(0.0385416\pi\)
\(312\) 0 0
\(313\) −11.8167 20.4670i −0.667917 1.15687i −0.978486 0.206315i \(-0.933853\pi\)
0.310569 0.950551i \(-0.399480\pi\)
\(314\) −4.97224 −0.280600
\(315\) 0 0
\(316\) 1.33053 0.0748483
\(317\) −0.197224 0.341603i −0.0110772 0.0191863i 0.860434 0.509562i \(-0.170193\pi\)
−0.871511 + 0.490376i \(0.836859\pi\)
\(318\) 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 0.588052 0.808823i \(-0.299895\pi\)
−0.994487 + 0.104856i \(0.966562\pi\)
\(332\) 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 −0.857661 0.514216i \(-0.828083\pi\)
0.874154 + 0.485648i \(0.161416\pi\)
\(338\) −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 −0.844073 0.536228i \(-0.819849\pi\)
0.886424 + 0.462875i \(0.153182\pi\)
\(348\) 0 0
\(349\) −12.9222 22.3819i −0.691710 1.19808i −0.971277 0.237950i \(-0.923524\pi\)
0.279568 0.960126i \(-0.409809\pi\)
\(350\) −6.00000 −0.320713
\(351\) 0 0
\(352\) −4.42221 −0.235704
\(353\) −10.8167 18.7350i −0.575712 0.997163i −0.995964 0.0897554i \(-0.971391\pi\)
0.420251 0.907408i \(-0.361942\pi\)
\(354\) 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 0.799644 0.600474i \(-0.205022\pi\)
−0.919848 + 0.392275i \(0.871688\pi\)
\(368\) −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 −0.691900 0.721993i \(-0.743226\pi\)
0.971214 + 0.238207i \(0.0765596\pi\)
\(374\) 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 −0.999624 0.0274277i \(-0.991268\pi\)
0.523565 + 0.851986i \(0.324602\pi\)
\(384\) 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 0.914168 0.405337i \(-0.132846\pi\)
−0.808116 + 0.589024i \(0.799512\pi\)
\(390\) 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 0.199207 + 0.979957i \(0.436163\pi\)
−0.948272 + 0.317460i \(0.897170\pi\)
\(402\) 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 −0.921192 0.389109i \(-0.872783\pi\)
0.797574 + 0.603220i \(0.206116\pi\)
\(410\) 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 −0.980118 0.198418i \(-0.936420\pi\)
0.661894 + 0.749598i \(0.269753\pi\)
\(420\) 0 0
\(421\) 11.7111 + 20.2842i 0.570764 + 0.988593i 0.996488 + 0.0837393i \(0.0266863\pi\)
−0.425723 + 0.904853i \(0.639980\pi\)
\(422\) −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 0.513196 0.858271i \(-0.328461\pi\)
−0.999883 + 0.0153049i \(0.995128\pi\)
\(440\) −7.81665 −0.372644
\(441\) 0 0
\(442\) 4.42221 0.210343
\(443\) 9.31665 + 16.1369i 0.442648 + 0.766688i 0.997885 0.0650038i \(-0.0207059\pi\)
−0.555237 + 0.831692i \(0.687373\pi\)
\(444\) 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 0.851515 0.524331i \(-0.175684\pi\)
−0.879841 + 0.475268i \(0.842351\pi\)
\(458\) 8.09167 0.378099
\(459\) 0 0
\(460\) 0.908327 0.0423510
\(461\) −10.8167 18.7350i −0.503782 0.872576i −0.999990 0.00437236i \(-0.998608\pi\)
0.496209 0.868203i \(-0.334725\pi\)
\(462\) 0 0
\(463\) 7.60555 13.1732i 0.353460 0.612211i −0.633393 0.773830i \(-0.718338\pi\)
0.986853 + 0.161620i \(0.0516717\pi\)
\(464\) −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 0.619803 0.784757i \(-0.287212\pi\)
−0.989521 + 0.144387i \(0.953879\pi\)
\(480\) 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 −0.684893 0.728644i \(-0.740151\pi\)
0.973470 + 0.228813i \(0.0734844\pi\)
\(492\) 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 −0.371972 0.928244i \(-0.621318\pi\)
0.989869 0.141985i \(-0.0453485\pi\)
\(500\) −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 −0.229867 0.973222i \(-0.573829\pi\)
0.957769 0.287540i \(-0.0928375\pi\)
\(510\) 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 0.927955 0.372692i \(-0.121565\pi\)
−0.786738 + 0.617286i \(0.788232\pi\)
\(548\) −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 −0.494238 0.869326i \(-0.664553\pi\)
0.999978 0.00664037i \(-0.00211371\pi\)
\(564\) 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 0.924303 + 0.381659i \(0.124647\pi\)
−0.131625 + 0.991300i \(0.542019\pi\)
\(570\) 0 0
\(571\) 18.2250 31.5666i 0.762692 1.32102i −0.178767 0.983891i \(-0.557211\pi\)
0.941458 0.337129i \(-0.109456\pi\)
\(572\) −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 0.997162 0.0752860i \(-0.0239870\pi\)
−0.563781 + 0.825925i \(0.690654\pi\)
\(588\) 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 −0.979331 0.202264i \(-0.935170\pi\)
0.664831 + 0.746994i \(0.268504\pi\)
\(600\) 0 0
\(601\) −16.3167 28.2613i −0.665570 1.15280i −0.979130 0.203233i \(-0.934855\pi\)
0.313560 0.949568i \(-0.398478\pi\)
\(602\) 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 −0.986775 0.162095i \(-0.948175\pi\)
0.633766 + 0.773525i \(0.281508\pi\)
\(608\) −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 0.466866 + 0.884328i \(0.345383\pi\)
−0.999284 + 0.0378463i \(0.987950\pi\)
\(618\) 0 0
\(619\) 3.81665 + 6.61064i 0.153404 + 0.265704i 0.932477 0.361230i \(-0.117643\pi\)
−0.779073 + 0.626934i \(0.784310\pi\)
\(620\) 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 0.525584 0.850741i \(-0.323847\pi\)
−0.999556 + 0.0297987i \(0.990513\pi\)
\(642\) 0 0
\(643\) 11.5139 19.9426i 0.454063 0.786460i −0.544571 0.838715i \(-0.683307\pi\)
0.998634 + 0.0522547i \(0.0166408\pi\)
\(644\) 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 −0.466289 0.884632i \(-0.654409\pi\)
0.999259 0.0384979i \(-0.0122573\pi\)
\(654\) 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 0.592549 0.805535i \(-0.298122\pi\)
−0.993888 + 0.110395i \(0.964788\pi\)
\(660\) 0 0
\(661\) −11.4222 + 19.7838i −0.444272 + 0.769502i −0.998001 0.0631948i \(-0.979871\pi\)
0.553729 + 0.832697i \(0.313204\pi\)
\(662\) 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 0.952510 0.304507i \(-0.0984917\pi\)
−0.739966 + 0.672645i \(0.765158\pi\)
\(674\) 0.788897 0.0303872
\(675\) 0 0
\(676\) 3.82506 0.147118
\(677\) −10.8167 18.7350i −0.415718 0.720044i 0.579786 0.814769i \(-0.303136\pi\)
−0.995504 + 0.0947247i \(0.969803\pi\)
\(678\) 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 0.842354 0.538924i \(-0.181169\pi\)
−0.887899 + 0.460038i \(0.847836\pi\)
\(692\) 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 −0.982068 0.188529i \(-0.939628\pi\)
0.327763 0.944760i \(-0.393705\pi\)
\(710\) −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 0.928081 0.372378i \(-0.121457\pi\)
−0.786529 + 0.617553i \(0.788124\pi\)
\(728\) −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 0.403128 + 0.915144i \(0.367923\pi\)
−0.994102 + 0.108453i \(0.965410\pi\)
\(734\) 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 0.355849 + 0.934544i \(0.384192\pi\)
−0.987263 + 0.159098i \(0.949141\pi\)
\(744\) 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 −0.915761 0.401723i \(-0.868411\pi\)
0.805783 + 0.592211i \(0.201745\pi\)
\(752\) −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 −0.269682 + 0.962949i \(0.586919\pi\)
−0.699097 + 0.715027i \(0.746415\pi\)
\(762\) 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 0.213585 + 0.976924i \(0.431486\pi\)
−0.952834 + 0.303492i \(0.901847\pi\)
\(770\) −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 −0.838322 0.545175i \(-0.816463\pi\)
0.891297 + 0.453421i \(0.149796\pi\)
\(788\) 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 0.311724 + 0.950173i \(0.399094\pi\)
−0.978736 + 0.205125i \(0.934240\pi\)
\(798\) 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 0.999626 + 0.0273557i \(0.00870868\pi\)
−0.476122 + 0.879379i \(0.657958\pi\)
\(822\) 0 0
\(823\) −1.90833 + 3.30532i −0.0665201 + 0.115216i −0.897367 0.441284i \(-0.854523\pi\)
0.830847 + 0.556501i \(0.187856\pi\)
\(824\) 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 0.981377 0.192092i \(-0.0615270\pi\)
−0.657045 + 0.753852i \(0.728194\pi\)
\(840\) 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 0.711219 0.702971i \(-0.248144\pi\)
−0.964400 + 0.264448i \(0.914810\pi\)
\(854\) −61.2666 −2.09650
\(855\) 0 0
\(856\) 0 0
\(857\) −22.6194 39.1780i −0.772665 1.33830i −0.936098 0.351741i \(-0.885590\pi\)
0.163433 0.986555i \(-0.447743\pi\)
\(858\) 0 0
\(859\) −3.01388 + 5.22019i −0.102832 + 0.178111i −0.912850 0.408294i \(-0.866124\pi\)
0.810018 + 0.586405i \(0.199457\pi\)
\(860\) 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 0.226117 0.974100i \(-0.427397\pi\)
0.730537 0.682873i \(-0.239270\pi\)
\(878\) 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 −0.740277 0.672302i \(-0.765306\pi\)
0.952369 + 0.304947i \(0.0986389\pi\)
\(888\) 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 −0.999983 0.00587164i \(-0.998131\pi\)
0.494906 0.868946i \(-0.335202\pi\)
\(908\) −7.93608 −0.263368
\(909\) 0 0
\(910\) −3.63331 −0.120443
\(911\) 15.5139 + 26.8708i 0.513998 + 0.890270i 0.999868 + 0.0162393i \(0.00516936\pi\)
−0.485870 + 0.874031i \(0.661497\pi\)
\(912\) 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 0.997413 0.0718876i \(-0.0229023\pi\)
−0.560963 + 0.827841i \(0.689569\pi\)
\(930\) 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 −0.535853 0.844311i \(-0.680010\pi\)
0.999122 + 0.0419065i \(0.0133432\pi\)
\(942\) 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 0.986796 + 0.161966i \(0.0517835\pi\)
−0.353131 + 0.935574i \(0.614883\pi\)
\(948\) 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 0.113055 + 0.993589i \(0.463936\pi\)
−0.917000 + 0.398886i \(0.869397\pi\)
\(968\) 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 −0.872266 0.489031i \(-0.837350\pi\)
0.859647 + 0.510889i \(0.170684\pi\)
\(978\) 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 0.871031 0.491228i \(-0.163452\pi\)
−0.860931 + 0.508721i \(0.830118\pi\)
\(984\) 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 −0.878420 0.477889i \(-0.841402\pi\)
0.0253457 0.999679i \(-0.491931\pi\)
\(998\) 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.271.2 4
3.2 odd 2 405.2.e.k.271.1 4
9.2 odd 6 405.2.e.k.136.1 4
9.4 even 3 135.2.a.d.1.1 yes 2
9.5 odd 6 135.2.a.c.1.2 2
9.7 even 3 inner 405.2.e.j.136.2 4
36.23 even 6 2160.2.a.ba.1.1 2
36.31 odd 6 2160.2.a.y.1.1 2
45.4 even 6 675.2.a.k.1.2 2
45.13 odd 12 675.2.b.h.649.3 4
45.14 odd 6 675.2.a.p.1.1 2
45.22 odd 12 675.2.b.h.649.2 4
45.23 even 12 675.2.b.i.649.2 4
45.32 even 12 675.2.b.i.649.3 4
63.13 odd 6 6615.2.a.v.1.1 2
63.41 even 6 6615.2.a.p.1.2 2
72.5 odd 6 8640.2.a.cr.1.2 2
72.13 even 6 8640.2.a.df.1.2 2
72.59 even 6 8640.2.a.ck.1.1 2
72.67 odd 6 8640.2.a.cy.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
135.2.a.c.1.2 2 9.5 odd 6
135.2.a.d.1.1 yes 2 9.4 even 3
405.2.e.j.136.2 4 9.7 even 3 inner
405.2.e.j.271.2 4 1.1 even 1 trivial
405.2.e.k.136.1 4 9.2 odd 6
405.2.e.k.271.1 4 3.2 odd 2
675.2.a.k.1.2 2 45.4 even 6
675.2.a.p.1.1 2 45.14 odd 6
675.2.b.h.649.2 4 45.22 odd 12
675.2.b.h.649.3 4 45.13 odd 12
675.2.b.i.649.2 4 45.23 even 12
675.2.b.i.649.3 4 45.32 even 12
2160.2.a.y.1.1 2 36.31 odd 6
2160.2.a.ba.1.1 2 36.23 even 6
6615.2.a.p.1.2 2 63.41 even 6
6615.2.a.v.1.1 2 63.13 odd 6
8640.2.a.ck.1.1 2 72.59 even 6
8640.2.a.cr.1.2 2 72.5 odd 6
8640.2.a.cy.1.1 2 72.67 odd 6
8640.2.a.df.1.2 2 72.13 even 6