Properties

Label 847.2.f.f.323.1
Level $847$
Weight $2$
Character 847.323
Analytic conductor $6.763$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [847,2,Mod(148,847)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(847, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("847.148");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 847 = 7 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 847.f (of order \(5\), degree \(4\), 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: \(6.76332905120\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{10})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{3} + x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 77)
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 323.1
Root \(0.809017 - 0.587785i\) of defining polynomial
Character \(\chi\) \(=\) 847.323
Dual form 847.2.f.f.729.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.309017 - 0.951057i) q^{3} +(-0.618034 - 1.90211i) q^{4} +(-2.42705 + 1.76336i) q^{5} +(0.309017 + 0.951057i) q^{7} +(1.61803 + 1.17557i) q^{9} +O(q^{10})\) \(q+(0.309017 - 0.951057i) q^{3} +(-0.618034 - 1.90211i) q^{4} +(-2.42705 + 1.76336i) q^{5} +(0.309017 + 0.951057i) q^{7} +(1.61803 + 1.17557i) q^{9} -2.00000 q^{12} +(3.23607 + 2.35114i) q^{13} +(0.927051 + 2.85317i) q^{15} +(-3.23607 + 2.35114i) q^{16} +(4.85410 - 3.52671i) q^{17} +(0.618034 - 1.90211i) q^{19} +(4.85410 + 3.52671i) q^{20} +1.00000 q^{21} +3.00000 q^{23} +(1.23607 - 3.80423i) q^{25} +(4.04508 - 2.93893i) q^{27} +(1.61803 - 1.17557i) q^{28} +(-1.85410 - 5.70634i) q^{29} +(-4.04508 - 2.93893i) q^{31} +(-2.42705 - 1.76336i) q^{35} +(1.23607 - 3.80423i) q^{36} +(3.39919 + 10.4616i) q^{37} +(3.23607 - 2.35114i) q^{39} +(1.85410 - 5.70634i) q^{41} +8.00000 q^{43} -6.00000 q^{45} +(1.23607 + 3.80423i) q^{48} +(-0.809017 + 0.587785i) q^{49} +(-1.85410 - 5.70634i) q^{51} +(2.47214 - 7.60845i) q^{52} +(4.85410 + 3.52671i) q^{53} +(-1.61803 - 1.17557i) q^{57} +(-2.78115 - 8.55951i) q^{59} +(4.85410 - 3.52671i) q^{60} +(8.09017 - 5.87785i) q^{61} +(-0.618034 + 1.90211i) q^{63} +(6.47214 + 4.70228i) q^{64} -12.0000 q^{65} +5.00000 q^{67} +(-9.70820 - 7.05342i) q^{68} +(0.927051 - 2.85317i) q^{69} +(-7.28115 + 5.29007i) q^{71} +(0.618034 + 1.90211i) q^{73} +(-3.23607 - 2.35114i) q^{75} -4.00000 q^{76} +(8.09017 + 5.87785i) q^{79} +(3.70820 - 11.4127i) q^{80} +(0.309017 + 0.951057i) q^{81} +(-9.70820 + 7.05342i) q^{83} +(-0.618034 - 1.90211i) q^{84} +(-5.56231 + 17.1190i) q^{85} -6.00000 q^{87} -3.00000 q^{89} +(-1.23607 + 3.80423i) q^{91} +(-1.85410 - 5.70634i) q^{92} +(-4.04508 + 2.93893i) q^{93} +(1.85410 + 5.70634i) q^{95} +(0.809017 + 0.587785i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - q^{3} + 2 q^{4} - 3 q^{5} - q^{7} + 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - q^{3} + 2 q^{4} - 3 q^{5} - q^{7} + 2 q^{9} - 8 q^{12} + 4 q^{13} - 3 q^{15} - 4 q^{16} + 6 q^{17} - 2 q^{19} + 6 q^{20} + 4 q^{21} + 12 q^{23} - 4 q^{25} + 5 q^{27} + 2 q^{28} + 6 q^{29} - 5 q^{31} - 3 q^{35} - 4 q^{36} - 11 q^{37} + 4 q^{39} - 6 q^{41} + 32 q^{43} - 24 q^{45} - 4 q^{48} - q^{49} + 6 q^{51} - 8 q^{52} + 6 q^{53} - 2 q^{57} + 9 q^{59} + 6 q^{60} + 10 q^{61} + 2 q^{63} + 8 q^{64} - 48 q^{65} + 20 q^{67} - 12 q^{68} - 3 q^{69} - 9 q^{71} - 2 q^{73} - 4 q^{75} - 16 q^{76} + 10 q^{79} - 12 q^{80} - q^{81} - 12 q^{83} + 2 q^{84} + 18 q^{85} - 24 q^{87} - 12 q^{89} + 4 q^{91} + 6 q^{92} - 5 q^{93} - 6 q^{95} + q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/847\mathbb{Z}\right)^\times\).

\(n\) \(122\) \(365\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{5}\right)\)

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 0 0.587785 0.809017i \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(3\) 0.309017 0.951057i 0.178411 0.549093i −0.821362 0.570408i \(-0.806785\pi\)
0.999773 + 0.0213149i \(0.00678525\pi\)
\(4\) −0.618034 1.90211i −0.309017 0.951057i
\(5\) −2.42705 + 1.76336i −1.08541 + 0.788597i −0.978618 0.205685i \(-0.934058\pi\)
−0.106792 + 0.994281i \(0.534058\pi\)
\(6\) 0 0
\(7\) 0.309017 + 0.951057i 0.116797 + 0.359466i
\(8\) 0 0
\(9\) 1.61803 + 1.17557i 0.539345 + 0.391857i
\(10\) 0 0
\(11\) 0 0
\(12\) −2.00000 −0.577350
\(13\) 3.23607 + 2.35114i 0.897524 + 0.652089i 0.937829 0.347098i \(-0.112833\pi\)
−0.0403050 + 0.999187i \(0.512833\pi\)
\(14\) 0 0
\(15\) 0.927051 + 2.85317i 0.239364 + 0.736685i
\(16\) −3.23607 + 2.35114i −0.809017 + 0.587785i
\(17\) 4.85410 3.52671i 1.17729 0.855353i 0.185429 0.982658i \(-0.440633\pi\)
0.991864 + 0.127304i \(0.0406325\pi\)
\(18\) 0 0
\(19\) 0.618034 1.90211i 0.141787 0.436375i −0.854797 0.518962i \(-0.826318\pi\)
0.996584 + 0.0825877i \(0.0263185\pi\)
\(20\) 4.85410 + 3.52671i 1.08541 + 0.788597i
\(21\) 1.00000 0.218218
\(22\) 0 0
\(23\) 3.00000 0.625543 0.312772 0.949828i \(-0.398743\pi\)
0.312772 + 0.949828i \(0.398743\pi\)
\(24\) 0 0
\(25\) 1.23607 3.80423i 0.247214 0.760845i
\(26\) 0 0
\(27\) 4.04508 2.93893i 0.778477 0.565597i
\(28\) 1.61803 1.17557i 0.305780 0.222162i
\(29\) −1.85410 5.70634i −0.344298 1.05964i −0.961958 0.273196i \(-0.911919\pi\)
0.617660 0.786445i \(-0.288081\pi\)
\(30\) 0 0
\(31\) −4.04508 2.93893i −0.726519 0.527847i 0.161942 0.986800i \(-0.448224\pi\)
−0.888460 + 0.458954i \(0.848224\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −2.42705 1.76336i −0.410246 0.298062i
\(36\) 1.23607 3.80423i 0.206011 0.634038i
\(37\) 3.39919 + 10.4616i 0.558823 + 1.71988i 0.685628 + 0.727952i \(0.259528\pi\)
−0.126805 + 0.991928i \(0.540472\pi\)
\(38\) 0 0
\(39\) 3.23607 2.35114i 0.518186 0.376484i
\(40\) 0 0
\(41\) 1.85410 5.70634i 0.289562 0.891180i −0.695432 0.718592i \(-0.744787\pi\)
0.984994 0.172588i \(-0.0552131\pi\)
\(42\) 0 0
\(43\) 8.00000 1.21999 0.609994 0.792406i \(-0.291172\pi\)
0.609994 + 0.792406i \(0.291172\pi\)
\(44\) 0 0
\(45\) −6.00000 −0.894427
\(46\) 0 0
\(47\) 0 0 −0.951057 0.309017i \(-0.900000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(48\) 1.23607 + 3.80423i 0.178411 + 0.549093i
\(49\) −0.809017 + 0.587785i −0.115574 + 0.0839693i
\(50\) 0 0
\(51\) −1.85410 5.70634i −0.259626 0.799047i
\(52\) 2.47214 7.60845i 0.342824 1.05510i
\(53\) 4.85410 + 3.52671i 0.666762 + 0.484431i 0.868940 0.494918i \(-0.164802\pi\)
−0.202178 + 0.979349i \(0.564802\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) −1.61803 1.17557i −0.214314 0.155708i
\(58\) 0 0
\(59\) −2.78115 8.55951i −0.362075 1.11435i −0.951792 0.306743i \(-0.900761\pi\)
0.589717 0.807610i \(-0.299239\pi\)
\(60\) 4.85410 3.52671i 0.626662 0.455296i
\(61\) 8.09017 5.87785i 1.03584 0.752582i 0.0663709 0.997795i \(-0.478858\pi\)
0.969469 + 0.245213i \(0.0788579\pi\)
\(62\) 0 0
\(63\) −0.618034 + 1.90211i −0.0778650 + 0.239644i
\(64\) 6.47214 + 4.70228i 0.809017 + 0.587785i
\(65\) −12.0000 −1.48842
\(66\) 0 0
\(67\) 5.00000 0.610847 0.305424 0.952217i \(-0.401202\pi\)
0.305424 + 0.952217i \(0.401202\pi\)
\(68\) −9.70820 7.05342i −1.17729 0.855353i
\(69\) 0.927051 2.85317i 0.111604 0.343481i
\(70\) 0 0
\(71\) −7.28115 + 5.29007i −0.864114 + 0.627815i −0.929001 0.370077i \(-0.879331\pi\)
0.0648872 + 0.997893i \(0.479331\pi\)
\(72\) 0 0
\(73\) 0.618034 + 1.90211i 0.0723354 + 0.222625i 0.980688 0.195580i \(-0.0626591\pi\)
−0.908352 + 0.418206i \(0.862659\pi\)
\(74\) 0 0
\(75\) −3.23607 2.35114i −0.373669 0.271486i
\(76\) −4.00000 −0.458831
\(77\) 0 0
\(78\) 0 0
\(79\) 8.09017 + 5.87785i 0.910215 + 0.661310i 0.941069 0.338214i \(-0.109823\pi\)
−0.0308541 + 0.999524i \(0.509823\pi\)
\(80\) 3.70820 11.4127i 0.414590 1.27598i
\(81\) 0.309017 + 0.951057i 0.0343352 + 0.105673i
\(82\) 0 0
\(83\) −9.70820 + 7.05342i −1.06561 + 0.774214i −0.975119 0.221683i \(-0.928845\pi\)
−0.0904951 + 0.995897i \(0.528845\pi\)
\(84\) −0.618034 1.90211i −0.0674330 0.207538i
\(85\) −5.56231 + 17.1190i −0.603317 + 1.85682i
\(86\) 0 0
\(87\) −6.00000 −0.643268
\(88\) 0 0
\(89\) −3.00000 −0.317999 −0.159000 0.987279i \(-0.550827\pi\)
−0.159000 + 0.987279i \(0.550827\pi\)
\(90\) 0 0
\(91\) −1.23607 + 3.80423i −0.129575 + 0.398791i
\(92\) −1.85410 5.70634i −0.193303 0.594927i
\(93\) −4.04508 + 2.93893i −0.419456 + 0.304752i
\(94\) 0 0
\(95\) 1.85410 + 5.70634i 0.190227 + 0.585458i
\(96\) 0 0
\(97\) 0.809017 + 0.587785i 0.0821432 + 0.0596806i 0.628099 0.778133i \(-0.283833\pi\)
−0.545956 + 0.837814i \(0.683833\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −8.00000 −0.800000
\(101\) 9.70820 + 7.05342i 0.966002 + 0.701842i 0.954537 0.298092i \(-0.0963504\pi\)
0.0114654 + 0.999934i \(0.496350\pi\)
\(102\) 0 0
\(103\) −1.23607 3.80423i −0.121793 0.374842i 0.871510 0.490378i \(-0.163141\pi\)
−0.993303 + 0.115536i \(0.963141\pi\)
\(104\) 0 0
\(105\) −2.42705 + 1.76336i −0.236856 + 0.172086i
\(106\) 0 0
\(107\) 1.85410 5.70634i 0.179243 0.551653i −0.820559 0.571562i \(-0.806338\pi\)
0.999802 + 0.0199092i \(0.00633772\pi\)
\(108\) −8.09017 5.87785i −0.778477 0.565597i
\(109\) 20.0000 1.91565 0.957826 0.287348i \(-0.0927736\pi\)
0.957826 + 0.287348i \(0.0927736\pi\)
\(110\) 0 0
\(111\) 11.0000 1.04407
\(112\) −3.23607 2.35114i −0.305780 0.222162i
\(113\) −0.927051 + 2.85317i −0.0872096 + 0.268404i −0.985145 0.171723i \(-0.945067\pi\)
0.897936 + 0.440127i \(0.145067\pi\)
\(114\) 0 0
\(115\) −7.28115 + 5.29007i −0.678971 + 0.493301i
\(116\) −9.70820 + 7.05342i −0.901384 + 0.654894i
\(117\) 2.47214 + 7.60845i 0.228549 + 0.703402i
\(118\) 0 0
\(119\) 4.85410 + 3.52671i 0.444975 + 0.323293i
\(120\) 0 0
\(121\) 0 0
\(122\) 0 0
\(123\) −4.85410 3.52671i −0.437680 0.317993i
\(124\) −3.09017 + 9.51057i −0.277505 + 0.854074i
\(125\) −0.927051 2.85317i −0.0829180 0.255195i
\(126\) 0 0
\(127\) −1.61803 + 1.17557i −0.143577 + 0.104315i −0.657255 0.753668i \(-0.728283\pi\)
0.513678 + 0.857983i \(0.328283\pi\)
\(128\) 0 0
\(129\) 2.47214 7.60845i 0.217659 0.669887i
\(130\) 0 0
\(131\) −6.00000 −0.524222 −0.262111 0.965038i \(-0.584419\pi\)
−0.262111 + 0.965038i \(0.584419\pi\)
\(132\) 0 0
\(133\) 2.00000 0.173422
\(134\) 0 0
\(135\) −4.63525 + 14.2658i −0.398939 + 1.22781i
\(136\) 0 0
\(137\) 2.42705 1.76336i 0.207357 0.150654i −0.479260 0.877673i \(-0.659095\pi\)
0.686617 + 0.727019i \(0.259095\pi\)
\(138\) 0 0
\(139\) 4.32624 + 13.3148i 0.366947 + 1.12935i 0.948753 + 0.316018i \(0.102346\pi\)
−0.581806 + 0.813327i \(0.697654\pi\)
\(140\) −1.85410 + 5.70634i −0.156700 + 0.482274i
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) −8.00000 −0.666667
\(145\) 14.5623 + 10.5801i 1.20933 + 0.878632i
\(146\) 0 0
\(147\) 0.309017 + 0.951057i 0.0254873 + 0.0784418i
\(148\) 17.7984 12.9313i 1.46302 1.06294i
\(149\) 4.85410 3.52671i 0.397664 0.288919i −0.370925 0.928663i \(-0.620959\pi\)
0.768589 + 0.639743i \(0.220959\pi\)
\(150\) 0 0
\(151\) −3.09017 + 9.51057i −0.251474 + 0.773959i 0.743029 + 0.669259i \(0.233388\pi\)
−0.994504 + 0.104700i \(0.966612\pi\)
\(152\) 0 0
\(153\) 12.0000 0.970143
\(154\) 0 0
\(155\) 15.0000 1.20483
\(156\) −6.47214 4.70228i −0.518186 0.376484i
\(157\) −4.01722 + 12.3637i −0.320609 + 0.986733i 0.652775 + 0.757552i \(0.273605\pi\)
−0.973384 + 0.229181i \(0.926395\pi\)
\(158\) 0 0
\(159\) 4.85410 3.52671i 0.384955 0.279686i
\(160\) 0 0
\(161\) 0.927051 + 2.85317i 0.0730619 + 0.224861i
\(162\) 0 0
\(163\) −16.1803 11.7557i −1.26734 0.920778i −0.268249 0.963350i \(-0.586445\pi\)
−0.999093 + 0.0425718i \(0.986445\pi\)
\(164\) −12.0000 −0.937043
\(165\) 0 0
\(166\) 0 0
\(167\) −4.85410 3.52671i −0.375622 0.272905i 0.383917 0.923368i \(-0.374575\pi\)
−0.759538 + 0.650463i \(0.774575\pi\)
\(168\) 0 0
\(169\) 0.927051 + 2.85317i 0.0713116 + 0.219475i
\(170\) 0 0
\(171\) 3.23607 2.35114i 0.247468 0.179796i
\(172\) −4.94427 15.2169i −0.376997 1.16028i
\(173\) 0 0 −0.951057 0.309017i \(-0.900000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(174\) 0 0
\(175\) 4.00000 0.302372
\(176\) 0 0
\(177\) −9.00000 −0.676481
\(178\) 0 0
\(179\) −4.63525 + 14.2658i −0.346455 + 1.06628i 0.614345 + 0.789038i \(0.289420\pi\)
−0.960800 + 0.277242i \(0.910580\pi\)
\(180\) 3.70820 + 11.4127i 0.276393 + 0.850651i
\(181\) 5.66312 4.11450i 0.420936 0.305828i −0.357078 0.934075i \(-0.616227\pi\)
0.778014 + 0.628246i \(0.216227\pi\)
\(182\) 0 0
\(183\) −3.09017 9.51057i −0.228432 0.703041i
\(184\) 0 0
\(185\) −26.6976 19.3969i −1.96284 1.42609i
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 4.04508 + 2.93893i 0.294237 + 0.213775i
\(190\) 0 0
\(191\) −8.34346 25.6785i −0.603711 1.85803i −0.505416 0.862876i \(-0.668661\pi\)
−0.0982952 0.995157i \(-0.531339\pi\)
\(192\) 6.47214 4.70228i 0.467086 0.339358i
\(193\) −11.3262 + 8.22899i −0.815280 + 0.592336i −0.915357 0.402644i \(-0.868091\pi\)
0.100076 + 0.994980i \(0.468091\pi\)
\(194\) 0 0
\(195\) −3.70820 + 11.4127i −0.265550 + 0.817279i
\(196\) 1.61803 + 1.17557i 0.115574 + 0.0839693i
\(197\) 18.0000 1.28245 0.641223 0.767354i \(-0.278427\pi\)
0.641223 + 0.767354i \(0.278427\pi\)
\(198\) 0 0
\(199\) −16.0000 −1.13421 −0.567105 0.823646i \(-0.691937\pi\)
−0.567105 + 0.823646i \(0.691937\pi\)
\(200\) 0 0
\(201\) 1.54508 4.75528i 0.108982 0.335412i
\(202\) 0 0
\(203\) 4.85410 3.52671i 0.340691 0.247527i
\(204\) −9.70820 + 7.05342i −0.679710 + 0.493838i
\(205\) 5.56231 + 17.1190i 0.388488 + 1.19564i
\(206\) 0 0
\(207\) 4.85410 + 3.52671i 0.337383 + 0.245123i
\(208\) −16.0000 −1.10940
\(209\) 0 0
\(210\) 0 0
\(211\) −11.3262 8.22899i −0.779730 0.566507i 0.125168 0.992136i \(-0.460053\pi\)
−0.904898 + 0.425628i \(0.860053\pi\)
\(212\) 3.70820 11.4127i 0.254680 0.783826i
\(213\) 2.78115 + 8.55951i 0.190561 + 0.586488i
\(214\) 0 0
\(215\) −19.4164 + 14.1068i −1.32419 + 0.962079i
\(216\) 0 0
\(217\) 1.54508 4.75528i 0.104887 0.322810i
\(218\) 0 0
\(219\) 2.00000 0.135147
\(220\) 0 0
\(221\) 24.0000 1.61441
\(222\) 0 0
\(223\) −5.87132 + 18.0701i −0.393173 + 1.21006i 0.537203 + 0.843453i \(0.319481\pi\)
−0.930375 + 0.366608i \(0.880519\pi\)
\(224\) 0 0
\(225\) 6.47214 4.70228i 0.431476 0.313485i
\(226\) 0 0
\(227\) −3.70820 11.4127i −0.246122 0.757486i −0.995450 0.0952867i \(-0.969623\pi\)
0.749328 0.662199i \(-0.230377\pi\)
\(228\) −1.23607 + 3.80423i −0.0818606 + 0.251941i
\(229\) −4.04508 2.93893i −0.267307 0.194210i 0.446055 0.895005i \(-0.352828\pi\)
−0.713362 + 0.700796i \(0.752828\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −4.85410 3.52671i −0.318003 0.231043i 0.417320 0.908760i \(-0.362969\pi\)
−0.735323 + 0.677717i \(0.762969\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) −14.5623 + 10.5801i −0.947925 + 0.688708i
\(237\) 8.09017 5.87785i 0.525513 0.381808i
\(238\) 0 0
\(239\) −3.70820 + 11.4127i −0.239864 + 0.738225i 0.756575 + 0.653907i \(0.226871\pi\)
−0.996439 + 0.0843180i \(0.973129\pi\)
\(240\) −9.70820 7.05342i −0.626662 0.455296i
\(241\) −28.0000 −1.80364 −0.901819 0.432113i \(-0.857768\pi\)
−0.901819 + 0.432113i \(0.857768\pi\)
\(242\) 0 0
\(243\) 16.0000 1.02640
\(244\) −16.1803 11.7557i −1.03584 0.752582i
\(245\) 0.927051 2.85317i 0.0592271 0.182282i
\(246\) 0 0
\(247\) 6.47214 4.70228i 0.411812 0.299199i
\(248\) 0 0
\(249\) 3.70820 + 11.4127i 0.234998 + 0.723249i
\(250\) 0 0
\(251\) 7.28115 + 5.29007i 0.459582 + 0.333906i 0.793367 0.608743i \(-0.208326\pi\)
−0.333785 + 0.942649i \(0.608326\pi\)
\(252\) 4.00000 0.251976
\(253\) 0 0
\(254\) 0 0
\(255\) 14.5623 + 10.5801i 0.911927 + 0.662554i
\(256\) 4.94427 15.2169i 0.309017 0.951057i
\(257\) −1.85410 5.70634i −0.115656 0.355952i 0.876428 0.481534i \(-0.159920\pi\)
−0.992083 + 0.125582i \(0.959920\pi\)
\(258\) 0 0
\(259\) −8.89919 + 6.46564i −0.552969 + 0.401755i
\(260\) 7.41641 + 22.8254i 0.459946 + 1.41557i
\(261\) 3.70820 11.4127i 0.229532 0.706427i
\(262\) 0 0
\(263\) −30.0000 −1.84988 −0.924940 0.380114i \(-0.875885\pi\)
−0.924940 + 0.380114i \(0.875885\pi\)
\(264\) 0 0
\(265\) −18.0000 −1.10573
\(266\) 0 0
\(267\) −0.927051 + 2.85317i −0.0567346 + 0.174611i
\(268\) −3.09017 9.51057i −0.188762 0.580950i
\(269\) −24.2705 + 17.6336i −1.47980 + 1.07514i −0.502178 + 0.864764i \(0.667468\pi\)
−0.977621 + 0.210373i \(0.932532\pi\)
\(270\) 0 0
\(271\) −4.94427 15.2169i −0.300343 0.924361i −0.981374 0.192106i \(-0.938468\pi\)
0.681031 0.732255i \(-0.261532\pi\)
\(272\) −7.41641 + 22.8254i −0.449686 + 1.38399i
\(273\) 3.23607 + 2.35114i 0.195856 + 0.142298i
\(274\) 0 0
\(275\) 0 0
\(276\) −6.00000 −0.361158
\(277\) −6.47214 4.70228i −0.388873 0.282533i 0.376121 0.926571i \(-0.377258\pi\)
−0.764994 + 0.644038i \(0.777258\pi\)
\(278\) 0 0
\(279\) −3.09017 9.51057i −0.185004 0.569383i
\(280\) 0 0
\(281\) −9.70820 + 7.05342i −0.579143 + 0.420772i −0.838415 0.545032i \(-0.816517\pi\)
0.259272 + 0.965804i \(0.416517\pi\)
\(282\) 0 0
\(283\) 9.88854 30.4338i 0.587813 1.80910i 0.000144882 1.00000i \(-0.499954\pi\)
0.587668 0.809102i \(-0.300046\pi\)
\(284\) 14.5623 + 10.5801i 0.864114 + 0.627815i
\(285\) 6.00000 0.355409
\(286\) 0 0
\(287\) 6.00000 0.354169
\(288\) 0 0
\(289\) 5.87132 18.0701i 0.345372 1.06295i
\(290\) 0 0
\(291\) 0.809017 0.587785i 0.0474254 0.0344566i
\(292\) 3.23607 2.35114i 0.189377 0.137590i
\(293\) −9.27051 28.5317i −0.541589 1.66684i −0.728965 0.684551i \(-0.759998\pi\)
0.187376 0.982288i \(-0.440002\pi\)
\(294\) 0 0
\(295\) 21.8435 + 15.8702i 1.27178 + 0.923999i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 9.70820 + 7.05342i 0.561440 + 0.407910i
\(300\) −2.47214 + 7.60845i −0.142729 + 0.439274i
\(301\) 2.47214 + 7.60845i 0.142492 + 0.438544i
\(302\) 0 0
\(303\) 9.70820 7.05342i 0.557722 0.405209i
\(304\) 2.47214 + 7.60845i 0.141787 + 0.436375i
\(305\) −9.27051 + 28.5317i −0.530828 + 1.63372i
\(306\) 0 0
\(307\) 20.0000 1.14146 0.570730 0.821138i \(-0.306660\pi\)
0.570730 + 0.821138i \(0.306660\pi\)
\(308\) 0 0
\(309\) −4.00000 −0.227552
\(310\) 0 0
\(311\) 0 0 −0.951057 0.309017i \(-0.900000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(312\) 0 0
\(313\) 15.3713 11.1679i 0.868839 0.631248i −0.0614365 0.998111i \(-0.519568\pi\)
0.930275 + 0.366863i \(0.119568\pi\)
\(314\) 0 0
\(315\) −1.85410 5.70634i −0.104467 0.321516i
\(316\) 6.18034 19.0211i 0.347671 1.07002i
\(317\) −7.28115 5.29007i −0.408950 0.297120i 0.364226 0.931310i \(-0.381333\pi\)
−0.773177 + 0.634191i \(0.781333\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) −24.0000 −1.34164
\(321\) −4.85410 3.52671i −0.270930 0.196842i
\(322\) 0 0
\(323\) −3.70820 11.4127i −0.206330 0.635018i
\(324\) 1.61803 1.17557i 0.0898908 0.0653095i
\(325\) 12.9443 9.40456i 0.718019 0.521671i
\(326\) 0 0
\(327\) 6.18034 19.0211i 0.341774 1.05187i
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −1.00000 −0.0549650 −0.0274825 0.999622i \(-0.508749\pi\)
−0.0274825 + 0.999622i \(0.508749\pi\)
\(332\) 19.4164 + 14.1068i 1.06561 + 0.774214i
\(333\) −6.79837 + 20.9232i −0.372549 + 1.14659i
\(334\) 0 0
\(335\) −12.1353 + 8.81678i −0.663020 + 0.481712i
\(336\) −3.23607 + 2.35114i −0.176542 + 0.128265i
\(337\) 4.32624 + 13.3148i 0.235665 + 0.725303i 0.997032 + 0.0769821i \(0.0245284\pi\)
−0.761367 + 0.648321i \(0.775472\pi\)
\(338\) 0 0
\(339\) 2.42705 + 1.76336i 0.131819 + 0.0957723i
\(340\) 36.0000 1.95237
\(341\) 0 0
\(342\) 0 0
\(343\) −0.809017 0.587785i −0.0436828 0.0317374i
\(344\) 0 0
\(345\) 2.78115 + 8.55951i 0.149732 + 0.460828i
\(346\) 0 0
\(347\) 14.5623 10.5801i 0.781746 0.567971i −0.123757 0.992313i \(-0.539494\pi\)
0.905502 + 0.424341i \(0.139494\pi\)
\(348\) 3.70820 + 11.4127i 0.198781 + 0.611784i
\(349\) −3.09017 + 9.51057i −0.165413 + 0.509089i −0.999066 0.0431990i \(-0.986245\pi\)
0.833653 + 0.552288i \(0.186245\pi\)
\(350\) 0 0
\(351\) 20.0000 1.06752
\(352\) 0 0
\(353\) −3.00000 −0.159674 −0.0798369 0.996808i \(-0.525440\pi\)
−0.0798369 + 0.996808i \(0.525440\pi\)
\(354\) 0 0
\(355\) 8.34346 25.6785i 0.442825 1.36287i
\(356\) 1.85410 + 5.70634i 0.0982672 + 0.302435i
\(357\) 4.85410 3.52671i 0.256906 0.186653i
\(358\) 0 0
\(359\) 7.41641 + 22.8254i 0.391423 + 1.20468i 0.931712 + 0.363197i \(0.118315\pi\)
−0.540289 + 0.841479i \(0.681685\pi\)
\(360\) 0 0
\(361\) 12.1353 + 8.81678i 0.638698 + 0.464041i
\(362\) 0 0
\(363\) 0 0
\(364\) 8.00000 0.419314
\(365\) −4.85410 3.52671i −0.254075 0.184597i
\(366\) 0 0
\(367\) 5.25329 + 16.1680i 0.274219 + 0.843961i 0.989425 + 0.145046i \(0.0463331\pi\)
−0.715205 + 0.698914i \(0.753667\pi\)
\(368\) −9.70820 + 7.05342i −0.506075 + 0.367685i
\(369\) 9.70820 7.05342i 0.505389 0.367187i
\(370\) 0 0
\(371\) −1.85410 + 5.70634i −0.0962602 + 0.296258i
\(372\) 8.09017 + 5.87785i 0.419456 + 0.304752i
\(373\) −4.00000 −0.207112 −0.103556 0.994624i \(-0.533022\pi\)
−0.103556 + 0.994624i \(0.533022\pi\)
\(374\) 0 0
\(375\) −3.00000 −0.154919
\(376\) 0 0
\(377\) 7.41641 22.8254i 0.381964 1.17557i
\(378\) 0 0
\(379\) −8.89919 + 6.46564i −0.457121 + 0.332118i −0.792401 0.610001i \(-0.791169\pi\)
0.335280 + 0.942118i \(0.391169\pi\)
\(380\) 9.70820 7.05342i 0.498020 0.361833i
\(381\) 0.618034 + 1.90211i 0.0316628 + 0.0974482i
\(382\) 0 0
\(383\) −16.9894 12.3435i −0.868116 0.630723i 0.0619651 0.998078i \(-0.480263\pi\)
−0.930081 + 0.367355i \(0.880263\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 12.9443 + 9.40456i 0.657994 + 0.478061i
\(388\) 0.618034 1.90211i 0.0313759 0.0965652i
\(389\) 10.1976 + 31.3849i 0.517037 + 1.59128i 0.779545 + 0.626346i \(0.215450\pi\)
−0.262508 + 0.964930i \(0.584550\pi\)
\(390\) 0 0
\(391\) 14.5623 10.5801i 0.736447 0.535060i
\(392\) 0 0
\(393\) −1.85410 + 5.70634i −0.0935271 + 0.287847i
\(394\) 0 0
\(395\) −30.0000 −1.50946
\(396\) 0 0
\(397\) 2.00000 0.100377 0.0501886 0.998740i \(-0.484018\pi\)
0.0501886 + 0.998740i \(0.484018\pi\)
\(398\) 0 0
\(399\) 0.618034 1.90211i 0.0309404 0.0952248i
\(400\) 4.94427 + 15.2169i 0.247214 + 0.760845i
\(401\) 4.85410 3.52671i 0.242402 0.176116i −0.459951 0.887945i \(-0.652133\pi\)
0.702353 + 0.711829i \(0.252133\pi\)
\(402\) 0 0
\(403\) −6.18034 19.0211i −0.307865 0.947510i
\(404\) 7.41641 22.8254i 0.368980 1.13560i
\(405\) −2.42705 1.76336i −0.120601 0.0876219i
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) −11.3262 8.22899i −0.560046 0.406898i 0.271430 0.962458i \(-0.412504\pi\)
−0.831476 + 0.555561i \(0.812504\pi\)
\(410\) 0 0
\(411\) −0.927051 2.85317i −0.0457281 0.140736i
\(412\) −6.47214 + 4.70228i −0.318859 + 0.231665i
\(413\) 7.28115 5.29007i 0.358282 0.260307i
\(414\) 0 0
\(415\) 11.1246 34.2380i 0.546086 1.68068i
\(416\) 0 0
\(417\) 14.0000 0.685583
\(418\) 0 0
\(419\) 24.0000 1.17248 0.586238 0.810139i \(-0.300608\pi\)
0.586238 + 0.810139i \(0.300608\pi\)
\(420\) 4.85410 + 3.52671i 0.236856 + 0.172086i
\(421\) −3.09017 + 9.51057i −0.150606 + 0.463517i −0.997689 0.0679432i \(-0.978356\pi\)
0.847084 + 0.531460i \(0.178356\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −7.41641 22.8254i −0.359749 1.10719i
\(426\) 0 0
\(427\) 8.09017 + 5.87785i 0.391511 + 0.284449i
\(428\) −12.0000 −0.580042
\(429\) 0 0
\(430\) 0 0
\(431\) −9.70820 7.05342i −0.467628 0.339751i 0.328888 0.944369i \(-0.393326\pi\)
−0.796516 + 0.604617i \(0.793326\pi\)
\(432\) −6.18034 + 19.0211i −0.297352 + 0.915155i
\(433\) 3.39919 + 10.4616i 0.163354 + 0.502753i 0.998911 0.0466507i \(-0.0148548\pi\)
−0.835557 + 0.549404i \(0.814855\pi\)
\(434\) 0 0
\(435\) 14.5623 10.5801i 0.698209 0.507279i
\(436\) −12.3607 38.0423i −0.591969 1.82189i
\(437\) 1.85410 5.70634i 0.0886937 0.272971i
\(438\) 0 0
\(439\) 26.0000 1.24091 0.620456 0.784241i \(-0.286947\pi\)
0.620456 + 0.784241i \(0.286947\pi\)
\(440\) 0 0
\(441\) −2.00000 −0.0952381
\(442\) 0 0
\(443\) 2.78115 8.55951i 0.132137 0.406675i −0.862997 0.505209i \(-0.831415\pi\)
0.995134 + 0.0985344i \(0.0314154\pi\)
\(444\) −6.79837 20.9232i −0.322637 0.992973i
\(445\) 7.28115 5.29007i 0.345160 0.250773i
\(446\) 0 0
\(447\) −1.85410 5.70634i −0.0876960 0.269901i
\(448\) −2.47214 + 7.60845i −0.116797 + 0.359466i
\(449\) 7.28115 + 5.29007i 0.343619 + 0.249654i 0.746187 0.665736i \(-0.231882\pi\)
−0.402568 + 0.915390i \(0.631882\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 6.00000 0.282216
\(453\) 8.09017 + 5.87785i 0.380109 + 0.276166i
\(454\) 0 0
\(455\) −3.70820 11.4127i −0.173843 0.535035i
\(456\) 0 0
\(457\) −6.47214 + 4.70228i −0.302754 + 0.219963i −0.728781 0.684747i \(-0.759913\pi\)
0.426027 + 0.904710i \(0.359913\pi\)
\(458\) 0 0
\(459\) 9.27051 28.5317i 0.432710 1.33175i
\(460\) 14.5623 + 10.5801i 0.678971 + 0.493301i
\(461\) −6.00000 −0.279448 −0.139724 0.990190i \(-0.544622\pi\)
−0.139724 + 0.990190i \(0.544622\pi\)
\(462\) 0 0
\(463\) 5.00000 0.232370 0.116185 0.993228i \(-0.462933\pi\)
0.116185 + 0.993228i \(0.462933\pi\)
\(464\) 19.4164 + 14.1068i 0.901384 + 0.654894i
\(465\) 4.63525 14.2658i 0.214955 0.661563i
\(466\) 0 0
\(467\) −12.1353 + 8.81678i −0.561553 + 0.407992i −0.832027 0.554735i \(-0.812820\pi\)
0.270474 + 0.962727i \(0.412820\pi\)
\(468\) 12.9443 9.40456i 0.598349 0.434726i
\(469\) 1.54508 + 4.75528i 0.0713454 + 0.219579i
\(470\) 0 0
\(471\) 10.5172 + 7.64121i 0.484608 + 0.352088i
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) −6.47214 4.70228i −0.296962 0.215755i
\(476\) 3.70820 11.4127i 0.169965 0.523099i
\(477\) 3.70820 + 11.4127i 0.169787 + 0.522551i
\(478\) 0 0
\(479\) 9.70820 7.05342i 0.443579 0.322279i −0.343476 0.939161i \(-0.611605\pi\)
0.787055 + 0.616882i \(0.211605\pi\)
\(480\) 0 0
\(481\) −13.5967 + 41.8465i −0.619958 + 1.90804i
\(482\) 0 0
\(483\) 3.00000 0.136505
\(484\) 0 0
\(485\) −3.00000 −0.136223
\(486\) 0 0
\(487\) 3.39919 10.4616i 0.154032 0.474061i −0.844030 0.536297i \(-0.819823\pi\)
0.998062 + 0.0622352i \(0.0198229\pi\)
\(488\) 0 0
\(489\) −16.1803 + 11.7557i −0.731700 + 0.531611i
\(490\) 0 0
\(491\) −9.27051 28.5317i −0.418372 1.28762i −0.909200 0.416361i \(-0.863305\pi\)
0.490827 0.871257i \(-0.336695\pi\)
\(492\) −3.70820 + 11.4127i −0.167179 + 0.514523i
\(493\) −29.1246 21.1603i −1.31171 0.953011i
\(494\) 0 0
\(495\) 0 0
\(496\) 20.0000 0.898027
\(497\) −7.28115 5.29007i −0.326604 0.237292i
\(498\) 0 0
\(499\) −1.23607 3.80423i −0.0553340 0.170301i 0.919570 0.392926i \(-0.128537\pi\)
−0.974904 + 0.222626i \(0.928537\pi\)
\(500\) −4.85410 + 3.52671i −0.217082 + 0.157719i
\(501\) −4.85410 + 3.52671i −0.216865 + 0.157562i
\(502\) 0 0
\(503\) 0 0 −0.951057 0.309017i \(-0.900000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(504\) 0 0
\(505\) −36.0000 −1.60198
\(506\) 0 0
\(507\) 3.00000 0.133235
\(508\) 3.23607 + 2.35114i 0.143577 + 0.104315i
\(509\) 6.48936 19.9722i 0.287636 0.885252i −0.697961 0.716136i \(-0.745909\pi\)
0.985596 0.169115i \(-0.0540911\pi\)
\(510\) 0 0
\(511\) −1.61803 + 1.17557i −0.0715776 + 0.0520042i
\(512\) 0 0
\(513\) −3.09017 9.51057i −0.136434 0.419902i
\(514\) 0 0
\(515\) 9.70820 + 7.05342i 0.427795 + 0.310811i
\(516\) −16.0000 −0.704361
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 0.927051 + 2.85317i 0.0406148 + 0.125000i 0.969308 0.245849i \(-0.0790668\pi\)
−0.928693 + 0.370849i \(0.879067\pi\)
\(522\) 0 0
\(523\) 12.9443 9.40456i 0.566013 0.411233i −0.267641 0.963519i \(-0.586244\pi\)
0.833655 + 0.552286i \(0.186244\pi\)
\(524\) 3.70820 + 11.4127i 0.161994 + 0.498565i
\(525\) 1.23607 3.80423i 0.0539464 0.166030i
\(526\) 0 0
\(527\) −30.0000 −1.30682
\(528\) 0 0
\(529\) −14.0000 −0.608696
\(530\) 0 0
\(531\) 5.56231 17.1190i 0.241384 0.742902i
\(532\) −1.23607 3.80423i −0.0535903 0.164934i
\(533\) 19.4164 14.1068i 0.841018 0.611035i
\(534\) 0 0
\(535\) 5.56231 + 17.1190i 0.240479 + 0.740120i
\(536\) 0 0
\(537\) 12.1353 + 8.81678i 0.523675 + 0.380472i
\(538\) 0 0
\(539\) 0 0
\(540\) 30.0000 1.29099
\(541\) 12.9443 + 9.40456i 0.556518 + 0.404334i 0.830183 0.557491i \(-0.188236\pi\)
−0.273665 + 0.961825i \(0.588236\pi\)
\(542\) 0 0
\(543\) −2.16312 6.65740i −0.0928283 0.285696i
\(544\) 0 0
\(545\) −48.5410 + 35.2671i −2.07927 + 1.51068i
\(546\) 0 0
\(547\) 2.47214 7.60845i 0.105701 0.325314i −0.884193 0.467121i \(-0.845291\pi\)
0.989894 + 0.141807i \(0.0452913\pi\)
\(548\) −4.85410 3.52671i −0.207357 0.150654i
\(549\) 20.0000 0.853579
\(550\) 0 0
\(551\) −12.0000 −0.511217
\(552\) 0 0
\(553\) −3.09017 + 9.51057i −0.131407 + 0.404430i
\(554\) 0 0
\(555\) −26.6976 + 19.3969i −1.13325 + 0.823353i
\(556\) 22.6525 16.4580i 0.960679 0.697974i
\(557\) 9.27051 + 28.5317i 0.392804 + 1.20893i 0.930659 + 0.365889i \(0.119235\pi\)
−0.537854 + 0.843038i \(0.680765\pi\)
\(558\) 0 0
\(559\) 25.8885 + 18.8091i 1.09497 + 0.795541i
\(560\) 12.0000 0.507093
\(561\) 0 0
\(562\) 0 0
\(563\) −29.1246 21.1603i −1.22746 0.891799i −0.230759 0.973011i \(-0.574121\pi\)
−0.996697 + 0.0812119i \(0.974121\pi\)
\(564\) 0 0
\(565\) −2.78115 8.55951i −0.117004 0.360101i
\(566\) 0 0
\(567\) −0.809017 + 0.587785i −0.0339755 + 0.0246847i
\(568\) 0 0
\(569\) −5.56231 + 17.1190i −0.233184 + 0.717667i 0.764173 + 0.645011i \(0.223147\pi\)
−0.997357 + 0.0726553i \(0.976853\pi\)
\(570\) 0 0
\(571\) −4.00000 −0.167395 −0.0836974 0.996491i \(-0.526673\pi\)
−0.0836974 + 0.996491i \(0.526673\pi\)
\(572\) 0 0
\(573\) −27.0000 −1.12794
\(574\) 0 0
\(575\) 3.70820 11.4127i 0.154643 0.475942i
\(576\) 4.94427 + 15.2169i 0.206011 + 0.634038i
\(577\) −8.89919 + 6.46564i −0.370478 + 0.269168i −0.757409 0.652941i \(-0.773535\pi\)
0.386931 + 0.922109i \(0.373535\pi\)
\(578\) 0 0
\(579\) 4.32624 + 13.3148i 0.179792 + 0.553344i
\(580\) 11.1246 34.2380i 0.461924 1.42166i
\(581\) −9.70820 7.05342i −0.402764 0.292625i
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) −19.4164 14.1068i −0.802770 0.583246i
\(586\) 0 0
\(587\) 3.70820 + 11.4127i 0.153054 + 0.471052i 0.997959 0.0638654i \(-0.0203428\pi\)
−0.844905 + 0.534917i \(0.820343\pi\)
\(588\) 1.61803 1.17557i 0.0667266 0.0484797i
\(589\) −8.09017 + 5.87785i −0.333350 + 0.242193i
\(590\) 0 0
\(591\) 5.56231 17.1190i 0.228803 0.704182i
\(592\) −35.5967 25.8626i −1.46302 1.06294i
\(593\) 6.00000 0.246390 0.123195 0.992382i \(-0.460686\pi\)
0.123195 + 0.992382i \(0.460686\pi\)
\(594\) 0 0
\(595\) −18.0000 −0.737928
\(596\) −9.70820 7.05342i −0.397664 0.288919i
\(597\) −4.94427 + 15.2169i −0.202356 + 0.622786i
\(598\) 0 0
\(599\) 0 0 −0.587785 0.809017i \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(600\) 0 0
\(601\) 2.47214 + 7.60845i 0.100841 + 0.310355i 0.988732 0.149698i \(-0.0478302\pi\)
−0.887891 + 0.460053i \(0.847830\pi\)
\(602\) 0 0
\(603\) 8.09017 + 5.87785i 0.329457 + 0.239365i
\(604\) 20.0000 0.813788
\(605\) 0 0
\(606\) 0 0
\(607\) −11.3262 8.22899i −0.459718 0.334005i 0.333703 0.942678i \(-0.391702\pi\)
−0.793421 + 0.608674i \(0.791702\pi\)
\(608\) 0 0
\(609\) −1.85410 5.70634i −0.0751320 0.231233i
\(610\) 0 0
\(611\) 0 0
\(612\) −7.41641 22.8254i −0.299791 0.922660i
\(613\) −4.94427 + 15.2169i −0.199697 + 0.614605i 0.800192 + 0.599744i \(0.204731\pi\)
−0.999890 + 0.0148615i \(0.995269\pi\)
\(614\) 0 0
\(615\) 18.0000 0.725830
\(616\) 0 0
\(617\) −30.0000 −1.20775 −0.603877 0.797077i \(-0.706378\pi\)
−0.603877 + 0.797077i \(0.706378\pi\)
\(618\) 0 0
\(619\) −5.87132 + 18.0701i −0.235988 + 0.726298i 0.761000 + 0.648751i \(0.224709\pi\)
−0.996989 + 0.0775461i \(0.975291\pi\)
\(620\) −9.27051 28.5317i −0.372313 1.14586i
\(621\) 12.1353 8.81678i 0.486971 0.353805i
\(622\) 0 0
\(623\) −0.927051 2.85317i −0.0371415 0.114310i
\(624\) −4.94427 + 15.2169i −0.197929 + 0.609164i
\(625\) 23.4615 + 17.0458i 0.938460 + 0.681831i
\(626\) 0 0
\(627\) 0 0
\(628\) 26.0000 1.03751
\(629\) 53.3951 + 38.7938i 2.12900 + 1.54681i
\(630\) 0 0
\(631\) 3.39919 + 10.4616i 0.135319 + 0.416471i 0.995640 0.0932836i \(-0.0297363\pi\)
−0.860320 + 0.509754i \(0.829736\pi\)
\(632\) 0 0
\(633\) −11.3262 + 8.22899i −0.450178 + 0.327073i
\(634\) 0 0
\(635\) 1.85410 5.70634i 0.0735778 0.226449i
\(636\) −9.70820 7.05342i −0.384955 0.279686i
\(637\) −4.00000 −0.158486
\(638\) 0 0
\(639\) −18.0000 −0.712069
\(640\) 0 0
\(641\) 4.63525 14.2658i 0.183082 0.563467i −0.816828 0.576881i \(-0.804270\pi\)
0.999910 + 0.0134135i \(0.00426978\pi\)
\(642\) 0 0
\(643\) 39.6418 28.8015i 1.56332 1.13582i 0.630102 0.776513i \(-0.283013\pi\)
0.933219 0.359307i \(-0.116987\pi\)
\(644\) 4.85410 3.52671i 0.191278 0.138972i
\(645\) 7.41641 + 22.8254i 0.292021 + 0.898748i
\(646\) 0 0
\(647\) 26.6976 + 19.3969i 1.04959 + 0.762571i 0.972134 0.234424i \(-0.0753206\pi\)
0.0774551 + 0.996996i \(0.475321\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) −4.04508 2.93893i −0.158539 0.115186i
\(652\) −12.3607 + 38.0423i −0.484082 + 1.48985i
\(653\) 12.0517 + 37.0912i 0.471618 + 1.45149i 0.850465 + 0.526032i \(0.176321\pi\)
−0.378847 + 0.925459i \(0.623679\pi\)
\(654\) 0 0
\(655\) 14.5623 10.5801i 0.568996 0.413400i
\(656\) 7.41641 + 22.8254i 0.289562 + 0.891180i
\(657\) −1.23607 + 3.80423i −0.0482236 + 0.148417i
\(658\) 0 0
\(659\) 30.0000 1.16863 0.584317 0.811525i \(-0.301362\pi\)
0.584317 + 0.811525i \(0.301362\pi\)
\(660\) 0 0
\(661\) −49.0000 −1.90588 −0.952940 0.303160i \(-0.901958\pi\)
−0.952940 + 0.303160i \(0.901958\pi\)
\(662\) 0 0
\(663\) 7.41641 22.8254i 0.288029 0.886463i
\(664\) 0 0
\(665\) −4.85410 + 3.52671i −0.188234 + 0.136760i
\(666\) 0 0
\(667\) −5.56231 17.1190i −0.215373 0.662851i
\(668\) −3.70820 + 11.4127i −0.143475 + 0.441570i
\(669\) 15.3713 + 11.1679i 0.594290 + 0.431777i
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 22.6525 + 16.4580i 0.873189 + 0.634409i 0.931441 0.363893i \(-0.118553\pi\)
−0.0582519 + 0.998302i \(0.518553\pi\)
\(674\) 0 0
\(675\) −6.18034 19.0211i −0.237881 0.732124i
\(676\) 4.85410 3.52671i 0.186696 0.135643i
\(677\) 14.5623 10.5801i 0.559675 0.406628i −0.271665 0.962392i \(-0.587574\pi\)
0.831340 + 0.555764i \(0.187574\pi\)
\(678\) 0 0
\(679\) −0.309017 + 0.951057i −0.0118590 + 0.0364982i
\(680\) 0 0
\(681\) −12.0000 −0.459841
\(682\) 0 0
\(683\) 12.0000 0.459167 0.229584 0.973289i \(-0.426264\pi\)
0.229584 + 0.973289i \(0.426264\pi\)
\(684\) −6.47214 4.70228i −0.247468 0.179796i
\(685\) −2.78115 + 8.55951i −0.106262 + 0.327042i
\(686\) 0 0
\(687\) −4.04508 + 2.93893i −0.154330 + 0.112127i
\(688\) −25.8885 + 18.8091i −0.986991 + 0.717091i
\(689\) 7.41641 + 22.8254i 0.282543 + 0.869577i
\(690\) 0 0
\(691\) −28.3156 20.5725i −1.07718 0.782614i −0.0999876 0.994989i \(-0.531880\pi\)
−0.977188 + 0.212375i \(0.931880\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −33.9787 24.6870i −1.28889 0.936431i
\(696\) 0 0
\(697\) −11.1246 34.2380i −0.421375 1.29686i
\(698\) 0 0
\(699\) −4.85410 + 3.52671i −0.183599 + 0.133392i
\(700\) −2.47214 7.60845i −0.0934380 0.287572i
\(701\) 0 0 −0.951057 0.309017i \(-0.900000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(702\) 0 0
\(703\) 22.0000 0.829746
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −3.70820 + 11.4127i −0.139461 + 0.429218i
\(708\) 5.56231 + 17.1190i 0.209044 + 0.643372i
\(709\) 0.809017 0.587785i 0.0303833 0.0220747i −0.572490 0.819912i \(-0.694022\pi\)
0.602873 + 0.797837i \(0.294022\pi\)
\(710\) 0 0
\(711\) 6.18034 + 19.0211i 0.231781 + 0.713348i
\(712\) 0 0
\(713\) −12.1353 8.81678i −0.454469 0.330191i
\(714\) 0 0
\(715\) 0 0
\(716\) 30.0000 1.12115
\(717\) 9.70820 + 7.05342i 0.362560 + 0.263415i
\(718\) 0 0
\(719\) −12.0517 37.0912i −0.449451 1.38327i −0.877528 0.479526i \(-0.840809\pi\)
0.428076 0.903743i \(-0.359191\pi\)
\(720\) 19.4164 14.1068i 0.723607 0.525731i
\(721\) 3.23607 2.35114i 0.120517 0.0875611i
\(722\) 0 0
\(723\) −8.65248 + 26.6296i −0.321789 + 0.990365i
\(724\) −11.3262 8.22899i −0.420936 0.305828i
\(725\) −24.0000 −0.891338
\(726\) 0 0
\(727\) 17.0000 0.630495 0.315248 0.949009i \(-0.397912\pi\)
0.315248 + 0.949009i \(0.397912\pi\)
\(728\) 0 0
\(729\) 4.01722 12.3637i 0.148786 0.457916i
\(730\) 0 0
\(731\) 38.8328 28.2137i 1.43628 1.04352i
\(732\) −16.1803 + 11.7557i −0.598043 + 0.434503i
\(733\) −1.23607 3.80423i −0.0456552 0.140512i 0.925630 0.378429i \(-0.123536\pi\)
−0.971286 + 0.237917i \(0.923536\pi\)
\(734\) 0 0
\(735\) −2.42705 1.76336i −0.0895231 0.0650424i
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) 27.5066 + 19.9847i 1.01185 + 0.735149i 0.964595 0.263734i \(-0.0849541\pi\)
0.0472504 + 0.998883i \(0.484954\pi\)
\(740\) −20.3951 + 62.7697i −0.749740 + 2.30746i
\(741\) −2.47214 7.60845i −0.0908162 0.279503i
\(742\) 0 0
\(743\) −19.4164 + 14.1068i −0.712319 + 0.517530i −0.883921 0.467636i \(-0.845106\pi\)
0.171602 + 0.985166i \(0.445106\pi\)
\(744\) 0 0
\(745\) −5.56231 + 17.1190i −0.203787 + 0.627192i
\(746\) 0 0
\(747\) −24.0000 −0.878114
\(748\) 0 0
\(749\) 6.00000 0.219235
\(750\) 0 0
\(751\) −9.57953 + 29.4828i −0.349562 + 1.07584i 0.609534 + 0.792760i \(0.291357\pi\)
−0.959096 + 0.283081i \(0.908643\pi\)
\(752\) 0 0
\(753\) 7.28115 5.29007i 0.265340 0.192781i
\(754\) 0 0
\(755\) −9.27051 28.5317i −0.337388 1.03837i
\(756\) 3.09017 9.51057i 0.112388 0.345896i
\(757\) −30.7426 22.3358i −1.11736 0.811810i −0.133554 0.991042i \(-0.542639\pi\)
−0.983807 + 0.179232i \(0.942639\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −38.8328 28.2137i −1.40769 1.02275i −0.993653 0.112485i \(-0.964119\pi\)
−0.414035 0.910261i \(-0.635881\pi\)
\(762\) 0 0
\(763\) 6.18034 + 19.0211i 0.223743 + 0.688611i
\(764\) −43.6869 + 31.7404i −1.58054 + 1.14833i
\(765\) −29.1246 + 21.1603i −1.05300 + 0.765051i
\(766\) 0 0
\(767\) 11.1246 34.2380i 0.401686 1.23626i
\(768\) −12.9443 9.40456i −0.467086 0.339358i
\(769\) −40.0000 −1.44244 −0.721218 0.692708i \(-0.756418\pi\)
−0.721218 + 0.692708i \(0.756418\pi\)
\(770\) 0 0
\(771\) −6.00000 −0.216085
\(772\) 22.6525 + 16.4580i 0.815280 + 0.592336i
\(773\) −1.85410 + 5.70634i −0.0666874 + 0.205243i −0.978847 0.204591i \(-0.934413\pi\)
0.912160 + 0.409834i \(0.134413\pi\)
\(774\) 0 0
\(775\) −16.1803 + 11.7557i −0.581215 + 0.422277i
\(776\) 0 0
\(777\) 3.39919 + 10.4616i 0.121945 + 0.375309i
\(778\) 0 0
\(779\) −9.70820 7.05342i −0.347833 0.252715i
\(780\) 24.0000 0.859338
\(781\) 0 0
\(782\) 0 0
\(783\) −24.2705 17.6336i −0.867357 0.630172i
\(784\) 1.23607 3.80423i 0.0441453 0.135865i
\(785\) −12.0517 37.0912i −0.430142 1.32384i
\(786\) 0 0
\(787\) −40.4508 + 29.3893i −1.44192 + 1.04761i −0.454280 + 0.890859i \(0.650103\pi\)
−0.987638 + 0.156755i \(0.949897\pi\)
\(788\) −11.1246 34.2380i −0.396298 1.21968i
\(789\) −9.27051 + 28.5317i −0.330039 + 1.01576i
\(790\) 0 0
\(791\) −3.00000 −0.106668
\(792\) 0 0
\(793\) 40.0000 1.42044
\(794\) 0 0
\(795\) −5.56231 + 17.1190i −0.197275 + 0.607149i
\(796\) 9.88854 + 30.4338i 0.350490 + 1.07870i
\(797\) 16.9894 12.3435i 0.601794 0.437229i −0.244721 0.969593i \(-0.578696\pi\)
0.846515 + 0.532365i \(0.178696\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0
\(801\) −4.85410 3.52671i −0.171511 0.124610i
\(802\) 0 0
\(803\) 0 0
\(804\) −10.0000 −0.352673
\(805\) −7.28115 5.29007i −0.256627 0.186450i
\(806\) 0 0
\(807\) 9.27051 + 28.5317i 0.326337 + 1.00436i
\(808\) 0 0
\(809\) −24.2705 + 17.6336i −0.853306 + 0.619963i −0.926055 0.377387i \(-0.876823\pi\)
0.0727498 + 0.997350i \(0.476823\pi\)
\(810\) 0 0
\(811\) 0.618034 1.90211i 0.0217021 0.0667922i −0.939619 0.342223i \(-0.888820\pi\)
0.961321 + 0.275430i \(0.0888203\pi\)
\(812\) −9.70820 7.05342i −0.340691 0.247527i
\(813\) −16.0000 −0.561144
\(814\) 0 0
\(815\) 60.0000 2.10171
\(816\) 19.4164 + 14.1068i 0.679710 + 0.493838i
\(817\) 4.94427 15.2169i 0.172978 0.532372i
\(818\) 0 0
\(819\) −6.47214 + 4.70228i −0.226155 + 0.164311i
\(820\) 29.1246 21.1603i 1.01708 0.738949i
\(821\) 5.56231 + 17.1190i 0.194126 + 0.597458i 0.999986 + 0.00535152i \(0.00170345\pi\)
−0.805860 + 0.592106i \(0.798297\pi\)
\(822\) 0 0
\(823\) −18.6074 13.5191i −0.648613 0.471245i 0.214186 0.976793i \(-0.431290\pi\)
−0.862798 + 0.505548i \(0.831290\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −29.1246 21.1603i −1.01276 0.735815i −0.0479754 0.998849i \(-0.515277\pi\)
−0.964787 + 0.263034i \(0.915277\pi\)
\(828\) 3.70820 11.4127i 0.128869 0.396618i
\(829\) −7.72542 23.7764i −0.268315 0.825789i −0.990911 0.134518i \(-0.957051\pi\)
0.722596 0.691271i \(-0.242949\pi\)
\(830\) 0 0
\(831\) −6.47214 + 4.70228i −0.224516 + 0.163120i
\(832\) 9.88854 + 30.4338i 0.342824 + 1.05510i
\(833\) −1.85410 + 5.70634i −0.0642408 + 0.197713i
\(834\) 0 0
\(835\) 18.0000 0.622916
\(836\) 0 0
\(837\) −25.0000 −0.864126
\(838\) 0 0
\(839\) −4.63525 + 14.2658i −0.160027 + 0.492512i −0.998635 0.0522225i \(-0.983369\pi\)
0.838609 + 0.544734i \(0.183369\pi\)
\(840\) 0 0
\(841\) −5.66312 + 4.11450i −0.195280 + 0.141879i
\(842\) 0 0
\(843\) 3.70820 + 11.4127i 0.127717 + 0.393074i
\(844\) −8.65248 + 26.6296i −0.297831 + 0.916628i
\(845\) −7.28115 5.29007i −0.250479 0.181984i
\(846\) 0 0
\(847\) 0 0
\(848\) −24.0000 −0.824163
\(849\) −25.8885 18.8091i −0.888493 0.645528i
\(850\) 0 0
\(851\) 10.1976 + 31.3849i 0.349568 + 1.07586i
\(852\) 14.5623 10.5801i 0.498896 0.362469i
\(853\) 8.09017 5.87785i 0.277002 0.201254i −0.440607 0.897700i \(-0.645237\pi\)
0.717609 + 0.696446i \(0.245237\pi\)
\(854\) 0 0
\(855\) −3.70820 + 11.4127i −0.126818 + 0.390305i
\(856\) 0 0
\(857\) −12.0000 −0.409912 −0.204956 0.978771i \(-0.565705\pi\)
−0.204956 + 0.978771i \(0.565705\pi\)
\(858\) 0 0
\(859\) −13.0000 −0.443554 −0.221777 0.975097i \(-0.571186\pi\)
−0.221777 + 0.975097i \(0.571186\pi\)
\(860\) 38.8328 + 28.2137i 1.32419 + 0.962079i
\(861\) 1.85410 5.70634i 0.0631876 0.194472i
\(862\) 0 0
\(863\) 9.70820 7.05342i 0.330471 0.240101i −0.410159 0.912014i \(-0.634527\pi\)
0.740630 + 0.671913i \(0.234527\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) −15.3713 11.1679i −0.522037 0.379282i
\(868\) −10.0000 −0.339422
\(869\) 0 0
\(870\) 0 0
\(871\) 16.1803 + 11.7557i 0.548250 + 0.398327i
\(872\) 0 0
\(873\) 0.618034 + 1.90211i 0.0209173 + 0.0643768i
\(874\) 0 0
\(875\) 2.42705 1.76336i 0.0820493 0.0596123i
\(876\) −1.23607 3.80423i −0.0417629 0.128533i
\(877\) −6.79837 + 20.9232i −0.229565 + 0.706528i 0.768231 + 0.640172i \(0.221137\pi\)
−0.997796 + 0.0663553i \(0.978863\pi\)
\(878\) 0 0
\(879\) −30.0000 −1.01187
\(880\) 0 0
\(881\) −9.00000 −0.303218 −0.151609 0.988441i \(-0.548445\pi\)
−0.151609 + 0.988441i \(0.548445\pi\)
\(882\) 0 0
\(883\) 6.18034 19.0211i 0.207985 0.640112i −0.791593 0.611049i \(-0.790748\pi\)
0.999578 0.0290628i \(-0.00925227\pi\)
\(884\) −14.8328 45.6507i −0.498882 1.53540i
\(885\) 21.8435 15.8702i 0.734260 0.533471i
\(886\) 0 0
\(887\) −12.9787 39.9444i −0.435783 1.34120i −0.892283 0.451477i \(-0.850897\pi\)
0.456500 0.889723i \(-0.349103\pi\)
\(888\) 0 0
\(889\) −1.61803 1.17557i −0.0542671 0.0394274i
\(890\) 0 0
\(891\) 0 0
\(892\) 38.0000 1.27233
\(893\) 0 0
\(894\) 0 0
\(895\) −13.9058 42.7975i −0.464818 1.43056i
\(896\) 0 0
\(897\) 9.70820 7.05342i 0.324147 0.235507i
\(898\) 0 0
\(899\) −9.27051 + 28.5317i −0.309189 + 0.951585i
\(900\) −12.9443 9.40456i −0.431476 0.313485i
\(901\) 36.0000 1.19933
\(902\) 0 0
\(903\) 8.00000 0.266223
\(904\) 0 0
\(905\) −6.48936 + 19.9722i −0.215714 + 0.663898i
\(906\) 0 0
\(907\) −6.47214 + 4.70228i −0.214904 + 0.156137i −0.690030 0.723781i \(-0.742403\pi\)
0.475126 + 0.879918i \(0.342403\pi\)
\(908\) −19.4164 + 14.1068i −0.644356 + 0.468152i
\(909\) 7.41641 + 22.8254i 0.245987 + 0.757069i
\(910\) 0 0
\(911\) −38.8328 28.2137i −1.28659 0.934761i −0.286858 0.957973i \(-0.592611\pi\)
−0.999731 + 0.0232118i \(0.992611\pi\)
\(912\) 8.00000 0.264906
\(913\) 0 0
\(914\) 0 0
\(915\) 24.2705 + 17.6336i 0.802358 + 0.582947i
\(916\) −3.09017 + 9.51057i −0.102102 + 0.314238i
\(917\) −1.85410 5.70634i −0.0612278 0.188440i
\(918\) 0 0
\(919\) 12.9443 9.40456i 0.426992 0.310228i −0.353453 0.935452i \(-0.614993\pi\)
0.780445 + 0.625224i \(0.214993\pi\)
\(920\) 0 0
\(921\) 6.18034 19.0211i 0.203649 0.626768i
\(922\) 0 0
\(923\) −36.0000 −1.18495
\(924\) 0 0
\(925\) 44.0000 1.44671
\(926\) 0 0
\(927\) 2.47214 7.60845i 0.0811956 0.249894i
\(928\) 0 0
\(929\) −14.5623 + 10.5801i −0.477774 + 0.347123i −0.800463 0.599382i \(-0.795413\pi\)
0.322689 + 0.946505i \(0.395413\pi\)
\(930\) 0 0
\(931\) 0.618034 + 1.90211i 0.0202552 + 0.0623392i
\(932\) −3.70820 + 11.4127i −0.121466 + 0.373835i
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) −16.1803 11.7557i −0.528589 0.384042i 0.291241 0.956650i \(-0.405932\pi\)
−0.819830 + 0.572608i \(0.805932\pi\)
\(938\) 0 0
\(939\) −5.87132 18.0701i −0.191603 0.589695i
\(940\) 0 0
\(941\) −14.5623 + 10.5801i −0.474718 + 0.344903i −0.799277 0.600963i \(-0.794784\pi\)
0.324559 + 0.945865i \(0.394784\pi\)
\(942\) 0 0
\(943\) 5.56231 17.1190i 0.181134 0.557472i
\(944\) 29.1246 + 21.1603i 0.947925 + 0.688708i
\(945\) −15.0000 −0.487950
\(946\) 0 0
\(947\) −27.0000 −0.877382 −0.438691 0.898638i \(-0.644558\pi\)
−0.438691 + 0.898638i \(0.644558\pi\)
\(948\) −16.1803 11.7557i −0.525513 0.381808i
\(949\) −2.47214 + 7.60845i −0.0802489 + 0.246981i
\(950\) 0 0
\(951\) −7.28115 + 5.29007i −0.236108 + 0.171542i
\(952\) 0 0
\(953\) −11.1246 34.2380i −0.360362 1.10908i −0.952835 0.303489i \(-0.901849\pi\)
0.592473 0.805590i \(-0.298151\pi\)
\(954\) 0 0
\(955\) 65.5304 + 47.6106i 2.12051 + 1.54064i
\(956\) 24.0000 0.776215
\(957\) 0 0
\(958\) 0 0
\(959\) 2.42705 + 1.76336i 0.0783736 + 0.0569417i
\(960\) −7.41641 + 22.8254i −0.239364 + 0.736685i
\(961\) −1.85410 5.70634i −0.0598097 0.184075i
\(962\) 0 0
\(963\) 9.70820 7.05342i 0.312842 0.227293i
\(964\) 17.3050 + 53.2592i 0.557355 + 1.71536i
\(965\) 12.9787 39.9444i 0.417800 1.28585i
\(966\) 0 0
\(967\) 14.0000 0.450210 0.225105 0.974335i \(-0.427728\pi\)
0.225105 + 0.974335i \(0.427728\pi\)
\(968\) 0 0
\(969\) −12.0000 −0.385496
\(970\) 0 0
\(971\) −12.0517 + 37.0912i −0.386756 + 1.19031i 0.548442 + 0.836189i \(0.315221\pi\)
−0.935198 + 0.354125i \(0.884779\pi\)
\(972\) −9.88854 30.4338i −0.317175 0.976165i
\(973\) −11.3262 + 8.22899i −0.363103 + 0.263809i
\(974\) 0 0
\(975\) −4.94427 15.2169i −0.158343 0.487331i
\(976\) −12.3607 + 38.0423i −0.395656 + 1.21770i
\(977\) −7.28115 5.29007i −0.232945 0.169244i 0.465190 0.885211i \(-0.345986\pi\)
−0.698134 + 0.715967i \(0.745986\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) −6.00000 −0.191663
\(981\) 32.3607 + 23.5114i 1.03320 + 0.750662i
\(982\) 0 0
\(983\) 10.1976 + 31.3849i 0.325252 + 1.00102i 0.971327 + 0.237748i \(0.0764092\pi\)
−0.646075 + 0.763274i \(0.723591\pi\)
\(984\) 0 0
\(985\) −43.6869 + 31.7404i −1.39198 + 1.01133i
\(986\) 0 0
\(987\) 0 0
\(988\) −12.9443 9.40456i −0.411812 0.299199i
\(989\) 24.0000 0.763156
\(990\) 0 0
\(991\) −16.0000 −0.508257 −0.254128 0.967170i \(-0.581789\pi\)
−0.254128 + 0.967170i \(0.581789\pi\)
\(992\) 0 0
\(993\) −0.309017 + 0.951057i −0.00980636 + 0.0301809i
\(994\) 0 0
\(995\) 38.8328 28.2137i 1.23108 0.894434i
\(996\) 19.4164 14.1068i 0.615232 0.446993i
\(997\) −8.65248 26.6296i −0.274027 0.843367i −0.989475 0.144702i \(-0.953778\pi\)
0.715449 0.698665i \(-0.246222\pi\)
\(998\) 0 0
\(999\) 44.4959 + 32.3282i 1.40779 + 1.02282i
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 847.2.f.f.323.1 4
11.2 odd 10 847.2.f.g.148.1 4
11.3 even 5 inner 847.2.f.f.729.1 4
11.4 even 5 inner 847.2.f.f.372.1 4
11.5 even 5 77.2.a.b.1.1 1
11.6 odd 10 847.2.a.c.1.1 1
11.7 odd 10 847.2.f.g.372.1 4
11.8 odd 10 847.2.f.g.729.1 4
11.9 even 5 inner 847.2.f.f.148.1 4
11.10 odd 2 847.2.f.g.323.1 4
33.5 odd 10 693.2.a.b.1.1 1
33.17 even 10 7623.2.a.i.1.1 1
44.27 odd 10 1232.2.a.d.1.1 1
55.27 odd 20 1925.2.b.g.1849.1 2
55.38 odd 20 1925.2.b.g.1849.2 2
55.49 even 10 1925.2.a.f.1.1 1
77.5 odd 30 539.2.e.e.67.1 2
77.6 even 10 5929.2.a.d.1.1 1
77.16 even 15 539.2.e.d.67.1 2
77.27 odd 10 539.2.a.b.1.1 1
77.38 odd 30 539.2.e.e.177.1 2
77.60 even 15 539.2.e.d.177.1 2
88.5 even 10 4928.2.a.i.1.1 1
88.27 odd 10 4928.2.a.x.1.1 1
231.104 even 10 4851.2.a.k.1.1 1
308.27 even 10 8624.2.a.s.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
77.2.a.b.1.1 1 11.5 even 5
539.2.a.b.1.1 1 77.27 odd 10
539.2.e.d.67.1 2 77.16 even 15
539.2.e.d.177.1 2 77.60 even 15
539.2.e.e.67.1 2 77.5 odd 30
539.2.e.e.177.1 2 77.38 odd 30
693.2.a.b.1.1 1 33.5 odd 10
847.2.a.c.1.1 1 11.6 odd 10
847.2.f.f.148.1 4 11.9 even 5 inner
847.2.f.f.323.1 4 1.1 even 1 trivial
847.2.f.f.372.1 4 11.4 even 5 inner
847.2.f.f.729.1 4 11.3 even 5 inner
847.2.f.g.148.1 4 11.2 odd 10
847.2.f.g.323.1 4 11.10 odd 2
847.2.f.g.372.1 4 11.7 odd 10
847.2.f.g.729.1 4 11.8 odd 10
1232.2.a.d.1.1 1 44.27 odd 10
1925.2.a.f.1.1 1 55.49 even 10
1925.2.b.g.1849.1 2 55.27 odd 20
1925.2.b.g.1849.2 2 55.38 odd 20
4851.2.a.k.1.1 1 231.104 even 10
4928.2.a.i.1.1 1 88.5 even 10
4928.2.a.x.1.1 1 88.27 odd 10
5929.2.a.d.1.1 1 77.6 even 10
7623.2.a.i.1.1 1 33.17 even 10
8624.2.a.s.1.1 1 308.27 even 10