Properties

Label 648.2.n.n.109.1
Level $648$
Weight $2$
Character 648.109
Analytic conductor $5.174$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [648,2,Mod(109,648)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(648, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 3, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("648.109");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 648 = 2^{3} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 648.n (of order \(6\), 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: \(5.17430605098\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: 8.0.49787136.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} + 3x^{6} + 5x^{4} + 12x^{2} + 16 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 216)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 109.1
Root \(-1.09445 - 0.895644i\) of defining polynomial
Character \(\chi\) \(=\) 648.109
Dual form 648.2.n.n.541.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.09445 - 0.895644i) q^{2} +(0.395644 + 1.96048i) q^{4} +(-0.866025 - 0.500000i) q^{5} +(-0.500000 - 0.866025i) q^{7} +(1.32288 - 2.50000i) q^{8} +O(q^{10})\) \(q+(-1.09445 - 0.895644i) q^{2} +(0.395644 + 1.96048i) q^{4} +(-0.866025 - 0.500000i) q^{5} +(-0.500000 - 0.866025i) q^{7} +(1.32288 - 2.50000i) q^{8} +(0.500000 + 1.32288i) q^{10} +(2.59808 - 1.50000i) q^{11} +(4.58258 + 2.64575i) q^{13} +(-0.228425 + 1.39564i) q^{14} +(-3.68693 + 1.55130i) q^{16} -5.29150 q^{17} +5.29150i q^{19} +(0.637600 - 1.89564i) q^{20} +(-4.18693 - 0.685275i) q^{22} +(2.64575 - 4.58258i) q^{23} +(-2.00000 - 3.46410i) q^{25} +(-2.64575 - 7.00000i) q^{26} +(1.50000 - 1.32288i) q^{28} +(5.19615 - 3.00000i) q^{29} +(3.50000 - 6.06218i) q^{31} +(5.42458 + 1.60436i) q^{32} +(5.79129 + 4.73930i) q^{34} +1.00000i q^{35} -5.29150i q^{37} +(4.73930 - 5.79129i) q^{38} +(-2.39564 + 1.50363i) q^{40} +(-2.64575 + 4.58258i) q^{41} +(9.16515 - 5.29150i) q^{43} +(3.96863 + 4.50000i) q^{44} +(-7.00000 + 2.64575i) q^{46} +(3.00000 - 5.19615i) q^{49} +(-0.913701 + 5.58258i) q^{50} +(-3.37386 + 10.0308i) q^{52} -9.00000i q^{53} -3.00000 q^{55} +(-2.82650 + 0.104356i) q^{56} +(-8.37386 - 1.37055i) q^{58} +(3.46410 + 2.00000i) q^{59} +(-9.26013 + 3.50000i) q^{62} +(-4.50000 - 6.61438i) q^{64} +(-2.64575 - 4.58258i) q^{65} +(-2.09355 - 10.3739i) q^{68} +(0.895644 - 1.09445i) q^{70} +15.8745 q^{71} +3.00000 q^{73} +(-4.73930 + 5.79129i) q^{74} +(-10.3739 + 2.09355i) q^{76} +(-2.59808 - 1.50000i) q^{77} +(-2.00000 - 3.46410i) q^{79} +(3.96863 + 0.500000i) q^{80} +(7.00000 - 2.64575i) q^{82} +(-6.06218 + 3.50000i) q^{83} +(4.58258 + 2.64575i) q^{85} +(-14.7701 - 2.41742i) q^{86} +(-0.313068 - 8.47950i) q^{88} -10.5830 q^{89} -5.29150i q^{91} +(10.0308 + 3.37386i) q^{92} +(2.64575 - 4.58258i) q^{95} +(-3.50000 - 6.06218i) q^{97} +(-7.93725 + 3.00000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 6 q^{4} - 4 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 6 q^{4} - 4 q^{7} + 4 q^{10} - 2 q^{16} - 6 q^{22} - 16 q^{25} + 12 q^{28} + 28 q^{31} + 28 q^{34} - 10 q^{40} - 56 q^{46} + 24 q^{49} + 28 q^{52} - 24 q^{55} - 12 q^{58} - 36 q^{64} - 2 q^{70} + 24 q^{73} - 28 q^{76} - 16 q^{79} + 56 q^{82} - 30 q^{88} - 28 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/648\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(487\) \(569\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.09445 0.895644i −0.773893 0.633316i
\(3\) 0 0
\(4\) 0.395644 + 1.96048i 0.197822 + 0.980238i
\(5\) −0.866025 0.500000i −0.387298 0.223607i 0.293691 0.955901i \(-0.405116\pi\)
−0.680989 + 0.732294i \(0.738450\pi\)
\(6\) 0 0
\(7\) −0.500000 0.866025i −0.188982 0.327327i 0.755929 0.654654i \(-0.227186\pi\)
−0.944911 + 0.327327i \(0.893852\pi\)
\(8\) 1.32288 2.50000i 0.467707 0.883883i
\(9\) 0 0
\(10\) 0.500000 + 1.32288i 0.158114 + 0.418330i
\(11\) 2.59808 1.50000i 0.783349 0.452267i −0.0542666 0.998526i \(-0.517282\pi\)
0.837616 + 0.546259i \(0.183949\pi\)
\(12\) 0 0
\(13\) 4.58258 + 2.64575i 1.27098 + 0.733799i 0.975172 0.221449i \(-0.0710785\pi\)
0.295806 + 0.955248i \(0.404412\pi\)
\(14\) −0.228425 + 1.39564i −0.0610492 + 0.373002i
\(15\) 0 0
\(16\) −3.68693 + 1.55130i −0.921733 + 0.387825i
\(17\) −5.29150 −1.28338 −0.641689 0.766965i \(-0.721766\pi\)
−0.641689 + 0.766965i \(0.721766\pi\)
\(18\) 0 0
\(19\) 5.29150i 1.21395i 0.794719 + 0.606977i \(0.207618\pi\)
−0.794719 + 0.606977i \(0.792382\pi\)
\(20\) 0.637600 1.89564i 0.142572 0.423879i
\(21\) 0 0
\(22\) −4.18693 0.685275i −0.892657 0.146101i
\(23\) 2.64575 4.58258i 0.551677 0.955533i −0.446476 0.894795i \(-0.647321\pi\)
0.998154 0.0607377i \(-0.0193453\pi\)
\(24\) 0 0
\(25\) −2.00000 3.46410i −0.400000 0.692820i
\(26\) −2.64575 7.00000i −0.518875 1.37281i
\(27\) 0 0
\(28\) 1.50000 1.32288i 0.283473 0.250000i
\(29\) 5.19615 3.00000i 0.964901 0.557086i 0.0672232 0.997738i \(-0.478586\pi\)
0.897678 + 0.440652i \(0.145253\pi\)
\(30\) 0 0
\(31\) 3.50000 6.06218i 0.628619 1.08880i −0.359211 0.933257i \(-0.616954\pi\)
0.987829 0.155543i \(-0.0497126\pi\)
\(32\) 5.42458 + 1.60436i 0.958939 + 0.283613i
\(33\) 0 0
\(34\) 5.79129 + 4.73930i 0.993198 + 0.812784i
\(35\) 1.00000i 0.169031i
\(36\) 0 0
\(37\) 5.29150i 0.869918i −0.900450 0.434959i \(-0.856763\pi\)
0.900450 0.434959i \(-0.143237\pi\)
\(38\) 4.73930 5.79129i 0.768816 0.939471i
\(39\) 0 0
\(40\) −2.39564 + 1.50363i −0.378785 + 0.237744i
\(41\) −2.64575 + 4.58258i −0.413197 + 0.715678i −0.995237 0.0974818i \(-0.968921\pi\)
0.582040 + 0.813160i \(0.302255\pi\)
\(42\) 0 0
\(43\) 9.16515 5.29150i 1.39767 0.806947i 0.403524 0.914969i \(-0.367785\pi\)
0.994148 + 0.108022i \(0.0344518\pi\)
\(44\) 3.96863 + 4.50000i 0.598293 + 0.678401i
\(45\) 0 0
\(46\) −7.00000 + 2.64575i −1.03209 + 0.390095i
\(47\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(48\) 0 0
\(49\) 3.00000 5.19615i 0.428571 0.742307i
\(50\) −0.913701 + 5.58258i −0.129217 + 0.789495i
\(51\) 0 0
\(52\) −3.37386 + 10.0308i −0.467871 + 1.39102i
\(53\) 9.00000i 1.23625i −0.786082 0.618123i \(-0.787894\pi\)
0.786082 0.618123i \(-0.212106\pi\)
\(54\) 0 0
\(55\) −3.00000 −0.404520
\(56\) −2.82650 + 0.104356i −0.377707 + 0.0139452i
\(57\) 0 0
\(58\) −8.37386 1.37055i −1.09954 0.179962i
\(59\) 3.46410 + 2.00000i 0.450988 + 0.260378i 0.708247 0.705965i \(-0.249486\pi\)
−0.257260 + 0.966342i \(0.582820\pi\)
\(60\) 0 0
\(61\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(62\) −9.26013 + 3.50000i −1.17604 + 0.444500i
\(63\) 0 0
\(64\) −4.50000 6.61438i −0.562500 0.826797i
\(65\) −2.64575 4.58258i −0.328165 0.568399i
\(66\) 0 0
\(67\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(68\) −2.09355 10.3739i −0.253880 1.25802i
\(69\) 0 0
\(70\) 0.895644 1.09445i 0.107050 0.130812i
\(71\) 15.8745 1.88396 0.941979 0.335673i \(-0.108964\pi\)
0.941979 + 0.335673i \(0.108964\pi\)
\(72\) 0 0
\(73\) 3.00000 0.351123 0.175562 0.984468i \(-0.443826\pi\)
0.175562 + 0.984468i \(0.443826\pi\)
\(74\) −4.73930 + 5.79129i −0.550933 + 0.673224i
\(75\) 0 0
\(76\) −10.3739 + 2.09355i −1.18996 + 0.240147i
\(77\) −2.59808 1.50000i −0.296078 0.170941i
\(78\) 0 0
\(79\) −2.00000 3.46410i −0.225018 0.389742i 0.731307 0.682048i \(-0.238911\pi\)
−0.956325 + 0.292306i \(0.905577\pi\)
\(80\) 3.96863 + 0.500000i 0.443706 + 0.0559017i
\(81\) 0 0
\(82\) 7.00000 2.64575i 0.773021 0.292174i
\(83\) −6.06218 + 3.50000i −0.665410 + 0.384175i −0.794335 0.607479i \(-0.792181\pi\)
0.128925 + 0.991654i \(0.458847\pi\)
\(84\) 0 0
\(85\) 4.58258 + 2.64575i 0.497050 + 0.286972i
\(86\) −14.7701 2.41742i −1.59270 0.260678i
\(87\) 0 0
\(88\) −0.313068 8.47950i −0.0333732 0.903918i
\(89\) −10.5830 −1.12180 −0.560898 0.827885i \(-0.689544\pi\)
−0.560898 + 0.827885i \(0.689544\pi\)
\(90\) 0 0
\(91\) 5.29150i 0.554700i
\(92\) 10.0308 + 3.37386i 1.04578 + 0.351750i
\(93\) 0 0
\(94\) 0 0
\(95\) 2.64575 4.58258i 0.271448 0.470162i
\(96\) 0 0
\(97\) −3.50000 6.06218i −0.355371 0.615521i 0.631810 0.775123i \(-0.282312\pi\)
−0.987181 + 0.159602i \(0.948979\pi\)
\(98\) −7.93725 + 3.00000i −0.801784 + 0.303046i
\(99\) 0 0
\(100\) 6.00000 5.29150i 0.600000 0.529150i
\(101\) −14.7224 + 8.50000i −1.46494 + 0.845782i −0.999233 0.0391591i \(-0.987532\pi\)
−0.465704 + 0.884941i \(0.654199\pi\)
\(102\) 0 0
\(103\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(104\) 12.6766 7.95644i 1.24304 0.780193i
\(105\) 0 0
\(106\) −8.06080 + 9.85005i −0.782934 + 0.956722i
\(107\) 3.00000i 0.290021i 0.989430 + 0.145010i \(0.0463216\pi\)
−0.989430 + 0.145010i \(0.953678\pi\)
\(108\) 0 0
\(109\) 5.29150i 0.506834i 0.967357 + 0.253417i \(0.0815545\pi\)
−0.967357 + 0.253417i \(0.918446\pi\)
\(110\) 3.28335 + 2.68693i 0.313055 + 0.256189i
\(111\) 0 0
\(112\) 3.18693 + 2.41733i 0.301137 + 0.228416i
\(113\) −7.93725 + 13.7477i −0.746674 + 1.29328i 0.202735 + 0.979234i \(0.435017\pi\)
−0.949409 + 0.314044i \(0.898316\pi\)
\(114\) 0 0
\(115\) −4.58258 + 2.64575i −0.427327 + 0.246718i
\(116\) 7.93725 + 9.00000i 0.736956 + 0.835629i
\(117\) 0 0
\(118\) −2.00000 5.29150i −0.184115 0.487122i
\(119\) 2.64575 + 4.58258i 0.242536 + 0.420084i
\(120\) 0 0
\(121\) −1.00000 + 1.73205i −0.0909091 + 0.157459i
\(122\) 0 0
\(123\) 0 0
\(124\) 13.2695 + 4.46320i 1.19164 + 0.400807i
\(125\) 9.00000i 0.804984i
\(126\) 0 0
\(127\) 13.0000 1.15356 0.576782 0.816898i \(-0.304308\pi\)
0.576782 + 0.816898i \(0.304308\pi\)
\(128\) −0.999100 + 11.2695i −0.0883088 + 0.996093i
\(129\) 0 0
\(130\) −1.20871 + 7.38505i −0.106011 + 0.647712i
\(131\) 6.06218 + 3.50000i 0.529655 + 0.305796i 0.740876 0.671642i \(-0.234411\pi\)
−0.211221 + 0.977438i \(0.567744\pi\)
\(132\) 0 0
\(133\) 4.58258 2.64575i 0.397360 0.229416i
\(134\) 0 0
\(135\) 0 0
\(136\) −7.00000 + 13.2288i −0.600245 + 1.13436i
\(137\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(138\) 0 0
\(139\) 9.16515 + 5.29150i 0.777378 + 0.448819i 0.835500 0.549490i \(-0.185178\pi\)
−0.0581222 + 0.998309i \(0.518511\pi\)
\(140\) −1.96048 + 0.395644i −0.165690 + 0.0334380i
\(141\) 0 0
\(142\) −17.3739 14.2179i −1.45798 1.19314i
\(143\) 15.8745 1.32749
\(144\) 0 0
\(145\) −6.00000 −0.498273
\(146\) −3.28335 2.68693i −0.271732 0.222372i
\(147\) 0 0
\(148\) 10.3739 2.09355i 0.852726 0.172089i
\(149\) 2.59808 + 1.50000i 0.212843 + 0.122885i 0.602632 0.798019i \(-0.294119\pi\)
−0.389789 + 0.920904i \(0.627452\pi\)
\(150\) 0 0
\(151\) −1.50000 2.59808i −0.122068 0.211428i 0.798515 0.601975i \(-0.205619\pi\)
−0.920583 + 0.390547i \(0.872286\pi\)
\(152\) 13.2288 + 7.00000i 1.07299 + 0.567775i
\(153\) 0 0
\(154\) 1.50000 + 3.96863i 0.120873 + 0.319801i
\(155\) −6.06218 + 3.50000i −0.486926 + 0.281127i
\(156\) 0 0
\(157\) −9.16515 5.29150i −0.731459 0.422308i 0.0874969 0.996165i \(-0.472113\pi\)
−0.818956 + 0.573857i \(0.805447\pi\)
\(158\) −0.913701 + 5.58258i −0.0726901 + 0.444126i
\(159\) 0 0
\(160\) −3.89564 4.10170i −0.307978 0.324268i
\(161\) −5.29150 −0.417029
\(162\) 0 0
\(163\) 5.29150i 0.414462i −0.978292 0.207231i \(-0.933555\pi\)
0.978292 0.207231i \(-0.0664452\pi\)
\(164\) −10.0308 3.37386i −0.783274 0.263454i
\(165\) 0 0
\(166\) 9.76951 + 1.59898i 0.758261 + 0.124105i
\(167\) 5.29150 9.16515i 0.409469 0.709221i −0.585361 0.810772i \(-0.699047\pi\)
0.994830 + 0.101552i \(0.0323807\pi\)
\(168\) 0 0
\(169\) 7.50000 + 12.9904i 0.576923 + 0.999260i
\(170\) −2.64575 7.00000i −0.202920 0.536875i
\(171\) 0 0
\(172\) 14.0000 + 15.8745i 1.06749 + 1.21042i
\(173\) 12.9904 7.50000i 0.987640 0.570214i 0.0830722 0.996544i \(-0.473527\pi\)
0.904568 + 0.426329i \(0.140193\pi\)
\(174\) 0 0
\(175\) −2.00000 + 3.46410i −0.151186 + 0.261861i
\(176\) −7.25198 + 9.56080i −0.546638 + 0.720672i
\(177\) 0 0
\(178\) 11.5826 + 9.47860i 0.868151 + 0.710451i
\(179\) 23.0000i 1.71910i 0.511051 + 0.859550i \(0.329256\pi\)
−0.511051 + 0.859550i \(0.670744\pi\)
\(180\) 0 0
\(181\) 21.1660i 1.57326i 0.617426 + 0.786629i \(0.288175\pi\)
−0.617426 + 0.786629i \(0.711825\pi\)
\(182\) −4.73930 + 5.79129i −0.351300 + 0.429279i
\(183\) 0 0
\(184\) −7.95644 12.6766i −0.586556 0.934528i
\(185\) −2.64575 + 4.58258i −0.194520 + 0.336918i
\(186\) 0 0
\(187\) −13.7477 + 7.93725i −1.00533 + 0.580429i
\(188\) 0 0
\(189\) 0 0
\(190\) −7.00000 + 2.64575i −0.507833 + 0.191943i
\(191\) 2.64575 + 4.58258i 0.191440 + 0.331584i 0.945728 0.324960i \(-0.105351\pi\)
−0.754288 + 0.656544i \(0.772018\pi\)
\(192\) 0 0
\(193\) 1.50000 2.59808i 0.107972 0.187014i −0.806976 0.590584i \(-0.798898\pi\)
0.914949 + 0.403570i \(0.132231\pi\)
\(194\) −1.59898 + 9.76951i −0.114800 + 0.701410i
\(195\) 0 0
\(196\) 11.3739 + 3.82560i 0.812419 + 0.273257i
\(197\) 13.0000i 0.926212i −0.886303 0.463106i \(-0.846735\pi\)
0.886303 0.463106i \(-0.153265\pi\)
\(198\) 0 0
\(199\) −17.0000 −1.20510 −0.602549 0.798082i \(-0.705848\pi\)
−0.602549 + 0.798082i \(0.705848\pi\)
\(200\) −11.3060 + 0.417424i −0.799455 + 0.0295164i
\(201\) 0 0
\(202\) 23.7259 + 3.88323i 1.66935 + 0.273223i
\(203\) −5.19615 3.00000i −0.364698 0.210559i
\(204\) 0 0
\(205\) 4.58258 2.64575i 0.320061 0.184787i
\(206\) 0 0
\(207\) 0 0
\(208\) −21.0000 2.64575i −1.45609 0.183450i
\(209\) 7.93725 + 13.7477i 0.549031 + 0.950950i
\(210\) 0 0
\(211\) 4.58258 + 2.64575i 0.315478 + 0.182141i 0.649375 0.760468i \(-0.275031\pi\)
−0.333897 + 0.942609i \(0.608364\pi\)
\(212\) 17.6443 3.56080i 1.21181 0.244556i
\(213\) 0 0
\(214\) 2.68693 3.28335i 0.183675 0.224445i
\(215\) −10.5830 −0.721755
\(216\) 0 0
\(217\) −7.00000 −0.475191
\(218\) 4.73930 5.79129i 0.320986 0.392236i
\(219\) 0 0
\(220\) −1.18693 5.88143i −0.0800229 0.396526i
\(221\) −24.2487 14.0000i −1.63114 0.941742i
\(222\) 0 0
\(223\) 8.00000 + 13.8564i 0.535720 + 0.927894i 0.999128 + 0.0417488i \(0.0132929\pi\)
−0.463409 + 0.886145i \(0.653374\pi\)
\(224\) −1.32288 5.50000i −0.0883883 0.367484i
\(225\) 0 0
\(226\) 21.0000 7.93725i 1.39690 0.527978i
\(227\) 3.46410 2.00000i 0.229920 0.132745i −0.380615 0.924734i \(-0.624288\pi\)
0.610535 + 0.791989i \(0.290954\pi\)
\(228\) 0 0
\(229\) −18.3303 10.5830i −1.21130 0.699345i −0.248258 0.968694i \(-0.579858\pi\)
−0.963043 + 0.269349i \(0.913191\pi\)
\(230\) 7.38505 + 1.20871i 0.486956 + 0.0797001i
\(231\) 0 0
\(232\) −0.626136 16.9590i −0.0411079 1.11341i
\(233\) −10.5830 −0.693316 −0.346658 0.937992i \(-0.612684\pi\)
−0.346658 + 0.937992i \(0.612684\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) −2.55040 + 7.58258i −0.166017 + 0.493584i
\(237\) 0 0
\(238\) 1.20871 7.38505i 0.0783492 0.478702i
\(239\) 7.93725 13.7477i 0.513418 0.889267i −0.486461 0.873703i \(-0.661712\pi\)
0.999879 0.0155640i \(-0.00495438\pi\)
\(240\) 0 0
\(241\) 5.00000 + 8.66025i 0.322078 + 0.557856i 0.980917 0.194429i \(-0.0622852\pi\)
−0.658838 + 0.752285i \(0.728952\pi\)
\(242\) 2.64575 1.00000i 0.170075 0.0642824i
\(243\) 0 0
\(244\) 0 0
\(245\) −5.19615 + 3.00000i −0.331970 + 0.191663i
\(246\) 0 0
\(247\) −14.0000 + 24.2487i −0.890799 + 1.54291i
\(248\) −10.5254 16.7695i −0.668362 1.06486i
\(249\) 0 0
\(250\) 8.06080 9.85005i 0.509809 0.622972i
\(251\) 12.0000i 0.757433i −0.925513 0.378717i \(-0.876365\pi\)
0.925513 0.378717i \(-0.123635\pi\)
\(252\) 0 0
\(253\) 15.8745i 0.998022i
\(254\) −14.2279 11.6434i −0.892735 0.730570i
\(255\) 0 0
\(256\) 11.1869 11.4391i 0.699183 0.714943i
\(257\) 7.93725 13.7477i 0.495112 0.857560i −0.504872 0.863194i \(-0.668460\pi\)
0.999984 + 0.00563467i \(0.00179358\pi\)
\(258\) 0 0
\(259\) −4.58258 + 2.64575i −0.284747 + 0.164399i
\(260\) 7.93725 7.00000i 0.492248 0.434122i
\(261\) 0 0
\(262\) −3.50000 9.26013i −0.216231 0.572093i
\(263\) −2.64575 4.58258i −0.163144 0.282574i 0.772851 0.634588i \(-0.218830\pi\)
−0.935995 + 0.352014i \(0.885497\pi\)
\(264\) 0 0
\(265\) −4.50000 + 7.79423i −0.276433 + 0.478796i
\(266\) −7.38505 1.20871i −0.452807 0.0741109i
\(267\) 0 0
\(268\) 0 0
\(269\) 18.0000i 1.09748i 0.835993 + 0.548740i \(0.184892\pi\)
−0.835993 + 0.548740i \(0.815108\pi\)
\(270\) 0 0
\(271\) 15.0000 0.911185 0.455593 0.890188i \(-0.349427\pi\)
0.455593 + 0.890188i \(0.349427\pi\)
\(272\) 19.5094 8.20871i 1.18293 0.497726i
\(273\) 0 0
\(274\) 0 0
\(275\) −10.3923 6.00000i −0.626680 0.361814i
\(276\) 0 0
\(277\) −9.16515 + 5.29150i −0.550681 + 0.317936i −0.749396 0.662122i \(-0.769656\pi\)
0.198716 + 0.980057i \(0.436323\pi\)
\(278\) −5.29150 14.0000i −0.317363 0.839664i
\(279\) 0 0
\(280\) 2.50000 + 1.32288i 0.149404 + 0.0790569i
\(281\) −7.93725 13.7477i −0.473497 0.820121i 0.526043 0.850458i \(-0.323675\pi\)
−0.999540 + 0.0303374i \(0.990342\pi\)
\(282\) 0 0
\(283\) −22.9129 13.2288i −1.36203 0.786368i −0.372135 0.928178i \(-0.621374\pi\)
−0.989894 + 0.141810i \(0.954708\pi\)
\(284\) 6.28065 + 31.1216i 0.372688 + 1.84673i
\(285\) 0 0
\(286\) −17.3739 14.2179i −1.02734 0.840722i
\(287\) 5.29150 0.312348
\(288\) 0 0
\(289\) 11.0000 0.647059
\(290\) 6.56670 + 5.37386i 0.385610 + 0.315564i
\(291\) 0 0
\(292\) 1.18693 + 5.88143i 0.0694599 + 0.344185i
\(293\) 25.9808 + 15.0000i 1.51781 + 0.876309i 0.999781 + 0.0209480i \(0.00666844\pi\)
0.518032 + 0.855361i \(0.326665\pi\)
\(294\) 0 0
\(295\) −2.00000 3.46410i −0.116445 0.201688i
\(296\) −13.2288 7.00000i −0.768906 0.406867i
\(297\) 0 0
\(298\) −1.50000 3.96863i −0.0868927 0.229896i
\(299\) 24.2487 14.0000i 1.40234 0.809641i
\(300\) 0 0
\(301\) −9.16515 5.29150i −0.528271 0.304997i
\(302\) −0.685275 + 4.18693i −0.0394332 + 0.240931i
\(303\) 0 0
\(304\) −8.20871 19.5094i −0.470802 1.11894i
\(305\) 0 0
\(306\) 0 0
\(307\) 15.8745i 0.906006i −0.891509 0.453003i \(-0.850353\pi\)
0.891509 0.453003i \(-0.149647\pi\)
\(308\) 1.91280 5.68693i 0.108992 0.324043i
\(309\) 0 0
\(310\) 9.76951 + 1.59898i 0.554871 + 0.0908157i
\(311\) −13.2288 + 22.9129i −0.750134 + 1.29927i 0.197623 + 0.980278i \(0.436678\pi\)
−0.947757 + 0.318992i \(0.896656\pi\)
\(312\) 0 0
\(313\) 0.500000 + 0.866025i 0.0282617 + 0.0489506i 0.879810 0.475325i \(-0.157669\pi\)
−0.851549 + 0.524276i \(0.824336\pi\)
\(314\) 5.29150 + 14.0000i 0.298617 + 0.790066i
\(315\) 0 0
\(316\) 6.00000 5.29150i 0.337526 0.297670i
\(317\) 11.2583 6.50000i 0.632331 0.365076i −0.149323 0.988788i \(-0.547710\pi\)
0.781654 + 0.623712i \(0.214376\pi\)
\(318\) 0 0
\(319\) 9.00000 15.5885i 0.503903 0.872786i
\(320\) 0.589925 + 7.97822i 0.0329778 + 0.445996i
\(321\) 0 0
\(322\) 5.79129 + 4.73930i 0.322736 + 0.264111i
\(323\) 28.0000i 1.55796i
\(324\) 0 0
\(325\) 21.1660i 1.17408i
\(326\) −4.73930 + 5.79129i −0.262486 + 0.320750i
\(327\) 0 0
\(328\) 7.95644 + 12.6766i 0.439321 + 0.699946i
\(329\) 0 0
\(330\) 0 0
\(331\) −18.3303 + 10.5830i −1.00752 + 0.581695i −0.910466 0.413584i \(-0.864277\pi\)
−0.0970586 + 0.995279i \(0.530943\pi\)
\(332\) −9.26013 10.5000i −0.508216 0.576262i
\(333\) 0 0
\(334\) −14.0000 + 5.29150i −0.766046 + 0.289538i
\(335\) 0 0
\(336\) 0 0
\(337\) −17.0000 + 29.4449i −0.926049 + 1.60396i −0.136184 + 0.990684i \(0.543484\pi\)
−0.789865 + 0.613280i \(0.789850\pi\)
\(338\) 3.42638 20.9347i 0.186370 1.13870i
\(339\) 0 0
\(340\) −3.37386 + 10.0308i −0.182973 + 0.543997i
\(341\) 21.0000i 1.13721i
\(342\) 0 0
\(343\) −13.0000 −0.701934
\(344\) −1.10440 29.9129i −0.0595453 1.61279i
\(345\) 0 0
\(346\) −20.9347 3.42638i −1.12545 0.184203i
\(347\) 19.9186 + 11.5000i 1.06929 + 0.617352i 0.927986 0.372615i \(-0.121539\pi\)
0.141299 + 0.989967i \(0.454872\pi\)
\(348\) 0 0
\(349\) −4.58258 + 2.64575i −0.245300 + 0.141624i −0.617610 0.786484i \(-0.711899\pi\)
0.372310 + 0.928108i \(0.378566\pi\)
\(350\) 5.29150 2.00000i 0.282843 0.106904i
\(351\) 0 0
\(352\) 16.5000 3.96863i 0.879453 0.211529i
\(353\) −7.93725 13.7477i −0.422457 0.731718i 0.573722 0.819050i \(-0.305499\pi\)
−0.996179 + 0.0873325i \(0.972166\pi\)
\(354\) 0 0
\(355\) −13.7477 7.93725i −0.729654 0.421266i
\(356\) −4.18710 20.7477i −0.221916 1.09963i
\(357\) 0 0
\(358\) 20.5998 25.1724i 1.08873 1.33040i
\(359\) −21.1660 −1.11710 −0.558550 0.829471i \(-0.688642\pi\)
−0.558550 + 0.829471i \(0.688642\pi\)
\(360\) 0 0
\(361\) −9.00000 −0.473684
\(362\) 18.9572 23.1652i 0.996369 1.21753i
\(363\) 0 0
\(364\) 10.3739 2.09355i 0.543738 0.109732i
\(365\) −2.59808 1.50000i −0.135990 0.0785136i
\(366\) 0 0
\(367\) 1.50000 + 2.59808i 0.0782994 + 0.135618i 0.902516 0.430656i \(-0.141718\pi\)
−0.824217 + 0.566274i \(0.808384\pi\)
\(368\) −2.64575 + 21.0000i −0.137919 + 1.09470i
\(369\) 0 0
\(370\) 7.00000 2.64575i 0.363913 0.137546i
\(371\) −7.79423 + 4.50000i −0.404656 + 0.233628i
\(372\) 0 0
\(373\) 22.9129 + 13.2288i 1.18638 + 0.684959i 0.957483 0.288491i \(-0.0931534\pi\)
0.228901 + 0.973450i \(0.426487\pi\)
\(374\) 22.1552 + 3.62614i 1.14562 + 0.187503i
\(375\) 0 0
\(376\) 0 0
\(377\) 31.7490 1.63516
\(378\) 0 0
\(379\) 21.1660i 1.08722i 0.839336 + 0.543612i \(0.182944\pi\)
−0.839336 + 0.543612i \(0.817056\pi\)
\(380\) 10.0308 + 3.37386i 0.514569 + 0.173076i
\(381\) 0 0
\(382\) 1.20871 7.38505i 0.0618431 0.377852i
\(383\) −7.93725 + 13.7477i −0.405575 + 0.702476i −0.994388 0.105793i \(-0.966262\pi\)
0.588813 + 0.808269i \(0.299595\pi\)
\(384\) 0 0
\(385\) 1.50000 + 2.59808i 0.0764471 + 0.132410i
\(386\) −3.96863 + 1.50000i −0.201998 + 0.0763480i
\(387\) 0 0
\(388\) 10.5000 9.26013i 0.533057 0.470112i
\(389\) 4.33013 2.50000i 0.219546 0.126755i −0.386194 0.922418i \(-0.626210\pi\)
0.605740 + 0.795663i \(0.292877\pi\)
\(390\) 0 0
\(391\) −14.0000 + 24.2487i −0.708010 + 1.22631i
\(392\) −9.02175 14.3739i −0.455667 0.725990i
\(393\) 0 0
\(394\) −11.6434 + 14.2279i −0.586585 + 0.716789i
\(395\) 4.00000i 0.201262i
\(396\) 0 0
\(397\) 5.29150i 0.265573i 0.991145 + 0.132786i \(0.0423924\pi\)
−0.991145 + 0.132786i \(0.957608\pi\)
\(398\) 18.6057 + 15.2259i 0.932617 + 0.763208i
\(399\) 0 0
\(400\) 12.7477 + 9.66930i 0.637386 + 0.483465i
\(401\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(402\) 0 0
\(403\) 32.0780 18.5203i 1.59792 0.922560i
\(404\) −22.4889 25.5000i −1.11886 1.26867i
\(405\) 0 0
\(406\) 3.00000 + 7.93725i 0.148888 + 0.393919i
\(407\) −7.93725 13.7477i −0.393435 0.681450i
\(408\) 0 0
\(409\) 5.50000 9.52628i 0.271957 0.471044i −0.697406 0.716677i \(-0.745662\pi\)
0.969363 + 0.245633i \(0.0789957\pi\)
\(410\) −7.38505 1.20871i −0.364722 0.0596940i
\(411\) 0 0
\(412\) 0 0
\(413\) 4.00000i 0.196827i
\(414\) 0 0
\(415\) 7.00000 0.343616
\(416\) 20.6138 + 21.7042i 1.01068 + 1.06413i
\(417\) 0 0
\(418\) 3.62614 22.1552i 0.177360 1.08364i
\(419\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(420\) 0 0
\(421\) −9.16515 + 5.29150i −0.446682 + 0.257892i −0.706428 0.707785i \(-0.749695\pi\)
0.259746 + 0.965677i \(0.416361\pi\)
\(422\) −2.64575 7.00000i −0.128793 0.340755i
\(423\) 0 0
\(424\) −22.5000 11.9059i −1.09270 0.578201i
\(425\) 10.5830 + 18.3303i 0.513351 + 0.889150i
\(426\) 0 0
\(427\) 0 0
\(428\) −5.88143 + 1.18693i −0.284290 + 0.0573725i
\(429\) 0 0
\(430\) 11.5826 + 9.47860i 0.558561 + 0.457099i
\(431\) −31.7490 −1.52930 −0.764648 0.644448i \(-0.777087\pi\)
−0.764648 + 0.644448i \(0.777087\pi\)
\(432\) 0 0
\(433\) 5.00000 0.240285 0.120142 0.992757i \(-0.461665\pi\)
0.120142 + 0.992757i \(0.461665\pi\)
\(434\) 7.66115 + 6.26951i 0.367747 + 0.300946i
\(435\) 0 0
\(436\) −10.3739 + 2.09355i −0.496818 + 0.100263i
\(437\) 24.2487 + 14.0000i 1.15997 + 0.669711i
\(438\) 0 0
\(439\) 10.5000 + 18.1865i 0.501138 + 0.867996i 0.999999 + 0.00131415i \(0.000418308\pi\)
−0.498861 + 0.866682i \(0.666248\pi\)
\(440\) −3.96863 + 7.50000i −0.189197 + 0.357548i
\(441\) 0 0
\(442\) 14.0000 + 37.0405i 0.665912 + 1.76184i
\(443\) −20.7846 + 12.0000i −0.987507 + 0.570137i −0.904528 0.426414i \(-0.859777\pi\)
−0.0829786 + 0.996551i \(0.526443\pi\)
\(444\) 0 0
\(445\) 9.16515 + 5.29150i 0.434470 + 0.250841i
\(446\) 3.65480 22.3303i 0.173060 1.05737i
\(447\) 0 0
\(448\) −3.47822 + 7.20430i −0.164330 + 0.340371i
\(449\) 15.8745 0.749164 0.374582 0.927194i \(-0.377786\pi\)
0.374582 + 0.927194i \(0.377786\pi\)
\(450\) 0 0
\(451\) 15.8745i 0.747501i
\(452\) −30.0924 10.1216i −1.41543 0.476080i
\(453\) 0 0
\(454\) −5.58258 0.913701i −0.262003 0.0428821i
\(455\) −2.64575 + 4.58258i −0.124035 + 0.214834i
\(456\) 0 0
\(457\) −8.50000 14.7224i −0.397613 0.688686i 0.595818 0.803120i \(-0.296828\pi\)
−0.993431 + 0.114433i \(0.963495\pi\)
\(458\) 10.5830 + 28.0000i 0.494511 + 1.30835i
\(459\) 0 0
\(460\) −7.00000 7.93725i −0.326377 0.370076i
\(461\) −7.79423 + 4.50000i −0.363013 + 0.209586i −0.670402 0.741998i \(-0.733878\pi\)
0.307388 + 0.951584i \(0.400545\pi\)
\(462\) 0 0
\(463\) 20.5000 35.5070i 0.952716 1.65015i 0.213205 0.977007i \(-0.431610\pi\)
0.739511 0.673145i \(-0.235057\pi\)
\(464\) −14.5040 + 19.1216i −0.673329 + 0.887698i
\(465\) 0 0
\(466\) 11.5826 + 9.47860i 0.536552 + 0.439088i
\(467\) 1.00000i 0.0462745i 0.999732 + 0.0231372i \(0.00736547\pi\)
−0.999732 + 0.0231372i \(0.992635\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 9.58258 6.01450i 0.441074 0.276840i
\(473\) 15.8745 27.4955i 0.729911 1.26424i
\(474\) 0 0
\(475\) 18.3303 10.5830i 0.841052 0.485582i
\(476\) −7.93725 + 7.00000i −0.363803 + 0.320844i
\(477\) 0 0
\(478\) −21.0000 + 7.93725i −0.960518 + 0.363042i
\(479\) −10.5830 18.3303i −0.483550 0.837533i 0.516272 0.856425i \(-0.327319\pi\)
−0.999822 + 0.0188920i \(0.993986\pi\)
\(480\) 0 0
\(481\) 14.0000 24.2487i 0.638345 1.10565i
\(482\) 2.28425 13.9564i 0.104045 0.635698i
\(483\) 0 0
\(484\) −3.79129 1.27520i −0.172331 0.0579637i
\(485\) 7.00000i 0.317854i
\(486\) 0 0
\(487\) −40.0000 −1.81257 −0.906287 0.422664i \(-0.861095\pi\)
−0.906287 + 0.422664i \(0.861095\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 8.37386 + 1.37055i 0.378293 + 0.0619152i
\(491\) −25.1147 14.5000i −1.13341 0.654376i −0.188621 0.982050i \(-0.560402\pi\)
−0.944791 + 0.327674i \(0.893735\pi\)
\(492\) 0 0
\(493\) −27.4955 + 15.8745i −1.23833 + 0.714952i
\(494\) 37.0405 14.0000i 1.66653 0.629890i
\(495\) 0 0
\(496\) −3.50000 + 27.7804i −0.157155 + 1.24738i
\(497\) −7.93725 13.7477i −0.356034 0.616670i
\(498\) 0 0
\(499\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(500\) −17.6443 + 3.56080i −0.789076 + 0.159244i
\(501\) 0 0
\(502\) −10.7477 + 13.1334i −0.479695 + 0.586173i
\(503\) 15.8745 0.707809 0.353905 0.935282i \(-0.384854\pi\)
0.353905 + 0.935282i \(0.384854\pi\)
\(504\) 0 0
\(505\) 17.0000 0.756490
\(506\) −14.2179 + 17.3739i −0.632063 + 0.772362i
\(507\) 0 0
\(508\) 5.14337 + 25.4862i 0.228200 + 1.13077i
\(509\) −18.1865 10.5000i −0.806104 0.465404i 0.0394971 0.999220i \(-0.487424\pi\)
−0.845601 + 0.533815i \(0.820758\pi\)
\(510\) 0 0
\(511\) −1.50000 2.59808i −0.0663561 0.114932i
\(512\) −22.4889 + 2.50000i −0.993878 + 0.110485i
\(513\) 0 0
\(514\) −21.0000 + 7.93725i −0.926270 + 0.350097i
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 7.38505 + 1.20871i 0.324481 + 0.0531078i
\(519\) 0 0
\(520\) −14.9564 + 0.552200i −0.655883 + 0.0242156i
\(521\) 15.8745 0.695475 0.347737 0.937592i \(-0.386950\pi\)
0.347737 + 0.937592i \(0.386950\pi\)
\(522\) 0 0
\(523\) 15.8745i 0.694144i 0.937839 + 0.347072i \(0.112824\pi\)
−0.937839 + 0.347072i \(0.887176\pi\)
\(524\) −4.46320 + 13.2695i −0.194976 + 0.579681i
\(525\) 0 0
\(526\) −1.20871 + 7.38505i −0.0527024 + 0.322004i
\(527\) −18.5203 + 32.0780i −0.806755 + 1.39734i
\(528\) 0 0
\(529\) −2.50000 4.33013i −0.108696 0.188266i
\(530\) 11.9059 4.50000i 0.517158 0.195468i
\(531\) 0 0
\(532\) 7.00000 + 7.93725i 0.303488 + 0.344124i
\(533\) −24.2487 + 14.0000i −1.05033 + 0.606407i
\(534\) 0 0
\(535\) 1.50000 2.59808i 0.0648507 0.112325i
\(536\) 0 0
\(537\) 0 0
\(538\) 16.1216 19.7001i 0.695051 0.849332i
\(539\) 18.0000i 0.775315i
\(540\) 0 0
\(541\) 10.5830i 0.454999i 0.973778 + 0.227499i \(0.0730550\pi\)
−0.973778 + 0.227499i \(0.926945\pi\)
\(542\) −16.4168 13.4347i −0.705160 0.577068i
\(543\) 0 0
\(544\) −28.7042 8.48945i −1.23068 0.363982i
\(545\) 2.64575 4.58258i 0.113332 0.196296i
\(546\) 0 0
\(547\) 4.58258 2.64575i 0.195937 0.113124i −0.398822 0.917028i \(-0.630581\pi\)
0.594759 + 0.803904i \(0.297248\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 6.00000 + 15.8745i 0.255841 + 0.676891i
\(551\) 15.8745 + 27.4955i 0.676277 + 1.17135i
\(552\) 0 0
\(553\) −2.00000 + 3.46410i −0.0850487 + 0.147309i
\(554\) 14.7701 + 2.41742i 0.627522 + 0.102707i
\(555\) 0 0
\(556\) −6.74773 + 20.0616i −0.286167 + 0.850802i
\(557\) 39.0000i 1.65248i 0.563316 + 0.826242i \(0.309525\pi\)
−0.563316 + 0.826242i \(0.690475\pi\)
\(558\) 0 0
\(559\) 56.0000 2.36855
\(560\) −1.55130 3.68693i −0.0655544 0.155801i
\(561\) 0 0
\(562\) −3.62614 + 22.1552i −0.152959 + 0.934559i
\(563\) −2.59808 1.50000i −0.109496 0.0632175i 0.444252 0.895902i \(-0.353470\pi\)
−0.553748 + 0.832684i \(0.686803\pi\)
\(564\) 0 0
\(565\) 13.7477 7.93725i 0.578371 0.333923i
\(566\) 13.2288 + 35.0000i 0.556046 + 1.47116i
\(567\) 0 0
\(568\) 21.0000 39.6863i 0.881140 1.66520i
\(569\) 15.8745 + 27.4955i 0.665494 + 1.15267i 0.979151 + 0.203133i \(0.0651124\pi\)
−0.313657 + 0.949536i \(0.601554\pi\)
\(570\) 0 0
\(571\) 22.9129 + 13.2288i 0.958874 + 0.553606i 0.895826 0.444404i \(-0.146585\pi\)
0.0630478 + 0.998011i \(0.479918\pi\)
\(572\) 6.28065 + 31.1216i 0.262607 + 1.30126i
\(573\) 0 0
\(574\) −5.79129 4.73930i −0.241724 0.197815i
\(575\) −21.1660 −0.882684
\(576\) 0 0
\(577\) −18.0000 −0.749350 −0.374675 0.927156i \(-0.622246\pi\)
−0.374675 + 0.927156i \(0.622246\pi\)
\(578\) −12.0390 9.85208i −0.500755 0.409793i
\(579\) 0 0
\(580\) −2.37386 11.7629i −0.0985693 0.488426i
\(581\) 6.06218 + 3.50000i 0.251502 + 0.145204i
\(582\) 0 0
\(583\) −13.5000 23.3827i −0.559113 0.968412i
\(584\) 3.96863 7.50000i 0.164223 0.310352i
\(585\) 0 0
\(586\) −15.0000 39.6863i −0.619644 1.63942i
\(587\) 19.9186 11.5000i 0.822128 0.474656i −0.0290218 0.999579i \(-0.509239\pi\)
0.851150 + 0.524923i \(0.175906\pi\)
\(588\) 0 0
\(589\) 32.0780 + 18.5203i 1.32175 + 0.763114i
\(590\) −0.913701 + 5.58258i −0.0376165 + 0.229831i
\(591\) 0 0
\(592\) 8.20871 + 19.5094i 0.337376 + 0.801832i
\(593\) 31.7490 1.30378 0.651888 0.758315i \(-0.273977\pi\)
0.651888 + 0.758315i \(0.273977\pi\)
\(594\) 0 0
\(595\) 5.29150i 0.216930i
\(596\) −1.91280 + 5.68693i −0.0783514 + 0.232946i
\(597\) 0 0
\(598\) −39.0780 6.39590i −1.59802 0.261548i
\(599\) 10.5830 18.3303i 0.432410 0.748956i −0.564670 0.825317i \(-0.690997\pi\)
0.997080 + 0.0763606i \(0.0243300\pi\)
\(600\) 0 0
\(601\) −2.50000 4.33013i −0.101977 0.176630i 0.810522 0.585708i \(-0.199184\pi\)
−0.912499 + 0.409079i \(0.865850\pi\)
\(602\) 5.29150 + 14.0000i 0.215666 + 0.570597i
\(603\) 0 0
\(604\) 4.50000 3.96863i 0.183102 0.161481i
\(605\) 1.73205 1.00000i 0.0704179 0.0406558i
\(606\) 0 0
\(607\) 4.00000 6.92820i 0.162355 0.281207i −0.773358 0.633970i \(-0.781424\pi\)
0.935713 + 0.352763i \(0.114758\pi\)
\(608\) −8.48945 + 28.7042i −0.344293 + 1.16411i
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 10.5830i 0.427444i −0.976895 0.213722i \(-0.931441\pi\)
0.976895 0.213722i \(-0.0685586\pi\)
\(614\) −14.2179 + 17.3739i −0.573788 + 0.701152i
\(615\) 0 0
\(616\) −7.18693 + 4.51088i −0.289570 + 0.181748i
\(617\) 2.64575 4.58258i 0.106514 0.184488i −0.807842 0.589399i \(-0.799364\pi\)
0.914356 + 0.404912i \(0.132698\pi\)
\(618\) 0 0
\(619\) 13.7477 7.93725i 0.552568 0.319025i −0.197589 0.980285i \(-0.563311\pi\)
0.750157 + 0.661260i \(0.229978\pi\)
\(620\) −9.26013 10.5000i −0.371896 0.421690i
\(621\) 0 0
\(622\) 35.0000 13.2288i 1.40337 0.530425i
\(623\) 5.29150 + 9.16515i 0.212000 + 0.367194i
\(624\) 0 0
\(625\) −5.50000 + 9.52628i −0.220000 + 0.381051i
\(626\) 0.228425 1.39564i 0.00912970 0.0557811i
\(627\) 0 0
\(628\) 6.74773 20.0616i 0.269264 0.800545i
\(629\) 28.0000i 1.11643i
\(630\) 0 0
\(631\) −23.0000 −0.915616 −0.457808 0.889051i \(-0.651365\pi\)
−0.457808 + 0.889051i \(0.651365\pi\)
\(632\) −11.3060 + 0.417424i −0.449729 + 0.0166042i
\(633\) 0 0
\(634\) −18.1434 2.96953i −0.720565 0.117935i
\(635\) −11.2583 6.50000i −0.446773 0.257945i
\(636\) 0 0
\(637\) 27.4955 15.8745i 1.08941 0.628971i
\(638\) −23.8118 + 9.00000i −0.942717 + 0.356313i
\(639\) 0 0
\(640\) 6.50000 9.26013i 0.256935 0.366039i
\(641\) 18.5203 + 32.0780i 0.731506 + 1.26701i 0.956239 + 0.292586i \(0.0945157\pi\)
−0.224733 + 0.974420i \(0.572151\pi\)
\(642\) 0 0
\(643\) 18.3303 + 10.5830i 0.722877 + 0.417353i 0.815811 0.578319i \(-0.196291\pi\)
−0.0929339 + 0.995672i \(0.529625\pi\)
\(644\) −2.09355 10.3739i −0.0824975 0.408787i
\(645\) 0 0
\(646\) −25.0780 + 30.6446i −0.986682 + 1.20570i
\(647\) −31.7490 −1.24818 −0.624091 0.781351i \(-0.714531\pi\)
−0.624091 + 0.781351i \(0.714531\pi\)
\(648\) 0 0
\(649\) 12.0000 0.471041
\(650\) −18.9572 + 23.1652i −0.743563 + 0.908612i
\(651\) 0 0
\(652\) 10.3739 2.09355i 0.406272 0.0819898i
\(653\) −2.59808 1.50000i −0.101671 0.0586995i 0.448303 0.893882i \(-0.352029\pi\)
−0.549973 + 0.835182i \(0.685362\pi\)
\(654\) 0 0
\(655\) −3.50000 6.06218i −0.136756 0.236869i
\(656\) 2.64575 21.0000i 0.103299 0.819912i
\(657\) 0 0
\(658\) 0 0
\(659\) 12.9904 7.50000i 0.506033 0.292159i −0.225168 0.974320i \(-0.572293\pi\)
0.731202 + 0.682161i \(0.238960\pi\)
\(660\) 0 0
\(661\) −22.9129 13.2288i −0.891208 0.514539i −0.0168704 0.999858i \(-0.505370\pi\)
−0.874337 + 0.485319i \(0.838704\pi\)
\(662\) 29.5402 + 4.83485i 1.14811 + 0.187912i
\(663\) 0 0
\(664\) 0.730493 + 19.7855i 0.0283486 + 0.767827i
\(665\) −5.29150 −0.205196
\(666\) 0 0
\(667\) 31.7490i 1.22933i
\(668\) 20.0616 + 6.74773i 0.776207 + 0.261077i
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) −14.5000 25.1147i −0.558934 0.968102i −0.997586 0.0694449i \(-0.977877\pi\)
0.438652 0.898657i \(-0.355456\pi\)
\(674\) 44.9778 17.0000i 1.73248 0.654816i
\(675\) 0 0
\(676\) −22.5000 + 19.8431i −0.865385 + 0.763197i
\(677\) 5.19615 3.00000i 0.199704 0.115299i −0.396813 0.917899i \(-0.629884\pi\)
0.596518 + 0.802600i \(0.296551\pi\)
\(678\) 0 0
\(679\) −3.50000 + 6.06218i −0.134318 + 0.232645i
\(680\) 12.6766 7.95644i 0.486124 0.305116i
\(681\) 0 0
\(682\) −18.8085 + 22.9835i −0.720216 + 0.880082i
\(683\) 44.0000i 1.68361i 0.539779 + 0.841807i \(0.318508\pi\)
−0.539779 + 0.841807i \(0.681492\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 14.2279 + 11.6434i 0.543222 + 0.444546i
\(687\) 0 0
\(688\) −25.5826 + 33.7273i −0.975327 + 1.28584i
\(689\) 23.8118 41.2432i 0.907156 1.57124i
\(690\) 0 0
\(691\) −36.6606 + 21.1660i −1.39464 + 0.805193i −0.993824 0.110968i \(-0.964605\pi\)
−0.400811 + 0.916161i \(0.631272\pi\)
\(692\) 19.8431 + 22.5000i 0.754323 + 0.855322i
\(693\) 0 0
\(694\) −11.5000 30.4261i −0.436534 1.15496i
\(695\) −5.29150 9.16515i −0.200718 0.347654i
\(696\) 0 0
\(697\) 14.0000 24.2487i 0.530288 0.918485i
\(698\) 7.38505 + 1.20871i 0.279528 + 0.0457504i
\(699\) 0 0
\(700\) −7.58258 2.55040i −0.286594 0.0963961i
\(701\) 1.00000i 0.0377695i 0.999822 + 0.0188847i \(0.00601156\pi\)
−0.999822 + 0.0188847i \(0.993988\pi\)
\(702\) 0 0
\(703\) 28.0000 1.05604
\(704\) −21.6129 10.4347i −0.814567 0.393271i
\(705\) 0 0
\(706\) −3.62614 + 22.1552i −0.136471 + 0.833820i
\(707\) 14.7224 + 8.50000i 0.553694 + 0.319675i
\(708\) 0 0
\(709\) 18.3303 10.5830i 0.688409 0.397453i −0.114607 0.993411i \(-0.536561\pi\)
0.803016 + 0.595958i \(0.203227\pi\)
\(710\) 7.93725 + 21.0000i 0.297880 + 0.788116i
\(711\) 0 0
\(712\) −14.0000 + 26.4575i −0.524672 + 0.991537i
\(713\) −18.5203 32.0780i −0.693589 1.20133i
\(714\) 0 0
\(715\) −13.7477 7.93725i −0.514136 0.296836i
\(716\) −45.0909 + 9.09981i −1.68513 + 0.340076i
\(717\) 0 0
\(718\) 23.1652 + 18.9572i 0.864516 + 0.707477i
\(719\) −21.1660 −0.789359 −0.394679 0.918819i \(-0.629144\pi\)
−0.394679 + 0.918819i \(0.629144\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 9.85005 + 8.06080i 0.366581 + 0.299992i
\(723\) 0 0
\(724\) −41.4955 + 8.37420i −1.54217 + 0.311225i
\(725\) −20.7846 12.0000i −0.771921 0.445669i
\(726\) 0 0
\(727\) −16.5000 28.5788i −0.611951 1.05993i −0.990911 0.134517i \(-0.957052\pi\)
0.378960 0.925413i \(-0.376282\pi\)
\(728\) −13.2288 7.00000i −0.490290 0.259437i
\(729\) 0 0
\(730\) 1.50000 + 3.96863i 0.0555175 + 0.146885i
\(731\) −48.4974 + 28.0000i −1.79374 + 1.03562i
\(732\) 0 0
\(733\) 4.58258 + 2.64575i 0.169261 + 0.0977231i 0.582237 0.813019i \(-0.302177\pi\)
−0.412976 + 0.910742i \(0.635511\pi\)
\(734\) 0.685275 4.18693i 0.0252940 0.154542i
\(735\) 0 0
\(736\) 21.7042 20.6138i 0.800026 0.759835i
\(737\) 0 0
\(738\) 0 0
\(739\) 5.29150i 0.194651i −0.995253 0.0973255i \(-0.968971\pi\)
0.995253 0.0973255i \(-0.0310288\pi\)
\(740\) −10.0308 3.37386i −0.368740 0.124026i
\(741\) 0 0
\(742\) 12.5608 + 2.05583i 0.461121 + 0.0754718i
\(743\) −18.5203 + 32.0780i −0.679442 + 1.17683i 0.295707 + 0.955279i \(0.404445\pi\)
−0.975149 + 0.221550i \(0.928888\pi\)
\(744\) 0 0
\(745\) −1.50000 2.59808i −0.0549557 0.0951861i
\(746\) −13.2288 35.0000i −0.484339 1.28144i
\(747\) 0 0
\(748\) −21.0000 23.8118i −0.767836 0.870644i
\(749\) 2.59808 1.50000i 0.0949316 0.0548088i
\(750\) 0 0
\(751\) 15.5000 26.8468i 0.565603 0.979653i −0.431390 0.902165i \(-0.641977\pi\)
0.996993 0.0774878i \(-0.0246899\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) −34.7477 28.4358i −1.26544 1.03557i
\(755\) 3.00000i 0.109181i
\(756\) 0 0
\(757\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(758\) 18.9572 23.1652i 0.688557 0.841396i
\(759\) 0 0
\(760\) −7.95644 12.6766i −0.288610 0.459827i
\(761\) −5.29150 + 9.16515i −0.191817 + 0.332236i −0.945852 0.324597i \(-0.894771\pi\)
0.754036 + 0.656834i \(0.228105\pi\)
\(762\) 0 0
\(763\) 4.58258 2.64575i 0.165900 0.0957826i
\(764\) −7.93725 + 7.00000i −0.287160 + 0.253251i
\(765\) 0 0
\(766\) 21.0000 7.93725i 0.758761 0.286785i
\(767\) 10.5830 + 18.3303i 0.382130 + 0.661869i
\(768\) 0 0
\(769\) 17.5000 30.3109i 0.631066 1.09304i −0.356268 0.934384i \(-0.615951\pi\)
0.987334 0.158655i \(-0.0507157\pi\)
\(770\) 0.685275 4.18693i 0.0246956 0.150887i
\(771\) 0 0
\(772\) 5.68693 + 1.91280i 0.204677 + 0.0688432i
\(773\) 14.0000i 0.503545i −0.967786 0.251773i \(-0.918987\pi\)
0.967786 0.251773i \(-0.0810135\pi\)
\(774\) 0 0
\(775\) −28.0000 −1.00579
\(776\) −19.7855 + 0.730493i −0.710258 + 0.0262232i
\(777\) 0 0
\(778\) −6.97822 1.14213i −0.250181 0.0409472i
\(779\) −24.2487 14.0000i −0.868800 0.501602i
\(780\) 0 0
\(781\) 41.2432 23.8118i 1.47580 0.852052i
\(782\) 37.0405 14.0000i 1.32457 0.500639i
\(783\) 0 0
\(784\) −3.00000 + 23.8118i −0.107143 + 0.850420i
\(785\) 5.29150 + 9.16515i 0.188862 + 0.327118i
\(786\) 0 0
\(787\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(788\) 25.4862 5.14337i 0.907908 0.183225i
\(789\) 0 0
\(790\) 3.58258 4.37780i 0.127462 0.155755i
\(791\) 15.8745 0.564433
\(792\) 0 0
\(793\) 0 0
\(794\) 4.73930 5.79129i 0.168192 0.205525i
\(795\) 0 0
\(796\) −6.72595 33.3281i −0.238395 1.18128i
\(797\) 42.4352 + 24.5000i 1.50313 + 0.867835i 0.999993 + 0.00362965i \(0.00115536\pi\)
0.503140 + 0.864205i \(0.332178\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) −5.29150 22.0000i −0.187083 0.777817i
\(801\) 0 0
\(802\) 0 0
\(803\) 7.79423 4.50000i 0.275052 0.158802i
\(804\) 0 0
\(805\) 4.58258 + 2.64575i 0.161515 + 0.0932505i
\(806\) −51.6954 8.46099i −1.82089 0.298025i
\(807\) 0 0
\(808\) 1.77405 + 48.0505i 0.0624110 + 1.69041i
\(809\) 31.7490 1.11624 0.558118 0.829762i \(-0.311524\pi\)
0.558118 + 0.829762i \(0.311524\pi\)
\(810\) 0 0
\(811\) 37.0405i 1.30067i −0.759648 0.650334i \(-0.774629\pi\)
0.759648 0.650334i \(-0.225371\pi\)
\(812\) 3.82560 11.3739i 0.134252 0.399144i
\(813\) 0 0
\(814\) −3.62614 + 22.1552i −0.127096 + 0.776538i
\(815\) −2.64575 + 4.58258i −0.0926766 + 0.160521i
\(816\) 0 0
\(817\) 28.0000 + 48.4974i 0.979596 + 1.69671i
\(818\) −14.5516 + 5.50000i −0.508786 + 0.192303i
\(819\) 0 0
\(820\) 7.00000 + 7.93725i 0.244451 + 0.277181i
\(821\) 8.66025 5.00000i 0.302245 0.174501i −0.341206 0.939989i \(-0.610835\pi\)
0.643451 + 0.765487i \(0.277502\pi\)
\(822\) 0 0
\(823\) −11.5000 + 19.9186i −0.400865 + 0.694318i −0.993831 0.110910i \(-0.964624\pi\)
0.592966 + 0.805228i \(0.297957\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) −3.58258 + 4.37780i −0.124654 + 0.152323i
\(827\) 36.0000i 1.25184i −0.779886 0.625921i \(-0.784723\pi\)
0.779886 0.625921i \(-0.215277\pi\)
\(828\) 0 0
\(829\) 21.1660i 0.735126i 0.929999 + 0.367563i \(0.119808\pi\)
−0.929999 + 0.367563i \(0.880192\pi\)
\(830\) −7.66115 6.26951i −0.265923 0.217618i
\(831\) 0 0
\(832\) −3.12159 42.2168i −0.108222 1.46360i
\(833\) −15.8745 + 27.4955i −0.550019 + 0.952661i
\(834\) 0 0
\(835\) −9.16515 + 5.29150i −0.317173 + 0.183120i
\(836\) −23.8118 + 21.0000i −0.823547 + 0.726300i
\(837\) 0 0
\(838\) 0 0
\(839\) −18.5203 32.0780i −0.639390 1.10746i −0.985567 0.169287i \(-0.945853\pi\)
0.346176 0.938169i \(-0.387480\pi\)
\(840\) 0 0
\(841\) 3.50000 6.06218i 0.120690 0.209041i
\(842\) 14.7701 + 2.41742i 0.509012 + 0.0833099i
\(843\) 0 0
\(844\) −3.37386 + 10.0308i −0.116133 + 0.345275i
\(845\) 15.0000i 0.516016i
\(846\) 0 0
\(847\) 2.00000 0.0687208
\(848\) 13.9617 + 33.1824i 0.479447 + 1.13949i
\(849\) 0 0
\(850\) 4.83485 29.5402i 0.165834 1.01322i
\(851\) −24.2487 14.0000i −0.831235 0.479914i
\(852\) 0 0
\(853\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 7.50000 + 3.96863i 0.256345 + 0.135645i
\(857\) −7.93725 13.7477i −0.271131 0.469613i 0.698020 0.716078i \(-0.254064\pi\)
−0.969152 + 0.246464i \(0.920731\pi\)
\(858\) 0 0
\(859\) 45.8258 + 26.4575i 1.56355 + 0.902719i 0.996893 + 0.0787681i \(0.0250987\pi\)
0.566662 + 0.823951i \(0.308235\pi\)
\(860\) −4.18710 20.7477i −0.142779 0.707492i
\(861\) 0 0
\(862\) 34.7477 + 28.4358i 1.18351 + 0.968528i
\(863\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(864\) 0 0
\(865\) −15.0000 −0.510015
\(866\) −5.47225 4.47822i −0.185955 0.152176i
\(867\) 0 0
\(868\) −2.76951 13.7233i −0.0940032 0.465800i
\(869\) −10.3923 6.00000i −0.352535 0.203536i
\(870\) 0 0
\(871\) 0 0
\(872\) 13.2288 + 7.00000i 0.447982 + 0.237050i
\(873\) 0 0
\(874\) −14.0000 37.0405i −0.473557 1.25291i
\(875\) 7.79423 4.50000i 0.263493 0.152128i
\(876\) 0 0
\(877\) −45.8258 26.4575i −1.54743 0.893407i −0.998337 0.0576426i \(-0.981642\pi\)
−0.549089 0.835764i \(-0.685025\pi\)
\(878\) 4.79693 29.3085i 0.161888 0.989115i
\(879\) 0 0
\(880\) 11.0608 4.65390i 0.372859 0.156883i
\(881\) −26.4575 −0.891376 −0.445688 0.895188i \(-0.647041\pi\)
−0.445688 + 0.895188i \(0.647041\pi\)
\(882\) 0 0
\(883\) 58.2065i 1.95881i 0.201916 + 0.979403i \(0.435283\pi\)
−0.201916 + 0.979403i \(0.564717\pi\)
\(884\) 17.8528 53.0780i 0.600455 1.78521i
\(885\) 0 0
\(886\) 33.4955 + 5.48220i 1.12530 + 0.184178i
\(887\) 7.93725 13.7477i 0.266507 0.461603i −0.701450 0.712718i \(-0.747464\pi\)
0.967957 + 0.251115i \(0.0807972\pi\)
\(888\) 0 0
\(889\) −6.50000 11.2583i −0.218003 0.377592i
\(890\) −5.29150 14.0000i −0.177372 0.469281i
\(891\) 0 0
\(892\) −24.0000 + 21.1660i −0.803579 + 0.708690i
\(893\) 0 0
\(894\) 0 0
\(895\) 11.5000 19.9186i 0.384403 0.665805i
\(896\) 10.2592 4.76951i 0.342737 0.159338i
\(897\) 0 0
\(898\) −17.3739 14.2179i −0.579773 0.474458i
\(899\) 42.0000i 1.40078i
\(900\) 0 0
\(901\) 47.6235i 1.58657i
\(902\) 14.2179 17.3739i 0.473405 0.578486i
\(903\) 0 0
\(904\) 23.8693 + 38.0297i 0.793882 + 1.26485i
\(905\) 10.5830 18.3303i 0.351791 0.609320i
\(906\) 0 0
\(907\) 4.58258 2.64575i 0.152162 0.0878507i −0.421986 0.906602i \(-0.638667\pi\)
0.574148 + 0.818752i \(0.305333\pi\)
\(908\) 5.29150 + 6.00000i 0.175605 + 0.199117i
\(909\) 0 0
\(910\) 7.00000 2.64575i 0.232048 0.0877058i
\(911\) −15.8745 27.4955i −0.525946 0.910965i −0.999543 0.0302235i \(-0.990378\pi\)
0.473597 0.880742i \(-0.342955\pi\)
\(912\) 0 0
\(913\) −10.5000 + 18.1865i −0.347499 + 0.601886i
\(914\) −3.88323 + 23.7259i −0.128446 + 0.784785i
\(915\) 0 0
\(916\) 13.4955 40.1232i 0.445902 1.32571i
\(917\) 7.00000i 0.231160i
\(918\) 0 0
\(919\) 3.00000 0.0989609 0.0494804 0.998775i \(-0.484243\pi\)
0.0494804 + 0.998775i \(0.484243\pi\)
\(920\) 0.552200 + 14.9564i 0.0182055 + 0.493099i
\(921\) 0 0
\(922\) 12.5608 + 2.05583i 0.413668 + 0.0677050i
\(923\) 72.7461 + 42.0000i 2.39447 + 1.38245i
\(924\) 0 0
\(925\) −18.3303 + 10.5830i −0.602697 + 0.347967i
\(926\) −54.2379 + 20.5000i −1.78237 + 0.673672i
\(927\) 0 0
\(928\) 33.0000 7.93725i 1.08328 0.260553i
\(929\) −5.29150 9.16515i −0.173609 0.300699i 0.766070 0.642757i \(-0.222209\pi\)
−0.939679 + 0.342058i \(0.888876\pi\)
\(930\) 0 0
\(931\) 27.4955 + 15.8745i 0.901127 + 0.520266i
\(932\) −4.18710 20.7477i −0.137153 0.679614i
\(933\) 0 0
\(934\) 0.895644 1.09445i 0.0293064 0.0358115i
\(935\) 15.8745 0.519152
\(936\) 0 0
\(937\) −19.0000 −0.620703 −0.310351 0.950622i \(-0.600447\pi\)
−0.310351 + 0.950622i \(0.600447\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 18.1865 + 10.5000i 0.592864 + 0.342290i 0.766229 0.642567i \(-0.222131\pi\)
−0.173365 + 0.984858i \(0.555464\pi\)
\(942\) 0 0
\(943\) 14.0000 + 24.2487i 0.455903 + 0.789647i
\(944\) −15.8745 2.00000i −0.516671 0.0650945i
\(945\) 0 0
\(946\) −42.0000 + 15.8745i −1.36554 + 0.516125i
\(947\) 33.7750 19.5000i 1.09754 0.633665i 0.161966 0.986796i \(-0.448217\pi\)
0.935574 + 0.353131i \(0.114883\pi\)
\(948\) 0 0
\(949\) 13.7477 + 7.93725i 0.446270 + 0.257654i
\(950\) −29.5402 4.83485i −0.958411 0.156863i
\(951\) 0 0
\(952\) 14.9564 0.552200i 0.484741 0.0178969i
\(953\) −31.7490 −1.02845 −0.514226 0.857655i \(-0.671921\pi\)
−0.514226 + 0.857655i \(0.671921\pi\)
\(954\) 0 0
\(955\) 5.29150i 0.171229i
\(956\) 30.0924 + 10.1216i 0.973258 + 0.327356i
\(957\) 0 0
\(958\) −4.83485 + 29.5402i −0.156207 + 0.954401i
\(959\) 0 0
\(960\) 0 0
\(961\) −9.00000 15.5885i −0.290323 0.502853i
\(962\) −37.0405 + 14.0000i −1.19423 + 0.451378i
\(963\) 0 0
\(964\) −15.0000 + 13.2288i −0.483117 + 0.426070i
\(965\) −2.59808 + 1.50000i −0.0836350 + 0.0482867i
\(966\) 0 0
\(967\) −20.5000 + 35.5070i −0.659236 + 1.14183i 0.321578 + 0.946883i \(0.395787\pi\)
−0.980814 + 0.194946i \(0.937547\pi\)
\(968\) 3.00725 + 4.79129i 0.0966567 + 0.153998i
\(969\) 0 0
\(970\) 6.26951 7.66115i 0.201302 0.245985i
\(971\) 15.0000i 0.481373i 0.970603 + 0.240686i \(0.0773725\pi\)
−0.970603 + 0.240686i \(0.922627\pi\)
\(972\) 0 0
\(973\) 10.5830i 0.339276i
\(974\) 43.7780 + 35.8258i 1.40274 + 1.14793i
\(975\) 0 0
\(976\) 0 0
\(977\) −5.29150 + 9.16515i −0.169290 + 0.293219i −0.938170 0.346174i \(-0.887481\pi\)
0.768880 + 0.639393i \(0.220814\pi\)
\(978\) 0 0
\(979\) −27.4955 + 15.8745i −0.878759 + 0.507351i
\(980\) −7.93725 9.00000i −0.253546 0.287494i
\(981\) 0 0
\(982\) 14.5000 + 38.3634i 0.462714 + 1.22423i
\(983\) 21.1660 + 36.6606i 0.675091 + 1.16929i 0.976442 + 0.215779i \(0.0692289\pi\)
−0.301351 + 0.953513i \(0.597438\pi\)
\(984\) 0 0
\(985\) −6.50000 + 11.2583i −0.207107 + 0.358720i
\(986\) 44.3103 + 7.25227i 1.41113 + 0.230959i
\(987\) 0 0
\(988\) −53.0780 17.8528i −1.68864 0.567973i
\(989\) 56.0000i 1.78070i
\(990\) 0 0
\(991\) 47.0000 1.49300 0.746502 0.665383i \(-0.231732\pi\)
0.746502 + 0.665383i \(0.231732\pi\)
\(992\) 28.7119 27.2695i 0.911604 0.865808i
\(993\) 0 0
\(994\) −3.62614 + 22.1552i −0.115014 + 0.702719i
\(995\) 14.7224 + 8.50000i 0.466732 + 0.269468i
\(996\) 0 0
\(997\) −13.7477 + 7.93725i −0.435395 + 0.251375i −0.701642 0.712529i \(-0.747550\pi\)
0.266247 + 0.963905i \(0.414216\pi\)
\(998\) 0 0
\(999\) 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 648.2.n.n.109.1 8
3.2 odd 2 inner 648.2.n.n.109.4 8
4.3 odd 2 2592.2.r.p.433.2 8
8.3 odd 2 2592.2.r.p.433.3 8
8.5 even 2 inner 648.2.n.n.109.2 8
9.2 odd 6 inner 648.2.n.n.541.3 8
9.4 even 3 216.2.d.b.109.3 yes 4
9.5 odd 6 216.2.d.b.109.2 yes 4
9.7 even 3 inner 648.2.n.n.541.2 8
12.11 even 2 2592.2.r.p.433.4 8
24.5 odd 2 inner 648.2.n.n.109.3 8
24.11 even 2 2592.2.r.p.433.1 8
36.7 odd 6 2592.2.r.p.2161.3 8
36.11 even 6 2592.2.r.p.2161.1 8
36.23 even 6 864.2.d.a.433.1 4
36.31 odd 6 864.2.d.a.433.3 4
72.5 odd 6 216.2.d.b.109.1 4
72.11 even 6 2592.2.r.p.2161.4 8
72.13 even 6 216.2.d.b.109.4 yes 4
72.29 odd 6 inner 648.2.n.n.541.4 8
72.43 odd 6 2592.2.r.p.2161.2 8
72.59 even 6 864.2.d.a.433.4 4
72.61 even 6 inner 648.2.n.n.541.1 8
72.67 odd 6 864.2.d.a.433.2 4
144.5 odd 12 6912.2.a.bu.1.1 2
144.13 even 12 6912.2.a.bu.1.2 2
144.59 even 12 6912.2.a.bv.1.1 2
144.67 odd 12 6912.2.a.bv.1.2 2
144.77 odd 12 6912.2.a.bc.1.2 2
144.85 even 12 6912.2.a.bc.1.1 2
144.131 even 12 6912.2.a.bd.1.2 2
144.139 odd 12 6912.2.a.bd.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
216.2.d.b.109.1 4 72.5 odd 6
216.2.d.b.109.2 yes 4 9.5 odd 6
216.2.d.b.109.3 yes 4 9.4 even 3
216.2.d.b.109.4 yes 4 72.13 even 6
648.2.n.n.109.1 8 1.1 even 1 trivial
648.2.n.n.109.2 8 8.5 even 2 inner
648.2.n.n.109.3 8 24.5 odd 2 inner
648.2.n.n.109.4 8 3.2 odd 2 inner
648.2.n.n.541.1 8 72.61 even 6 inner
648.2.n.n.541.2 8 9.7 even 3 inner
648.2.n.n.541.3 8 9.2 odd 6 inner
648.2.n.n.541.4 8 72.29 odd 6 inner
864.2.d.a.433.1 4 36.23 even 6
864.2.d.a.433.2 4 72.67 odd 6
864.2.d.a.433.3 4 36.31 odd 6
864.2.d.a.433.4 4 72.59 even 6
2592.2.r.p.433.1 8 24.11 even 2
2592.2.r.p.433.2 8 4.3 odd 2
2592.2.r.p.433.3 8 8.3 odd 2
2592.2.r.p.433.4 8 12.11 even 2
2592.2.r.p.2161.1 8 36.11 even 6
2592.2.r.p.2161.2 8 72.43 odd 6
2592.2.r.p.2161.3 8 36.7 odd 6
2592.2.r.p.2161.4 8 72.11 even 6
6912.2.a.bc.1.1 2 144.85 even 12
6912.2.a.bc.1.2 2 144.77 odd 12
6912.2.a.bd.1.1 2 144.139 odd 12
6912.2.a.bd.1.2 2 144.131 even 12
6912.2.a.bu.1.1 2 144.5 odd 12
6912.2.a.bu.1.2 2 144.13 even 12
6912.2.a.bv.1.1 2 144.59 even 12
6912.2.a.bv.1.2 2 144.67 odd 12