Properties

Label 546.2.bx.b.223.3
Level $546$
Weight $2$
Character 546.223
Analytic conductor $4.360$
Analytic rank $0$
Dimension $40$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [546,2,Mod(97,546)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(546, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([0, 6, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("546.97");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 546.bx (of order \(12\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(4.35983195036\)
Analytic rank: \(0\)
Dimension: \(40\)
Relative dimension: \(10\) over \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 223.3
Character \(\chi\) \(=\) 546.223
Dual form 546.2.bx.b.475.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.965926 - 0.258819i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.866025 + 0.500000i) q^{4} +(0.781970 + 0.781970i) q^{5} +(0.965926 - 0.258819i) q^{6} +(-2.22139 - 1.43716i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.965926 - 0.258819i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.866025 + 0.500000i) q^{4} +(0.781970 + 0.781970i) q^{5} +(0.965926 - 0.258819i) q^{6} +(-2.22139 - 1.43716i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.500000 - 0.866025i) q^{9} +(-0.552937 - 0.957714i) q^{10} +(0.312928 - 1.16786i) q^{11} -1.00000 q^{12} +(-2.62553 + 2.47115i) q^{13} +(1.77373 + 1.96313i) q^{14} +(-1.06819 - 0.286221i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-1.19466 + 2.06921i) q^{17} +(-0.707107 + 0.707107i) q^{18} +(-4.87770 + 1.30697i) q^{19} +(0.286221 + 1.06819i) q^{20} +(2.64236 + 0.133920i) q^{21} +(-0.604530 + 1.04708i) q^{22} +(5.04730 - 2.91406i) q^{23} +(0.965926 + 0.258819i) q^{24} -3.77704i q^{25} +(3.17565 - 1.70741i) q^{26} +1.00000i q^{27} +(-1.20520 - 2.35531i) q^{28} +(-4.18735 - 7.25271i) q^{29} +(0.957714 + 0.552937i) q^{30} +(-6.07089 - 6.07089i) q^{31} +(-0.258819 - 0.965926i) q^{32} +(0.312928 + 1.16786i) q^{33} +(1.68950 - 1.68950i) q^{34} +(-0.613247 - 2.86088i) q^{35} +(0.866025 - 0.500000i) q^{36} +(-2.63773 + 9.84416i) q^{37} +5.04976 q^{38} +(1.03820 - 3.45284i) q^{39} -1.10587i q^{40} +(-0.0706665 + 0.263731i) q^{41} +(-2.51766 - 0.813250i) q^{42} +(-9.39867 - 5.42633i) q^{43} +(0.854934 - 0.854934i) q^{44} +(1.06819 - 0.286221i) q^{45} +(-5.62953 + 1.50843i) q^{46} +(-4.79531 + 4.79531i) q^{47} +(-0.866025 - 0.500000i) q^{48} +(2.86915 + 6.38498i) q^{49} +(-0.977571 + 3.64834i) q^{50} -2.38932i q^{51} +(-3.50935 + 0.827311i) q^{52} +3.52584 q^{53} +(0.258819 - 0.965926i) q^{54} +(1.15793 - 0.668533i) q^{55} +(0.554536 + 2.58698i) q^{56} +(3.57072 - 3.57072i) q^{57} +(2.16753 + 8.08934i) q^{58} +(-2.46090 - 9.18419i) q^{59} +(-0.781970 - 0.781970i) q^{60} +(-9.83139 - 5.67615i) q^{61} +(4.29276 + 7.43529i) q^{62} +(-2.35531 + 1.20520i) q^{63} +1.00000i q^{64} +(-3.98545 - 0.120724i) q^{65} -1.20906i q^{66} +(-5.76691 - 1.54524i) q^{67} +(-2.06921 + 1.19466i) q^{68} +(-2.91406 + 5.04730i) q^{69} +(-0.148099 + 2.92211i) q^{70} +(-2.24186 - 8.36673i) q^{71} +(-0.965926 + 0.258819i) q^{72} +(-4.16937 + 4.16937i) q^{73} +(5.09571 - 8.82603i) q^{74} +(1.88852 + 3.27102i) q^{75} +(-4.87770 - 1.30697i) q^{76} +(-2.37354 + 2.14455i) q^{77} +(-1.89649 + 3.06648i) q^{78} +7.38288 q^{79} +(-0.286221 + 1.06819i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(0.136517 - 0.236455i) q^{82} +(2.18308 + 2.18308i) q^{83} +(2.22139 + 1.43716i) q^{84} +(-2.55225 + 0.683873i) q^{85} +(7.67399 + 7.67399i) q^{86} +(7.25271 + 4.18735i) q^{87} +(-1.04708 + 0.604530i) q^{88} +(15.1646 + 4.06333i) q^{89} -1.10587 q^{90} +(9.38377 - 1.71608i) q^{91} +5.82812 q^{92} +(8.29298 + 2.22210i) q^{93} +(5.87303 - 3.39079i) q^{94} +(-4.83623 - 2.79220i) q^{95} +(0.707107 + 0.707107i) q^{96} +(1.77794 - 0.476399i) q^{97} +(-1.11883 - 6.91001i) q^{98} +(-0.854934 - 0.854934i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40 q + 8 q^{7} + 20 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 40 q + 8 q^{7} + 20 q^{9} + 8 q^{11} - 40 q^{12} - 8 q^{14} + 20 q^{16} - 16 q^{17} - 16 q^{19} + 4 q^{21} + 8 q^{22} - 32 q^{26} - 8 q^{28} + 8 q^{33} - 16 q^{34} + 40 q^{35} + 40 q^{37} + 16 q^{38} - 16 q^{39} + 4 q^{41} - 12 q^{42} + 24 q^{43} + 8 q^{44} - 4 q^{46} - 16 q^{47} - 20 q^{49} - 16 q^{50} + 8 q^{52} + 32 q^{53} + 72 q^{55} + 12 q^{56} + 8 q^{57} - 36 q^{58} - 84 q^{59} + 48 q^{61} + 4 q^{62} + 4 q^{63} - 16 q^{65} - 12 q^{68} + 8 q^{69} - 20 q^{70} - 40 q^{71} + 48 q^{73} + 8 q^{74} - 36 q^{75} - 16 q^{76} + 24 q^{77} - 8 q^{78} - 48 q^{79} - 20 q^{81} - 36 q^{83} - 8 q^{84} + 8 q^{85} - 8 q^{86} - 12 q^{89} + 32 q^{91} - 16 q^{92} - 24 q^{93} - 96 q^{95} - 8 q^{98} - 8 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).

\(n\) \(157\) \(365\) \(379\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{1}{12}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.965926 0.258819i −0.683013 0.183013i
\(3\) −0.866025 + 0.500000i −0.500000 + 0.288675i
\(4\) 0.866025 + 0.500000i 0.433013 + 0.250000i
\(5\) 0.781970 + 0.781970i 0.349708 + 0.349708i 0.860001 0.510293i \(-0.170463\pi\)
−0.510293 + 0.860001i \(0.670463\pi\)
\(6\) 0.965926 0.258819i 0.394338 0.105662i
\(7\) −2.22139 1.43716i −0.839607 0.543195i
\(8\) −0.707107 0.707107i −0.250000 0.250000i
\(9\) 0.500000 0.866025i 0.166667 0.288675i
\(10\) −0.552937 0.957714i −0.174854 0.302856i
\(11\) 0.312928 1.16786i 0.0943512 0.352124i −0.902569 0.430545i \(-0.858321\pi\)
0.996920 + 0.0784215i \(0.0249880\pi\)
\(12\) −1.00000 −0.288675
\(13\) −2.62553 + 2.47115i −0.728192 + 0.685373i
\(14\) 1.77373 + 1.96313i 0.474051 + 0.524668i
\(15\) −1.06819 0.286221i −0.275806 0.0739020i
\(16\) 0.500000 + 0.866025i 0.125000 + 0.216506i
\(17\) −1.19466 + 2.06921i −0.289747 + 0.501857i −0.973749 0.227623i \(-0.926905\pi\)
0.684002 + 0.729480i \(0.260238\pi\)
\(18\) −0.707107 + 0.707107i −0.166667 + 0.166667i
\(19\) −4.87770 + 1.30697i −1.11902 + 0.299841i −0.770487 0.637456i \(-0.779987\pi\)
−0.348533 + 0.937296i \(0.613320\pi\)
\(20\) 0.286221 + 1.06819i 0.0640010 + 0.238855i
\(21\) 2.64236 + 0.133920i 0.576610 + 0.0292238i
\(22\) −0.604530 + 1.04708i −0.128886 + 0.223237i
\(23\) 5.04730 2.91406i 1.05243 0.607623i 0.129104 0.991631i \(-0.458790\pi\)
0.923330 + 0.384008i \(0.125456\pi\)
\(24\) 0.965926 + 0.258819i 0.197169 + 0.0528312i
\(25\) 3.77704i 0.755409i
\(26\) 3.17565 1.70741i 0.622796 0.334850i
\(27\) 1.00000i 0.192450i
\(28\) −1.20520 2.35531i −0.227762 0.445112i
\(29\) −4.18735 7.25271i −0.777572 1.34679i −0.933338 0.359000i \(-0.883118\pi\)
0.155766 0.987794i \(-0.450216\pi\)
\(30\) 0.957714 + 0.552937i 0.174854 + 0.100952i
\(31\) −6.07089 6.07089i −1.09036 1.09036i −0.995489 0.0948739i \(-0.969755\pi\)
−0.0948739 0.995489i \(-0.530245\pi\)
\(32\) −0.258819 0.965926i −0.0457532 0.170753i
\(33\) 0.312928 + 1.16786i 0.0544737 + 0.203299i
\(34\) 1.68950 1.68950i 0.289747 0.289747i
\(35\) −0.613247 2.86088i −0.103658 0.483576i
\(36\) 0.866025 0.500000i 0.144338 0.0833333i
\(37\) −2.63773 + 9.84416i −0.433641 + 1.61837i 0.310657 + 0.950522i \(0.399451\pi\)
−0.744298 + 0.667847i \(0.767216\pi\)
\(38\) 5.04976 0.819180
\(39\) 1.03820 3.45284i 0.166246 0.552898i
\(40\) 1.10587i 0.174854i
\(41\) −0.0706665 + 0.263731i −0.0110363 + 0.0411879i −0.971224 0.238166i \(-0.923454\pi\)
0.960188 + 0.279354i \(0.0901203\pi\)
\(42\) −2.51766 0.813250i −0.388484 0.125487i
\(43\) −9.39867 5.42633i −1.43328 0.827507i −0.435915 0.899988i \(-0.643575\pi\)
−0.997370 + 0.0724809i \(0.976908\pi\)
\(44\) 0.854934 0.854934i 0.128886 0.128886i
\(45\) 1.06819 0.286221i 0.159237 0.0426673i
\(46\) −5.62953 + 1.50843i −0.830029 + 0.222405i
\(47\) −4.79531 + 4.79531i −0.699467 + 0.699467i −0.964296 0.264828i \(-0.914685\pi\)
0.264828 + 0.964296i \(0.414685\pi\)
\(48\) −0.866025 0.500000i −0.125000 0.0721688i
\(49\) 2.86915 + 6.38498i 0.409879 + 0.912140i
\(50\) −0.977571 + 3.64834i −0.138249 + 0.515954i
\(51\) 2.38932i 0.334571i
\(52\) −3.50935 + 0.827311i −0.486660 + 0.114727i
\(53\) 3.52584 0.484311 0.242156 0.970237i \(-0.422146\pi\)
0.242156 + 0.970237i \(0.422146\pi\)
\(54\) 0.258819 0.965926i 0.0352208 0.131446i
\(55\) 1.15793 0.668533i 0.156136 0.0901450i
\(56\) 0.554536 + 2.58698i 0.0741030 + 0.345700i
\(57\) 3.57072 3.57072i 0.472954 0.472954i
\(58\) 2.16753 + 8.08934i 0.284611 + 1.06218i
\(59\) −2.46090 9.18419i −0.320381 1.19568i −0.918874 0.394551i \(-0.870900\pi\)
0.598492 0.801129i \(-0.295767\pi\)
\(60\) −0.781970 0.781970i −0.100952 0.100952i
\(61\) −9.83139 5.67615i −1.25878 0.726757i −0.285943 0.958247i \(-0.592307\pi\)
−0.972837 + 0.231490i \(0.925640\pi\)
\(62\) 4.29276 + 7.43529i 0.545182 + 0.944282i
\(63\) −2.35531 + 1.20520i −0.296741 + 0.151841i
\(64\) 1.00000i 0.125000i
\(65\) −3.98545 0.120724i −0.494335 0.0149740i
\(66\) 1.20906i 0.148825i
\(67\) −5.76691 1.54524i −0.704540 0.188781i −0.111277 0.993789i \(-0.535494\pi\)
−0.593263 + 0.805009i \(0.702161\pi\)
\(68\) −2.06921 + 1.19466i −0.250929 + 0.144874i
\(69\) −2.91406 + 5.04730i −0.350811 + 0.607623i
\(70\) −0.148099 + 2.92211i −0.0177012 + 0.349260i
\(71\) −2.24186 8.36673i −0.266060 0.992948i −0.961599 0.274459i \(-0.911501\pi\)
0.695539 0.718488i \(-0.255166\pi\)
\(72\) −0.965926 + 0.258819i −0.113835 + 0.0305021i
\(73\) −4.16937 + 4.16937i −0.487988 + 0.487988i −0.907671 0.419683i \(-0.862141\pi\)
0.419683 + 0.907671i \(0.362141\pi\)
\(74\) 5.09571 8.82603i 0.592364 1.02601i
\(75\) 1.88852 + 3.27102i 0.218068 + 0.377704i
\(76\) −4.87770 1.30697i −0.559510 0.149920i
\(77\) −2.37354 + 2.14455i −0.270490 + 0.244394i
\(78\) −1.89649 + 3.06648i −0.214735 + 0.347211i
\(79\) 7.38288 0.830639 0.415319 0.909676i \(-0.363670\pi\)
0.415319 + 0.909676i \(0.363670\pi\)
\(80\) −0.286221 + 1.06819i −0.0320005 + 0.119427i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 0.136517 0.236455i 0.0150758 0.0261121i
\(83\) 2.18308 + 2.18308i 0.239624 + 0.239624i 0.816695 0.577070i \(-0.195804\pi\)
−0.577070 + 0.816695i \(0.695804\pi\)
\(84\) 2.22139 + 1.43716i 0.242374 + 0.156807i
\(85\) −2.55225 + 0.683873i −0.276830 + 0.0741765i
\(86\) 7.67399 + 7.67399i 0.827507 + 0.827507i
\(87\) 7.25271 + 4.18735i 0.777572 + 0.448931i
\(88\) −1.04708 + 0.604530i −0.111619 + 0.0644431i
\(89\) 15.1646 + 4.06333i 1.60744 + 0.430712i 0.947278 0.320412i \(-0.103821\pi\)
0.660161 + 0.751124i \(0.270488\pi\)
\(90\) −1.10587 −0.116569
\(91\) 9.38377 1.71608i 0.983686 0.179894i
\(92\) 5.82812 0.607623
\(93\) 8.29298 + 2.22210i 0.859942 + 0.230421i
\(94\) 5.87303 3.39079i 0.605756 0.349734i
\(95\) −4.83623 2.79220i −0.496187 0.286474i
\(96\) 0.707107 + 0.707107i 0.0721688 + 0.0721688i
\(97\) 1.77794 0.476399i 0.180523 0.0483710i −0.167425 0.985885i \(-0.553545\pi\)
0.347948 + 0.937514i \(0.386879\pi\)
\(98\) −1.11883 6.91001i −0.113019 0.698016i
\(99\) −0.854934 0.854934i −0.0859241 0.0859241i
\(100\) 1.88852 3.27102i 0.188852 0.327102i
\(101\) −3.65414 6.32916i −0.363601 0.629775i 0.624950 0.780665i \(-0.285119\pi\)
−0.988551 + 0.150890i \(0.951786\pi\)
\(102\) −0.618401 + 2.30790i −0.0612308 + 0.228517i
\(103\) 8.98605 0.885422 0.442711 0.896664i \(-0.354017\pi\)
0.442711 + 0.896664i \(0.354017\pi\)
\(104\) 3.60390 + 0.109166i 0.353391 + 0.0107046i
\(105\) 1.96153 + 2.17097i 0.191425 + 0.211865i
\(106\) −3.40570 0.912554i −0.330791 0.0886351i
\(107\) 6.95581 + 12.0478i 0.672444 + 1.16471i 0.977209 + 0.212280i \(0.0680887\pi\)
−0.304765 + 0.952428i \(0.598578\pi\)
\(108\) −0.500000 + 0.866025i −0.0481125 + 0.0833333i
\(109\) −3.22554 + 3.22554i −0.308951 + 0.308951i −0.844502 0.535552i \(-0.820104\pi\)
0.535552 + 0.844502i \(0.320104\pi\)
\(110\) −1.29151 + 0.346058i −0.123140 + 0.0329954i
\(111\) −2.63773 9.84416i −0.250363 0.934366i
\(112\) 0.133920 2.64236i 0.0126543 0.249680i
\(113\) −10.0372 + 17.3849i −0.944217 + 1.63543i −0.186906 + 0.982378i \(0.559846\pi\)
−0.757311 + 0.653054i \(0.773487\pi\)
\(114\) −4.37322 + 2.52488i −0.409590 + 0.236477i
\(115\) 6.22554 + 1.66813i 0.580535 + 0.155554i
\(116\) 8.37471i 0.777572i
\(117\) 0.827311 + 3.50935i 0.0764849 + 0.324440i
\(118\) 9.50818i 0.875298i
\(119\) 5.62759 2.87961i 0.515880 0.263973i
\(120\) 0.552937 + 0.957714i 0.0504760 + 0.0874270i
\(121\) 8.26030 + 4.76909i 0.750937 + 0.433553i
\(122\) 8.02729 + 8.02729i 0.726757 + 0.726757i
\(123\) −0.0706665 0.263731i −0.00637179 0.0237798i
\(124\) −2.22210 8.29298i −0.199550 0.744732i
\(125\) 6.86339 6.86339i 0.613880 0.613880i
\(126\) 2.58698 0.554536i 0.230467 0.0494020i
\(127\) 9.65396 5.57371i 0.856650 0.494587i −0.00623902 0.999981i \(-0.501986\pi\)
0.862889 + 0.505393i \(0.168653\pi\)
\(128\) 0.258819 0.965926i 0.0228766 0.0853766i
\(129\) 10.8527 0.955523
\(130\) 3.81841 + 1.14812i 0.334897 + 0.100697i
\(131\) 3.86156i 0.337386i 0.985669 + 0.168693i \(0.0539546\pi\)
−0.985669 + 0.168693i \(0.946045\pi\)
\(132\) −0.312928 + 1.16786i −0.0272369 + 0.101649i
\(133\) 12.7136 + 4.10672i 1.10241 + 0.356098i
\(134\) 5.17047 + 2.98517i 0.446660 + 0.257879i
\(135\) −0.781970 + 0.781970i −0.0673013 + 0.0673013i
\(136\) 2.30790 0.618401i 0.197901 0.0530275i
\(137\) −10.7828 + 2.88925i −0.921240 + 0.246846i −0.688115 0.725601i \(-0.741562\pi\)
−0.233125 + 0.972447i \(0.574895\pi\)
\(138\) 4.12110 4.12110i 0.350811 0.350811i
\(139\) −9.33502 5.38958i −0.791786 0.457138i 0.0488046 0.998808i \(-0.484459\pi\)
−0.840591 + 0.541670i \(0.817792\pi\)
\(140\) 0.899351 2.78422i 0.0760091 0.235309i
\(141\) 1.75520 6.55051i 0.147815 0.551652i
\(142\) 8.66187i 0.726888i
\(143\) 2.06436 + 3.83955i 0.172630 + 0.321079i
\(144\) 1.00000 0.0833333
\(145\) 2.39702 8.94579i 0.199061 0.742907i
\(146\) 5.10642 2.94819i 0.422610 0.243994i
\(147\) −5.67725 4.09498i −0.468252 0.337748i
\(148\) −7.20642 + 7.20642i −0.592364 + 0.592364i
\(149\) 5.97456 + 22.2974i 0.489455 + 1.82667i 0.559101 + 0.829100i \(0.311147\pi\)
−0.0696456 + 0.997572i \(0.522187\pi\)
\(150\) −0.977571 3.64834i −0.0798183 0.297886i
\(151\) 2.31792 + 2.31792i 0.188629 + 0.188629i 0.795103 0.606474i \(-0.207417\pi\)
−0.606474 + 0.795103i \(0.707417\pi\)
\(152\) 4.37322 + 2.52488i 0.354715 + 0.204795i
\(153\) 1.19466 + 2.06921i 0.0965825 + 0.167286i
\(154\) 2.84771 1.45716i 0.229475 0.117421i
\(155\) 9.49451i 0.762617i
\(156\) 2.62553 2.47115i 0.210211 0.197850i
\(157\) 2.78978i 0.222648i 0.993784 + 0.111324i \(0.0355092\pi\)
−0.993784 + 0.111324i \(0.964491\pi\)
\(158\) −7.13131 1.91083i −0.567337 0.152017i
\(159\) −3.05347 + 1.76292i −0.242156 + 0.139809i
\(160\) 0.552937 0.957714i 0.0437135 0.0757140i
\(161\) −15.4000 0.780502i −1.21369 0.0615122i
\(162\) 0.258819 + 0.965926i 0.0203347 + 0.0758903i
\(163\) −10.9557 + 2.93557i −0.858116 + 0.229931i −0.660942 0.750437i \(-0.729843\pi\)
−0.197174 + 0.980369i \(0.563176\pi\)
\(164\) −0.193065 + 0.193065i −0.0150758 + 0.0150758i
\(165\) −0.668533 + 1.15793i −0.0520452 + 0.0901450i
\(166\) −1.54367 2.67372i −0.119812 0.207521i
\(167\) −5.05024 1.35321i −0.390799 0.104714i 0.0580684 0.998313i \(-0.481506\pi\)
−0.448868 + 0.893598i \(0.648173\pi\)
\(168\) −1.77373 1.96313i −0.136847 0.151458i
\(169\) 0.786849 12.9762i 0.0605268 0.998167i
\(170\) 2.64228 0.202654
\(171\) −1.30697 + 4.87770i −0.0999469 + 0.373007i
\(172\) −5.42633 9.39867i −0.413754 0.716642i
\(173\) 7.54949 13.0761i 0.573977 0.994157i −0.422175 0.906514i \(-0.638733\pi\)
0.996152 0.0876430i \(-0.0279335\pi\)
\(174\) −5.92181 5.92181i −0.448931 0.448931i
\(175\) −5.42821 + 8.39029i −0.410334 + 0.634246i
\(176\) 1.16786 0.312928i 0.0880309 0.0235878i
\(177\) 6.72330 + 6.72330i 0.505354 + 0.505354i
\(178\) −13.5962 7.84975i −1.01908 0.588364i
\(179\) 1.52673 0.881456i 0.114113 0.0658831i −0.441857 0.897085i \(-0.645680\pi\)
0.555970 + 0.831202i \(0.312347\pi\)
\(180\) 1.06819 + 0.286221i 0.0796183 + 0.0213337i
\(181\) 23.7089 1.76227 0.881136 0.472863i \(-0.156780\pi\)
0.881136 + 0.472863i \(0.156780\pi\)
\(182\) −9.50818 0.771091i −0.704793 0.0571571i
\(183\) 11.3523 0.839187
\(184\) −5.62953 1.50843i −0.415014 0.111203i
\(185\) −9.76047 + 5.63521i −0.717604 + 0.414309i
\(186\) −7.43529 4.29276i −0.545182 0.314761i
\(187\) 2.04271 + 2.04271i 0.149378 + 0.149378i
\(188\) −6.55051 + 1.75520i −0.477745 + 0.128011i
\(189\) 1.43716 2.22139i 0.104538 0.161582i
\(190\) 3.94877 + 3.94877i 0.286474 + 0.286474i
\(191\) −1.51664 + 2.62689i −0.109740 + 0.190075i −0.915665 0.401943i \(-0.868335\pi\)
0.805925 + 0.592018i \(0.201668\pi\)
\(192\) −0.500000 0.866025i −0.0360844 0.0625000i
\(193\) 2.86384 10.6880i 0.206144 0.769338i −0.782954 0.622079i \(-0.786288\pi\)
0.989098 0.147259i \(-0.0470451\pi\)
\(194\) −1.84066 −0.132152
\(195\) 3.51187 1.88818i 0.251490 0.135215i
\(196\) −0.707730 + 6.96413i −0.0505521 + 0.497438i
\(197\) −19.3179 5.17622i −1.37634 0.368790i −0.506552 0.862210i \(-0.669080\pi\)
−0.869792 + 0.493419i \(0.835747\pi\)
\(198\) 0.604530 + 1.04708i 0.0429621 + 0.0744125i
\(199\) −3.74351 + 6.48394i −0.265370 + 0.459635i −0.967661 0.252256i \(-0.918827\pi\)
0.702290 + 0.711891i \(0.252161\pi\)
\(200\) −2.67077 + 2.67077i −0.188852 + 0.188852i
\(201\) 5.76691 1.54524i 0.406766 0.108993i
\(202\) 1.89152 + 7.05926i 0.133087 + 0.496688i
\(203\) −1.12154 + 22.1290i −0.0787168 + 1.55315i
\(204\) 1.19466 2.06921i 0.0836429 0.144874i
\(205\) −0.261489 + 0.150971i −0.0182632 + 0.0105443i
\(206\) −8.67986 2.32576i −0.604754 0.162043i
\(207\) 5.82812i 0.405082i
\(208\) −3.45284 1.03820i −0.239412 0.0719865i
\(209\) 6.10546i 0.422324i
\(210\) −1.33280 2.60468i −0.0919720 0.179740i
\(211\) 6.85324 + 11.8702i 0.471797 + 0.817176i 0.999479 0.0322660i \(-0.0102724\pi\)
−0.527683 + 0.849442i \(0.676939\pi\)
\(212\) 3.05347 + 1.76292i 0.209713 + 0.121078i
\(213\) 6.12487 + 6.12487i 0.419669 + 0.419669i
\(214\) −3.60059 13.4376i −0.246132 0.918576i
\(215\) −3.10626 11.5927i −0.211845 0.790616i
\(216\) 0.707107 0.707107i 0.0481125 0.0481125i
\(217\) 4.76099 + 22.2106i 0.323197 + 1.50776i
\(218\) 3.95046 2.28080i 0.267559 0.154475i
\(219\) 1.52610 5.69547i 0.103124 0.384864i
\(220\) 1.33707 0.0901450
\(221\) −1.97671 8.38496i −0.132968 0.564033i
\(222\) 10.1914i 0.684003i
\(223\) 0.473727 1.76797i 0.0317231 0.118392i −0.948249 0.317529i \(-0.897147\pi\)
0.979972 + 0.199136i \(0.0638137\pi\)
\(224\) −0.813250 + 2.51766i −0.0543375 + 0.168218i
\(225\) −3.27102 1.88852i −0.218068 0.125901i
\(226\) 14.1947 14.1947i 0.944217 0.944217i
\(227\) 7.87073 2.10896i 0.522399 0.139976i 0.0120228 0.999928i \(-0.496173\pi\)
0.510376 + 0.859951i \(0.329506\pi\)
\(228\) 4.87770 1.30697i 0.323033 0.0865565i
\(229\) −15.5142 + 15.5142i −1.02521 + 1.02521i −0.0255355 + 0.999674i \(0.508129\pi\)
−0.999674 + 0.0255355i \(0.991871\pi\)
\(230\) −5.58167 3.22258i −0.368044 0.212491i
\(231\) 0.983268 3.04400i 0.0646943 0.200281i
\(232\) −2.16753 + 8.08934i −0.142306 + 0.531091i
\(233\) 22.9719i 1.50494i −0.658628 0.752469i \(-0.728863\pi\)
0.658628 0.752469i \(-0.271137\pi\)
\(234\) 0.109166 3.60390i 0.00713643 0.235594i
\(235\) −7.49958 −0.489218
\(236\) 2.46090 9.18419i 0.160191 0.597840i
\(237\) −6.39376 + 3.69144i −0.415319 + 0.239785i
\(238\) −6.18113 + 1.32496i −0.400663 + 0.0858846i
\(239\) 6.51113 6.51113i 0.421170 0.421170i −0.464436 0.885606i \(-0.653743\pi\)
0.885606 + 0.464436i \(0.153743\pi\)
\(240\) −0.286221 1.06819i −0.0184755 0.0689515i
\(241\) 2.09265 + 7.80988i 0.134800 + 0.503079i 0.999999 + 0.00165034i \(0.000525320\pi\)
−0.865199 + 0.501429i \(0.832808\pi\)
\(242\) −6.74451 6.74451i −0.433553 0.433553i
\(243\) 0.866025 + 0.500000i 0.0555556 + 0.0320750i
\(244\) −5.67615 9.83139i −0.363379 0.629390i
\(245\) −2.74927 + 7.23646i −0.175645 + 0.462320i
\(246\) 0.273034i 0.0174080i
\(247\) 9.57682 15.4850i 0.609359 0.985288i
\(248\) 8.58553i 0.545182i
\(249\) −2.98215 0.799063i −0.188986 0.0506386i
\(250\) −8.40590 + 4.85315i −0.531636 + 0.306940i
\(251\) −0.625511 + 1.08342i −0.0394819 + 0.0683847i −0.885091 0.465418i \(-0.845904\pi\)
0.845609 + 0.533802i \(0.179237\pi\)
\(252\) −2.64236 0.133920i −0.166453 0.00843617i
\(253\) −1.82378 6.80643i −0.114660 0.427917i
\(254\) −10.7676 + 2.88517i −0.675619 + 0.181031i
\(255\) 1.86838 1.86838i 0.117002 0.117002i
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 6.98041 + 12.0904i 0.435426 + 0.754180i 0.997330 0.0730222i \(-0.0232644\pi\)
−0.561904 + 0.827202i \(0.689931\pi\)
\(258\) −10.4829 2.80887i −0.652634 0.174873i
\(259\) 20.0070 18.0769i 1.24318 1.12324i
\(260\) −3.39114 2.09728i −0.210310 0.130068i
\(261\) −8.37471 −0.518381
\(262\) 0.999445 3.72998i 0.0617459 0.230439i
\(263\) 4.41208 + 7.64194i 0.272060 + 0.471222i 0.969389 0.245529i \(-0.0789616\pi\)
−0.697329 + 0.716751i \(0.745628\pi\)
\(264\) 0.604530 1.04708i 0.0372062 0.0644431i
\(265\) 2.75710 + 2.75710i 0.169367 + 0.169367i
\(266\) −11.2175 7.25731i −0.687789 0.444974i
\(267\) −15.1646 + 4.06333i −0.928056 + 0.248672i
\(268\) −4.22167 4.22167i −0.257879 0.257879i
\(269\) −4.96802 2.86829i −0.302906 0.174883i 0.340842 0.940121i \(-0.389288\pi\)
−0.643747 + 0.765238i \(0.722621\pi\)
\(270\) 0.957714 0.552937i 0.0582846 0.0336507i
\(271\) −24.3208 6.51674i −1.47738 0.395864i −0.571928 0.820304i \(-0.693804\pi\)
−0.905456 + 0.424440i \(0.860471\pi\)
\(272\) −2.38932 −0.144874
\(273\) −7.26854 + 6.17805i −0.439912 + 0.373913i
\(274\) 11.1632 0.674395
\(275\) −4.41107 1.18194i −0.265997 0.0712738i
\(276\) −5.04730 + 2.91406i −0.303812 + 0.175406i
\(277\) −12.7981 7.38897i −0.768962 0.443960i 0.0635422 0.997979i \(-0.479760\pi\)
−0.832504 + 0.554019i \(0.813094\pi\)
\(278\) 7.62202 + 7.62202i 0.457138 + 0.457138i
\(279\) −8.29298 + 2.22210i −0.496488 + 0.133034i
\(280\) −1.58931 + 2.45658i −0.0949797 + 0.146809i
\(281\) 10.3251 + 10.3251i 0.615941 + 0.615941i 0.944488 0.328547i \(-0.106559\pi\)
−0.328547 + 0.944488i \(0.606559\pi\)
\(282\) −3.39079 + 5.87303i −0.201919 + 0.349734i
\(283\) −3.04731 5.27810i −0.181144 0.313750i 0.761127 0.648603i \(-0.224647\pi\)
−0.942270 + 0.334853i \(0.891313\pi\)
\(284\) 2.24186 8.36673i 0.133030 0.496474i
\(285\) 5.58440 0.330791
\(286\) −1.00027 4.24302i −0.0591471 0.250895i
\(287\) 0.536001 0.484291i 0.0316391 0.0285868i
\(288\) −0.965926 0.258819i −0.0569177 0.0152511i
\(289\) 5.64558 + 9.77843i 0.332093 + 0.575202i
\(290\) −4.63068 + 8.02058i −0.271923 + 0.470984i
\(291\) −1.30155 + 1.30155i −0.0762980 + 0.0762980i
\(292\) −5.69547 + 1.52610i −0.333302 + 0.0893081i
\(293\) −8.55998 31.9463i −0.500079 1.86632i −0.499487 0.866321i \(-0.666478\pi\)
−0.000592145 1.00000i \(-0.500188\pi\)
\(294\) 4.42394 + 5.42482i 0.258010 + 0.316382i
\(295\) 5.25742 9.10612i 0.306099 0.530179i
\(296\) 8.82603 5.09571i 0.513003 0.296182i
\(297\) 1.16786 + 0.312928i 0.0677662 + 0.0181579i
\(298\) 23.0839i 1.33722i
\(299\) −6.05077 + 20.1236i −0.349925 + 1.16378i
\(300\) 3.77704i 0.218068i
\(301\) 13.0796 + 25.5614i 0.753898 + 1.47333i
\(302\) −1.63902 2.83886i −0.0943147 0.163358i
\(303\) 6.32916 + 3.65414i 0.363601 + 0.209925i
\(304\) −3.57072 3.57072i −0.204795 0.204795i
\(305\) −3.24927 12.1264i −0.186053 0.694358i
\(306\) −0.618401 2.30790i −0.0353516 0.131934i
\(307\) −13.1561 + 13.1561i −0.750860 + 0.750860i −0.974640 0.223779i \(-0.928160\pi\)
0.223779 + 0.974640i \(0.428160\pi\)
\(308\) −3.12782 + 0.670467i −0.178224 + 0.0382034i
\(309\) −7.78215 + 4.49303i −0.442711 + 0.255599i
\(310\) −2.45736 + 9.17099i −0.139569 + 0.520877i
\(311\) −24.1181 −1.36761 −0.683806 0.729664i \(-0.739676\pi\)
−0.683806 + 0.729664i \(0.739676\pi\)
\(312\) −3.17565 + 1.70741i −0.179786 + 0.0966630i
\(313\) 0.653940i 0.0369629i 0.999829 + 0.0184814i \(0.00588316\pi\)
−0.999829 + 0.0184814i \(0.994117\pi\)
\(314\) 0.722048 2.69472i 0.0407475 0.152072i
\(315\) −2.78422 0.899351i −0.156873 0.0506727i
\(316\) 6.39376 + 3.69144i 0.359677 + 0.207660i
\(317\) −16.2853 + 16.2853i −0.914672 + 0.914672i −0.996635 0.0819636i \(-0.973881\pi\)
0.0819636 + 0.996635i \(0.473881\pi\)
\(318\) 3.40570 0.912554i 0.190982 0.0511735i
\(319\) −9.78050 + 2.62068i −0.547603 + 0.146730i
\(320\) −0.781970 + 0.781970i −0.0437135 + 0.0437135i
\(321\) −12.0478 6.95581i −0.672444 0.388236i
\(322\) 14.6732 + 4.73971i 0.817707 + 0.264134i
\(323\) 3.12278 11.6544i 0.173756 0.648466i
\(324\) 1.00000i 0.0555556i
\(325\) 9.33364 + 9.91676i 0.517737 + 0.550083i
\(326\) 11.3422 0.628184
\(327\) 1.18063 4.40617i 0.0652890 0.243662i
\(328\) 0.236455 0.136517i 0.0130560 0.00753790i
\(329\) 17.5439 3.76064i 0.967224 0.207331i
\(330\) 0.945449 0.945449i 0.0520452 0.0520452i
\(331\) −3.68510 13.7530i −0.202551 0.755931i −0.990182 0.139784i \(-0.955359\pi\)
0.787631 0.616147i \(-0.211307\pi\)
\(332\) 0.799063 + 2.98215i 0.0438543 + 0.163666i
\(333\) 7.20642 + 7.20642i 0.394910 + 0.394910i
\(334\) 4.52792 + 2.61420i 0.247757 + 0.143042i
\(335\) −3.30122 5.71788i −0.180365 0.312401i
\(336\) 1.20520 + 2.35531i 0.0657491 + 0.128493i
\(337\) 7.20150i 0.392290i −0.980575 0.196145i \(-0.937158\pi\)
0.980575 0.196145i \(-0.0628424\pi\)
\(338\) −4.11852 + 12.3304i −0.224018 + 0.670683i
\(339\) 20.0743i 1.09029i
\(340\) −2.55225 0.683873i −0.138415 0.0370882i
\(341\) −8.98970 + 5.19021i −0.486820 + 0.281065i
\(342\) 2.52488 4.37322i 0.136530 0.236477i
\(343\) 2.80271 18.3070i 0.151332 0.988483i
\(344\) 2.80887 + 10.4829i 0.151444 + 0.565198i
\(345\) −6.22554 + 1.66813i −0.335172 + 0.0898091i
\(346\) −10.6766 + 10.6766i −0.573977 + 0.573977i
\(347\) −11.9217 + 20.6491i −0.639993 + 1.10850i 0.345441 + 0.938440i \(0.387729\pi\)
−0.985434 + 0.170059i \(0.945604\pi\)
\(348\) 4.18735 + 7.25271i 0.224466 + 0.388786i
\(349\) 24.0068 + 6.43260i 1.28505 + 0.344329i 0.835780 0.549064i \(-0.185016\pi\)
0.449275 + 0.893394i \(0.351682\pi\)
\(350\) 7.41482 6.69947i 0.396339 0.358102i
\(351\) −2.47115 2.62553i −0.131900 0.140141i
\(352\) −1.20906 −0.0644431
\(353\) 7.04325 26.2858i 0.374874 1.39905i −0.478654 0.878004i \(-0.658875\pi\)
0.853528 0.521047i \(-0.174458\pi\)
\(354\) −4.75409 8.23432i −0.252677 0.437649i
\(355\) 4.78947 8.29560i 0.254198 0.440285i
\(356\) 11.1012 + 11.1012i 0.588364 + 0.588364i
\(357\) −3.43383 + 5.30761i −0.181737 + 0.280908i
\(358\) −1.70284 + 0.456275i −0.0899980 + 0.0241149i
\(359\) −10.9412 10.9412i −0.577455 0.577455i 0.356747 0.934201i \(-0.383886\pi\)
−0.934201 + 0.356747i \(0.883886\pi\)
\(360\) −0.957714 0.552937i −0.0504760 0.0291423i
\(361\) 5.62926 3.25005i 0.296277 0.171055i
\(362\) −22.9011 6.13632i −1.20365 0.322518i
\(363\) −9.53818 −0.500624
\(364\) 8.98462 + 3.20571i 0.470922 + 0.168025i
\(365\) −6.52066 −0.341307
\(366\) −10.9655 2.93819i −0.573175 0.153582i
\(367\) 18.7743 10.8394i 0.980012 0.565810i 0.0777381 0.996974i \(-0.475230\pi\)
0.902274 + 0.431164i \(0.141897\pi\)
\(368\) 5.04730 + 2.91406i 0.263108 + 0.151906i
\(369\) 0.193065 + 0.193065i 0.0100505 + 0.0100505i
\(370\) 10.8864 2.91700i 0.565956 0.151648i
\(371\) −7.83227 5.06719i −0.406631 0.263075i
\(372\) 6.07089 + 6.07089i 0.314761 + 0.314761i
\(373\) 3.42220 5.92742i 0.177195 0.306910i −0.763724 0.645543i \(-0.776631\pi\)
0.940919 + 0.338633i \(0.109964\pi\)
\(374\) −1.44441 2.50180i −0.0746889 0.129365i
\(375\) −2.51217 + 9.37556i −0.129728 + 0.484152i
\(376\) 6.78159 0.349734
\(377\) 28.9166 + 8.69465i 1.48928 + 0.447797i
\(378\) −1.96313 + 1.77373i −0.100972 + 0.0912311i
\(379\) −13.6802 3.66560i −0.702704 0.188289i −0.110263 0.993902i \(-0.535169\pi\)
−0.592442 + 0.805613i \(0.701836\pi\)
\(380\) −2.79220 4.83623i −0.143237 0.248093i
\(381\) −5.57371 + 9.65396i −0.285550 + 0.494587i
\(382\) 2.14485 2.14485i 0.109740 0.109740i
\(383\) 6.45564 1.72978i 0.329868 0.0883879i −0.0900840 0.995934i \(-0.528714\pi\)
0.419952 + 0.907546i \(0.362047\pi\)
\(384\) 0.258819 + 0.965926i 0.0132078 + 0.0492922i
\(385\) −3.53301 0.179060i −0.180059 0.00912575i
\(386\) −5.53251 + 9.58259i −0.281597 + 0.487741i
\(387\) −9.39867 + 5.42633i −0.477761 + 0.275836i
\(388\) 1.77794 + 0.476399i 0.0902615 + 0.0241855i
\(389\) 14.5487i 0.737648i −0.929499 0.368824i \(-0.879760\pi\)
0.929499 0.368824i \(-0.120240\pi\)
\(390\) −3.88090 + 0.914901i −0.196517 + 0.0463278i
\(391\) 13.9252i 0.704229i
\(392\) 2.48606 6.54366i 0.125565 0.330505i
\(393\) −1.93078 3.34421i −0.0973950 0.168693i
\(394\) 17.3200 + 9.99968i 0.872567 + 0.503777i
\(395\) 5.77319 + 5.77319i 0.290481 + 0.290481i
\(396\) −0.312928 1.16786i −0.0157252 0.0586873i
\(397\) −2.27144 8.47714i −0.114000 0.425455i 0.885210 0.465192i \(-0.154015\pi\)
−0.999210 + 0.0397367i \(0.987348\pi\)
\(398\) 5.29412 5.29412i 0.265370 0.265370i
\(399\) −13.0637 + 2.80028i −0.654001 + 0.140189i
\(400\) 3.27102 1.88852i 0.163551 0.0944261i
\(401\) 3.76070 14.0351i 0.187801 0.700881i −0.806213 0.591625i \(-0.798487\pi\)
0.994014 0.109256i \(-0.0348468\pi\)
\(402\) −5.97034 −0.297774
\(403\) 30.9414 + 0.937251i 1.54130 + 0.0466878i
\(404\) 7.30828i 0.363601i
\(405\) 0.286221 1.06819i 0.0142224 0.0530789i
\(406\) 6.81073 21.0847i 0.338011 1.04642i
\(407\) 10.6712 + 6.16102i 0.528951 + 0.305390i
\(408\) −1.68950 + 1.68950i −0.0836429 + 0.0836429i
\(409\) 12.4960 3.34829i 0.617887 0.165562i 0.0637202 0.997968i \(-0.479703\pi\)
0.554167 + 0.832405i \(0.313037\pi\)
\(410\) 0.291653 0.0781482i 0.0144037 0.00385946i
\(411\) 7.89359 7.89359i 0.389362 0.389362i
\(412\) 7.78215 + 4.49303i 0.383399 + 0.221355i
\(413\) −7.73252 + 23.9384i −0.380493 + 1.17793i
\(414\) −1.50843 + 5.62953i −0.0741352 + 0.276676i
\(415\) 3.41421i 0.167597i
\(416\) 3.06648 + 1.89649i 0.150347 + 0.0929831i
\(417\) 10.7792 0.527858
\(418\) 1.58021 5.89743i 0.0772906 0.288453i
\(419\) −5.77665 + 3.33515i −0.282208 + 0.162933i −0.634423 0.772986i \(-0.718762\pi\)
0.352215 + 0.935919i \(0.385429\pi\)
\(420\) 0.613247 + 2.86088i 0.0299234 + 0.139597i
\(421\) 9.25192 9.25192i 0.450911 0.450911i −0.444746 0.895657i \(-0.646706\pi\)
0.895657 + 0.444746i \(0.146706\pi\)
\(422\) −3.54750 13.2394i −0.172690 0.644486i
\(423\) 1.75520 + 6.55051i 0.0853409 + 0.318497i
\(424\) −2.49314 2.49314i −0.121078 0.121078i
\(425\) 7.81550 + 4.51228i 0.379107 + 0.218878i
\(426\) −4.33094 7.50140i −0.209835 0.363444i
\(427\) 13.6818 + 26.7382i 0.662110 + 1.29395i
\(428\) 13.9116i 0.672444i
\(429\) −3.70756 2.29297i −0.179003 0.110706i
\(430\) 12.0017i 0.578771i
\(431\) −0.548540 0.146981i −0.0264222 0.00707981i 0.245584 0.969375i \(-0.421020\pi\)
−0.272006 + 0.962296i \(0.587687\pi\)
\(432\) −0.866025 + 0.500000i −0.0416667 + 0.0240563i
\(433\) 0.449881 0.779216i 0.0216199 0.0374467i −0.855013 0.518607i \(-0.826451\pi\)
0.876633 + 0.481160i \(0.159784\pi\)
\(434\) 1.14977 22.6861i 0.0551910 1.08897i
\(435\) 2.39702 + 8.94579i 0.114928 + 0.428918i
\(436\) −4.40617 + 1.18063i −0.211017 + 0.0565419i
\(437\) −20.8106 + 20.8106i −0.995505 + 0.995505i
\(438\) −2.94819 + 5.10642i −0.140870 + 0.243994i
\(439\) −16.5233 28.6192i −0.788613 1.36592i −0.926817 0.375514i \(-0.877466\pi\)
0.138203 0.990404i \(-0.455867\pi\)
\(440\) −1.29151 0.346058i −0.0615702 0.0164977i
\(441\) 6.96413 + 0.707730i 0.331625 + 0.0337014i
\(442\) −0.260833 + 8.61086i −0.0124066 + 0.409577i
\(443\) 7.24534 0.344237 0.172118 0.985076i \(-0.444939\pi\)
0.172118 + 0.985076i \(0.444939\pi\)
\(444\) 2.63773 9.84416i 0.125181 0.467183i
\(445\) 8.68083 + 15.0356i 0.411511 + 0.712758i
\(446\) −0.915170 + 1.58512i −0.0433345 + 0.0750576i
\(447\) −16.3228 16.3228i −0.772042 0.772042i
\(448\) 1.43716 2.22139i 0.0678993 0.104951i
\(449\) 11.8519 3.17571i 0.559327 0.149871i 0.0319296 0.999490i \(-0.489835\pi\)
0.527397 + 0.849619i \(0.323168\pi\)
\(450\) 2.67077 + 2.67077i 0.125901 + 0.125901i
\(451\) 0.285888 + 0.165057i 0.0134619 + 0.00777225i
\(452\) −17.3849 + 10.0372i −0.817716 + 0.472109i
\(453\) −3.16633 0.848417i −0.148767 0.0398621i
\(454\) −8.14838 −0.382422
\(455\) 8.67975 + 5.99590i 0.406913 + 0.281092i
\(456\) −5.04976 −0.236477
\(457\) −31.9182 8.55245i −1.49307 0.400067i −0.582298 0.812976i \(-0.697846\pi\)
−0.910772 + 0.412909i \(0.864513\pi\)
\(458\) 19.0010 10.9702i 0.887857 0.512605i
\(459\) −2.06921 1.19466i −0.0965825 0.0557619i
\(460\) 4.55741 + 4.55741i 0.212491 + 0.212491i
\(461\) 7.33403 1.96515i 0.341580 0.0915261i −0.0839511 0.996470i \(-0.526754\pi\)
0.425531 + 0.904944i \(0.360087\pi\)
\(462\) −1.73761 + 2.68579i −0.0808409 + 0.124954i
\(463\) −5.06087 5.06087i −0.235198 0.235198i 0.579660 0.814858i \(-0.303185\pi\)
−0.814858 + 0.579660i \(0.803185\pi\)
\(464\) 4.18735 7.25271i 0.194393 0.336699i
\(465\) 4.74725 + 8.22248i 0.220149 + 0.381309i
\(466\) −5.94556 + 22.1891i −0.275423 + 1.02789i
\(467\) 39.0856 1.80866 0.904332 0.426829i \(-0.140369\pi\)
0.904332 + 0.426829i \(0.140369\pi\)
\(468\) −1.03820 + 3.45284i −0.0479910 + 0.159608i
\(469\) 10.5898 + 11.7205i 0.488992 + 0.541204i
\(470\) 7.24403 + 1.94103i 0.334142 + 0.0895332i
\(471\) −1.39489 2.41602i −0.0642731 0.111324i
\(472\) −4.75409 + 8.23432i −0.218825 + 0.379015i
\(473\) −9.27831 + 9.27831i −0.426617 + 0.426617i
\(474\) 7.13131 1.91083i 0.327552 0.0877673i
\(475\) 4.93650 + 18.4233i 0.226502 + 0.845318i
\(476\) 6.31344 + 0.319978i 0.289376 + 0.0146662i
\(477\) 1.76292 3.05347i 0.0807185 0.139809i
\(478\) −7.97447 + 4.60406i −0.364744 + 0.210585i
\(479\) −14.9831 4.01471i −0.684595 0.183437i −0.100274 0.994960i \(-0.531972\pi\)
−0.584320 + 0.811523i \(0.698639\pi\)
\(480\) 1.10587i 0.0504760i
\(481\) −17.4009 32.3644i −0.793413 1.47569i
\(482\) 8.08539i 0.368279i
\(483\) 13.7270 7.02405i 0.624601 0.319606i
\(484\) 4.76909 + 8.26030i 0.216777 + 0.375468i
\(485\) 1.76283 + 1.01777i 0.0800460 + 0.0462146i
\(486\) −0.707107 0.707107i −0.0320750 0.0320750i
\(487\) 1.27050 + 4.74157i 0.0575718 + 0.214861i 0.988719 0.149783i \(-0.0478574\pi\)
−0.931147 + 0.364644i \(0.881191\pi\)
\(488\) 2.93819 + 10.9655i 0.133006 + 0.496384i
\(489\) 8.02012 8.02012i 0.362682 0.362682i
\(490\) 4.52853 6.27832i 0.204578 0.283625i
\(491\) 11.4684 6.62129i 0.517562 0.298815i −0.218374 0.975865i \(-0.570075\pi\)
0.735937 + 0.677050i \(0.236742\pi\)
\(492\) 0.0706665 0.263731i 0.00318589 0.0118899i
\(493\) 20.0098 0.901198
\(494\) −13.2583 + 12.4787i −0.596520 + 0.561444i
\(495\) 1.33707i 0.0600967i
\(496\) 2.22210 8.29298i 0.0997752 0.372366i
\(497\) −7.04427 + 21.8077i −0.315979 + 0.978208i
\(498\) 2.67372 + 1.54367i 0.119812 + 0.0691736i
\(499\) 3.07331 3.07331i 0.137580 0.137580i −0.634963 0.772543i \(-0.718985\pi\)
0.772543 + 0.634963i \(0.218985\pi\)
\(500\) 9.37556 2.51217i 0.419288 0.112348i
\(501\) 5.05024 1.35321i 0.225628 0.0604568i
\(502\) 0.884607 0.884607i 0.0394819 0.0394819i
\(503\) 3.00987 + 1.73775i 0.134203 + 0.0774824i 0.565599 0.824681i \(-0.308645\pi\)
−0.431395 + 0.902163i \(0.641979\pi\)
\(504\) 2.51766 + 0.813250i 0.112146 + 0.0362250i
\(505\) 2.09178 7.80664i 0.0930832 0.347391i
\(506\) 7.04654i 0.313257i
\(507\) 5.80665 + 11.6311i 0.257882 + 0.516556i
\(508\) 11.1474 0.494587
\(509\) 4.49134 16.7619i 0.199075 0.742958i −0.792099 0.610392i \(-0.791012\pi\)
0.991174 0.132566i \(-0.0423216\pi\)
\(510\) −2.28828 + 1.32114i −0.101327 + 0.0585011i
\(511\) 15.2539 3.26976i 0.674791 0.144646i
\(512\) 0.707107 0.707107i 0.0312500 0.0312500i
\(513\) −1.30697 4.87770i −0.0577043 0.215356i
\(514\) −3.61333 13.4851i −0.159377 0.594803i
\(515\) 7.02683 + 7.02683i 0.309639 + 0.309639i
\(516\) 9.39867 + 5.42633i 0.413754 + 0.238881i
\(517\) 4.09967 + 7.10084i 0.180303 + 0.312295i
\(518\) −24.0040 + 12.2827i −1.05467 + 0.539672i
\(519\) 15.0990i 0.662772i
\(520\) 2.73278 + 2.90351i 0.119840 + 0.127327i
\(521\) 30.4244i 1.33292i −0.745542 0.666458i \(-0.767810\pi\)
0.745542 0.666458i \(-0.232190\pi\)
\(522\) 8.08934 + 2.16753i 0.354061 + 0.0948704i
\(523\) −33.0212 + 19.0648i −1.44391 + 0.833644i −0.998108 0.0614851i \(-0.980416\pi\)
−0.445806 + 0.895129i \(0.647083\pi\)
\(524\) −1.93078 + 3.34421i −0.0843465 + 0.146092i
\(525\) 0.505822 9.98031i 0.0220759 0.435576i
\(526\) −2.28386 8.52348i −0.0995810 0.371641i
\(527\) 19.8146 5.30930i 0.863137 0.231277i
\(528\) −0.854934 + 0.854934i −0.0372062 + 0.0372062i
\(529\) 5.48347 9.49764i 0.238412 0.412941i
\(530\) −1.94957 3.37675i −0.0846837 0.146677i
\(531\) −9.18419 2.46090i −0.398560 0.106794i
\(532\) 8.95694 + 9.91332i 0.388333 + 0.429797i
\(533\) −0.466181 0.867062i −0.0201926 0.0375566i
\(534\) 15.6995 0.679384
\(535\) −3.98180 + 14.8603i −0.172148 + 0.642466i
\(536\) 2.98517 + 5.17047i 0.128940 + 0.223330i
\(537\) −0.881456 + 1.52673i −0.0380376 + 0.0658831i
\(538\) 4.05637 + 4.05637i 0.174883 + 0.174883i
\(539\) 8.35461 1.35274i 0.359859 0.0582665i
\(540\) −1.06819 + 0.286221i −0.0459676 + 0.0123170i
\(541\) 9.06066 + 9.06066i 0.389548 + 0.389548i 0.874526 0.484978i \(-0.161172\pi\)
−0.484978 + 0.874526i \(0.661172\pi\)
\(542\) 21.8054 + 12.5894i 0.936624 + 0.540760i
\(543\) −20.5325 + 11.8545i −0.881136 + 0.508724i
\(544\) 2.30790 + 0.618401i 0.0989506 + 0.0265137i
\(545\) −5.04455 −0.216085
\(546\) 8.61987 4.08630i 0.368896 0.174878i
\(547\) −31.9488 −1.36603 −0.683017 0.730403i \(-0.739332\pi\)
−0.683017 + 0.730403i \(0.739332\pi\)
\(548\) −10.7828 2.88925i −0.460620 0.123423i
\(549\) −9.83139 + 5.67615i −0.419593 + 0.242252i
\(550\) 3.95485 + 2.28334i 0.168636 + 0.0973618i
\(551\) 29.9037 + 29.9037i 1.27394 + 1.27394i
\(552\) 5.62953 1.50843i 0.239609 0.0642029i
\(553\) −16.4003 10.6104i −0.697410 0.451199i
\(554\) 10.4496 + 10.4496i 0.443960 + 0.443960i
\(555\) 5.63521 9.76047i 0.239201 0.414309i
\(556\) −5.38958 9.33502i −0.228569 0.395893i
\(557\) 1.51254 5.64488i 0.0640884 0.239181i −0.926450 0.376418i \(-0.877156\pi\)
0.990538 + 0.137237i \(0.0438222\pi\)
\(558\) 8.58553 0.363454
\(559\) 38.0858 8.97852i 1.61086 0.379751i
\(560\) 2.17097 1.96153i 0.0917402 0.0828896i
\(561\) −2.79039 0.747684i −0.117811 0.0315672i
\(562\) −7.30091 12.6456i −0.307970 0.533420i
\(563\) −6.13173 + 10.6205i −0.258421 + 0.447599i −0.965819 0.259217i \(-0.916536\pi\)
0.707398 + 0.706816i \(0.249869\pi\)
\(564\) 4.79531 4.79531i 0.201919 0.201919i
\(565\) −21.4432 + 5.74570i −0.902124 + 0.241723i
\(566\) 1.57740 + 5.88695i 0.0663032 + 0.247447i
\(567\) −0.133920 + 2.64236i −0.00562411 + 0.110969i
\(568\) −4.33094 + 7.50140i −0.181722 + 0.314752i
\(569\) −10.3741 + 5.98948i −0.434904 + 0.251092i −0.701434 0.712735i \(-0.747456\pi\)
0.266529 + 0.963827i \(0.414123\pi\)
\(570\) −5.39411 1.44535i −0.225935 0.0605390i
\(571\) 33.0802i 1.38436i 0.721723 + 0.692182i \(0.243350\pi\)
−0.721723 + 0.692182i \(0.756650\pi\)
\(572\) −0.131989 + 4.35733i −0.00551872 + 0.182189i
\(573\) 3.03327i 0.126717i
\(574\) −0.643081 + 0.329062i −0.0268417 + 0.0137348i
\(575\) −11.0065 19.0639i −0.459004 0.795018i
\(576\) 0.866025 + 0.500000i 0.0360844 + 0.0208333i
\(577\) −12.2625 12.2625i −0.510495 0.510495i 0.404183 0.914678i \(-0.367556\pi\)
−0.914678 + 0.404183i \(0.867556\pi\)
\(578\) −2.92237 10.9064i −0.121554 0.453647i
\(579\) 2.86384 + 10.6880i 0.119017 + 0.444178i
\(580\) 6.54877 6.54877i 0.271923 0.271923i
\(581\) −1.71204 7.98691i −0.0710276 0.331353i
\(582\) 1.59406 0.920332i 0.0660760 0.0381490i
\(583\) 1.10333 4.11769i 0.0456954 0.170537i
\(584\) 5.89639 0.243994
\(585\) −2.09728 + 3.39114i −0.0867118 + 0.140207i
\(586\) 33.0732i 1.36624i
\(587\) −10.1586 + 37.9123i −0.419289 + 1.56481i 0.356796 + 0.934182i \(0.383869\pi\)
−0.776086 + 0.630627i \(0.782798\pi\)
\(588\) −2.86915 6.38498i −0.118322 0.263312i
\(589\) 37.5464 + 21.6774i 1.54707 + 0.893203i
\(590\) −7.43511 + 7.43511i −0.306099 + 0.306099i
\(591\) 19.3179 5.17622i 0.794632 0.212921i
\(592\) −9.84416 + 2.63773i −0.404592 + 0.108410i
\(593\) 2.17721 2.17721i 0.0894075 0.0894075i −0.660989 0.750396i \(-0.729863\pi\)
0.750396 + 0.660989i \(0.229863\pi\)
\(594\) −1.04708 0.604530i −0.0429621 0.0248042i
\(595\) 6.65238 + 2.14884i 0.272721 + 0.0880937i
\(596\) −5.97456 + 22.2974i −0.244728 + 0.913336i
\(597\) 7.48701i 0.306423i
\(598\) 11.0530 17.8718i 0.451989 0.730833i
\(599\) 22.6747 0.926462 0.463231 0.886238i \(-0.346690\pi\)
0.463231 + 0.886238i \(0.346690\pi\)
\(600\) 0.977571 3.64834i 0.0399092 0.148943i
\(601\) −8.67955 + 5.01114i −0.354046 + 0.204409i −0.666466 0.745535i \(-0.732194\pi\)
0.312420 + 0.949944i \(0.398860\pi\)
\(602\) −6.01819 28.0757i −0.245283 1.14428i
\(603\) −4.22167 + 4.22167i −0.171920 + 0.171920i
\(604\) 0.848417 + 3.16633i 0.0345216 + 0.128836i
\(605\) 2.73003 + 10.1886i 0.110991 + 0.414225i
\(606\) −5.16773 5.16773i −0.209925 0.209925i
\(607\) −9.83901 5.68056i −0.399353 0.230567i 0.286852 0.957975i \(-0.407391\pi\)
−0.686205 + 0.727408i \(0.740725\pi\)
\(608\) 2.52488 + 4.37322i 0.102397 + 0.177358i
\(609\) −10.0932 19.7250i −0.408997 0.799299i
\(610\) 12.5542i 0.508305i
\(611\) 0.740321 24.4401i 0.0299502 0.988743i
\(612\) 2.38932i 0.0965825i
\(613\) 27.6878 + 7.41894i 1.11830 + 0.299648i 0.770196 0.637807i \(-0.220158\pi\)
0.348106 + 0.937455i \(0.386825\pi\)
\(614\) 16.1129 9.30279i 0.650264 0.375430i
\(615\) 0.150971 0.261489i 0.00608773 0.0105443i
\(616\) 3.19477 + 0.161917i 0.128721 + 0.00652384i
\(617\) −5.37234 20.0498i −0.216282 0.807176i −0.985711 0.168444i \(-0.946126\pi\)
0.769429 0.638732i \(-0.220541\pi\)
\(618\) 8.67986 2.32576i 0.349155 0.0935558i
\(619\) −14.9807 + 14.9807i −0.602125 + 0.602125i −0.940876 0.338751i \(-0.889996\pi\)
0.338751 + 0.940876i \(0.389996\pi\)
\(620\) 4.74725 8.22248i 0.190654 0.330223i
\(621\) 2.91406 + 5.04730i 0.116937 + 0.202541i
\(622\) 23.2963 + 6.24222i 0.934096 + 0.250290i
\(623\) −27.8468 30.8201i −1.11566 1.23478i
\(624\) 3.50935 0.827311i 0.140487 0.0331189i
\(625\) −8.15129 −0.326051
\(626\) 0.169252 0.631657i 0.00676467 0.0252461i
\(627\) −3.05273 5.28749i −0.121914 0.211162i
\(628\) −1.39489 + 2.41602i −0.0556621 + 0.0964096i
\(629\) −17.2184 17.2184i −0.686544 0.686544i
\(630\) 2.45658 + 1.58931i 0.0978724 + 0.0633198i
\(631\) −26.9457 + 7.22008i −1.07269 + 0.287427i −0.751598 0.659621i \(-0.770717\pi\)
−0.321093 + 0.947048i \(0.604050\pi\)
\(632\) −5.22048 5.22048i −0.207660 0.207660i
\(633\) −11.8702 6.85324i −0.471797 0.272392i
\(634\) 19.9453 11.5154i 0.792129 0.457336i
\(635\) 11.9076 + 3.19063i 0.472538 + 0.126616i
\(636\) −3.52584 −0.139809
\(637\) −23.3113 9.67387i −0.923627 0.383293i
\(638\) 10.1255 0.400873
\(639\) −8.36673 2.24186i −0.330983 0.0886865i
\(640\) 0.957714 0.552937i 0.0378570 0.0218567i
\(641\) 32.8941 + 18.9914i 1.29924 + 0.750117i 0.980273 0.197649i \(-0.0633305\pi\)
0.318968 + 0.947766i \(0.396664\pi\)
\(642\) 9.83701 + 9.83701i 0.388236 + 0.388236i
\(643\) 7.84802 2.10287i 0.309496 0.0829292i −0.100728 0.994914i \(-0.532117\pi\)
0.410224 + 0.911985i \(0.365451\pi\)
\(644\) −12.9465 8.37592i −0.510164 0.330058i
\(645\) 8.48646 + 8.48646i 0.334154 + 0.334154i
\(646\) −6.03275 + 10.4490i −0.237355 + 0.411111i
\(647\) −12.0787 20.9209i −0.474863 0.822487i 0.524722 0.851273i \(-0.324169\pi\)
−0.999586 + 0.0287863i \(0.990836\pi\)
\(648\) −0.258819 + 0.965926i −0.0101674 + 0.0379452i
\(649\) −11.4959 −0.451255
\(650\) −6.44896 11.9946i −0.252949 0.470466i
\(651\) −15.2285 16.8545i −0.596850 0.660579i
\(652\) −10.9557 2.93557i −0.429058 0.114966i
\(653\) −8.38354 14.5207i −0.328073 0.568240i 0.654056 0.756446i \(-0.273066\pi\)
−0.982129 + 0.188206i \(0.939733\pi\)
\(654\) −2.28080 + 3.95046i −0.0891864 + 0.154475i
\(655\) −3.01963 + 3.01963i −0.117987 + 0.117987i
\(656\) −0.263731 + 0.0706665i −0.0102970 + 0.00275906i
\(657\) 1.52610 + 5.69547i 0.0595387 + 0.222201i
\(658\) −17.9194 0.908191i −0.698571 0.0354050i
\(659\) −14.4094 + 24.9579i −0.561312 + 0.972221i 0.436070 + 0.899913i \(0.356370\pi\)
−0.997382 + 0.0723085i \(0.976963\pi\)
\(660\) −1.15793 + 0.668533i −0.0450725 + 0.0260226i
\(661\) −13.0128 3.48676i −0.506138 0.135619i −0.00329085 0.999995i \(-0.501048\pi\)
−0.502847 + 0.864375i \(0.667714\pi\)
\(662\) 14.2381i 0.553380i
\(663\) 5.90436 + 6.27323i 0.229306 + 0.243632i
\(664\) 3.08734i 0.119812i
\(665\) 6.73033 + 13.1530i 0.260991 + 0.510051i
\(666\) −5.09571 8.82603i −0.197455 0.342002i
\(667\) −42.2696 24.4044i −1.63669 0.944941i
\(668\) −3.69703 3.69703i −0.143042 0.143042i
\(669\) 0.473727 + 1.76797i 0.0183153 + 0.0683537i
\(670\) 1.70884 + 6.37747i 0.0660182 + 0.246383i
\(671\) −9.70548 + 9.70548i −0.374676 + 0.374676i
\(672\) −0.554536 2.58698i −0.0213917 0.0997951i
\(673\) 7.61373 4.39579i 0.293488 0.169445i −0.346026 0.938225i \(-0.612469\pi\)
0.639514 + 0.768780i \(0.279136\pi\)
\(674\) −1.86388 + 6.95611i −0.0717941 + 0.267939i
\(675\) 3.77704 0.145379
\(676\) 7.16951 10.8443i 0.275751 0.417087i
\(677\) 30.0874i 1.15635i 0.815912 + 0.578176i \(0.196235\pi\)
−0.815912 + 0.578176i \(0.803765\pi\)
\(678\) −5.19562 + 19.3903i −0.199537 + 0.744681i
\(679\) −4.63417 1.49692i −0.177843 0.0574465i
\(680\) 2.28828 + 1.32114i 0.0877517 + 0.0506635i
\(681\) −5.76177 + 5.76177i −0.220792 + 0.220792i
\(682\) 10.0267 2.68665i 0.383943 0.102877i
\(683\) 5.94428 1.59276i 0.227451 0.0609454i −0.143293 0.989680i \(-0.545769\pi\)
0.370745 + 0.928735i \(0.379103\pi\)
\(684\) −3.57072 + 3.57072i −0.136530 + 0.136530i
\(685\) −10.6912 6.17255i −0.408489 0.235841i
\(686\) −7.44540 + 16.9578i −0.284267 + 0.647451i
\(687\) 5.67860 21.1928i 0.216652 0.808557i
\(688\) 10.8527i 0.413754i
\(689\) −9.25721 + 8.71287i −0.352672 + 0.331934i
\(690\) 6.44516 0.245363
\(691\) 8.79499 32.8233i 0.334577 1.24866i −0.569750 0.821818i \(-0.692960\pi\)
0.904327 0.426841i \(-0.140373\pi\)
\(692\) 13.0761 7.54949i 0.497079 0.286988i
\(693\) 0.670467 + 3.12782i 0.0254689 + 0.118816i
\(694\) 16.8599 16.8599i 0.639993 0.639993i
\(695\) −3.08522 11.5142i −0.117029 0.436759i
\(696\) −2.16753 8.08934i −0.0821601 0.306626i
\(697\) −0.461293 0.461293i −0.0174727 0.0174727i
\(698\) −21.5239 12.4268i −0.814692 0.470363i
\(699\) 11.4859 + 19.8942i 0.434438 + 0.752469i
\(700\) −8.89611 + 4.55210i −0.336241 + 0.172053i
\(701\) 37.8085i 1.42801i −0.700142 0.714004i \(-0.746880\pi\)
0.700142 0.714004i \(-0.253120\pi\)
\(702\) 1.70741 + 3.17565i 0.0644420 + 0.119857i
\(703\) 51.4643i 1.94101i
\(704\) 1.16786 + 0.312928i 0.0440154 + 0.0117939i
\(705\) 6.49482 3.74979i 0.244609 0.141225i
\(706\) −13.6065 + 23.5672i −0.512088 + 0.886962i
\(707\) −0.978726 + 19.3111i −0.0368088 + 0.726269i
\(708\) 2.46090 + 9.18419i 0.0924862 + 0.345163i
\(709\) −21.8936 + 5.86637i −0.822231 + 0.220316i −0.645321 0.763911i \(-0.723277\pi\)
−0.176909 + 0.984227i \(0.556610\pi\)
\(710\) −6.77333 + 6.77333i −0.254198 + 0.254198i
\(711\) 3.69144 6.39376i 0.138440 0.239785i
\(712\) −7.84975 13.5962i −0.294182 0.509538i
\(713\) −48.3325 12.9506i −1.81007 0.485005i
\(714\) 4.69053 4.23802i 0.175539 0.158604i
\(715\) −1.38815 + 4.61668i −0.0519138 + 0.172654i
\(716\) 1.76291 0.0658831
\(717\) −2.38324 + 8.89437i −0.0890037 + 0.332166i
\(718\) 7.73660 + 13.4002i 0.288727 + 0.500090i
\(719\) 15.9710 27.6626i 0.595618 1.03164i −0.397842 0.917454i \(-0.630241\pi\)
0.993459 0.114186i \(-0.0364261\pi\)
\(720\) 0.781970 + 0.781970i 0.0291423 + 0.0291423i
\(721\) −19.9615 12.9144i −0.743406 0.480956i
\(722\) −6.27862 + 1.68235i −0.233666 + 0.0626106i
\(723\) −5.71723 5.71723i −0.212626 0.212626i
\(724\) 20.5325 + 11.8545i 0.763086 + 0.440568i
\(725\) −27.3938 + 15.8158i −1.01738 + 0.587385i
\(726\) 9.21317 + 2.46866i 0.341933 + 0.0916206i
\(727\) 1.41270 0.0523943 0.0261971 0.999657i \(-0.491660\pi\)
0.0261971 + 0.999657i \(0.491660\pi\)
\(728\) −7.84878 5.42187i −0.290895 0.200948i
\(729\) −1.00000 −0.0370370
\(730\) 6.29847 + 1.68767i 0.233117 + 0.0624635i
\(731\) 22.4564 12.9652i 0.830581 0.479536i
\(732\) 9.83139 + 5.67615i 0.363379 + 0.209797i
\(733\) −28.1696 28.1696i −1.04047 1.04047i −0.999146 0.0413211i \(-0.986843\pi\)
−0.0413211 0.999146i \(-0.513157\pi\)
\(734\) −20.9400 + 5.61087i −0.772911 + 0.207101i
\(735\) −1.23729 7.64159i −0.0456381 0.281864i
\(736\) −4.12110 4.12110i −0.151906 0.151906i
\(737\) −3.60925 + 6.25140i −0.132948 + 0.230273i
\(738\) −0.136517 0.236455i −0.00502527 0.00870402i
\(739\) −8.26449 + 30.8435i −0.304014 + 1.13460i 0.629777 + 0.776776i \(0.283146\pi\)
−0.933791 + 0.357820i \(0.883520\pi\)
\(740\) −11.2704 −0.414309
\(741\) −0.551264 + 18.1988i −0.0202512 + 0.668551i
\(742\) 6.25390 + 6.92167i 0.229588 + 0.254102i
\(743\) 33.6460 + 9.01542i 1.23435 + 0.330744i 0.816273 0.577667i \(-0.196037\pi\)
0.418079 + 0.908411i \(0.362703\pi\)
\(744\) −4.29276 7.43529i −0.157380 0.272591i
\(745\) −12.7640 + 22.1078i −0.467635 + 0.809968i
\(746\) −4.83972 + 4.83972i −0.177195 + 0.177195i
\(747\) 2.98215 0.799063i 0.109111 0.0292362i
\(748\) 0.747684 + 2.79039i 0.0273380 + 0.102027i
\(749\) 1.86305 36.7595i 0.0680742 1.34316i
\(750\) 4.85315 8.40590i 0.177212 0.306940i
\(751\) 8.98109 5.18524i 0.327725 0.189212i −0.327106 0.944988i \(-0.606073\pi\)
0.654831 + 0.755776i \(0.272740\pi\)
\(752\) −6.55051 1.75520i −0.238873 0.0640057i
\(753\) 1.25102i 0.0455898i
\(754\) −25.6809 15.8825i −0.935243 0.578408i
\(755\) 3.62509i 0.131930i
\(756\) 2.35531 1.20520i 0.0856618 0.0438328i
\(757\) −0.746201 1.29246i −0.0271211 0.0469752i 0.852146 0.523304i \(-0.175301\pi\)
−0.879267 + 0.476328i \(0.841967\pi\)
\(758\) 12.2653 + 7.08139i 0.445497 + 0.257208i
\(759\) 4.98266 + 4.98266i 0.180859 + 0.180859i
\(760\) 1.44535 + 5.39411i 0.0524283 + 0.195665i
\(761\) 4.16868 + 15.5577i 0.151115 + 0.563967i 0.999407 + 0.0344388i \(0.0109644\pi\)
−0.848292 + 0.529528i \(0.822369\pi\)
\(762\) 7.88242 7.88242i 0.285550 0.285550i
\(763\) 11.8008 2.52957i 0.427217 0.0915767i
\(764\) −2.62689 + 1.51664i −0.0950376 + 0.0548700i
\(765\) −0.683873 + 2.55225i −0.0247255 + 0.0922768i
\(766\) −6.68337 −0.241480
\(767\) 29.1567 + 18.0322i 1.05279 + 0.651104i
\(768\) 1.00000i 0.0360844i
\(769\) −3.65824 + 13.6528i −0.131920 + 0.492331i −0.999992 0.00410760i \(-0.998693\pi\)
0.868072 + 0.496438i \(0.165359\pi\)
\(770\) 3.36628 + 1.08737i 0.121312 + 0.0391861i
\(771\) −12.0904 6.98041i −0.435426 0.251393i
\(772\) 7.82415 7.82415i 0.281597 0.281597i
\(773\) 51.3533 13.7601i 1.84705 0.494915i 0.847682 0.530505i \(-0.177998\pi\)
0.999366 + 0.0355902i \(0.0113311\pi\)
\(774\) 10.4829 2.80887i 0.376799 0.100963i
\(775\) −22.9300 + 22.9300i −0.823670 + 0.823670i
\(776\) −1.59406 0.920332i −0.0572235 0.0330380i
\(777\) −8.28817 + 25.6586i −0.297337 + 0.920496i
\(778\) −3.76548 + 14.0530i −0.134999 + 0.503823i
\(779\) 1.37876i 0.0493992i
\(780\) 3.98545 + 0.120724i 0.142702 + 0.00432262i
\(781\) −10.4727 −0.374743
\(782\) 3.60411 13.4507i 0.128883 0.480997i
\(783\) 7.25271 4.18735i 0.259191 0.149644i
\(784\) −4.09498 + 5.67725i −0.146249 + 0.202759i
\(785\) −2.18152 + 2.18152i −0.0778619 + 0.0778619i
\(786\) 0.999445 + 3.72998i 0.0356490 + 0.133044i
\(787\) 8.89838 + 33.2092i 0.317193 + 1.18378i 0.921930 + 0.387356i \(0.126611\pi\)
−0.604737 + 0.796425i \(0.706722\pi\)
\(788\) −14.1417 14.1417i −0.503777 0.503777i
\(789\) −7.64194 4.41208i −0.272060 0.157074i
\(790\) −4.08226 7.07069i −0.145240 0.251564i
\(791\) 47.2813 24.1936i 1.68113 0.860226i
\(792\) 1.20906i 0.0429621i
\(793\) 39.8393 9.39189i 1.41473 0.333516i
\(794\) 8.77618i 0.311455i
\(795\) −3.76627 1.00917i −0.133576 0.0357916i
\(796\) −6.48394 + 3.74351i −0.229817 + 0.132685i
\(797\) −5.62330 + 9.73984i −0.199188 + 0.345003i −0.948265 0.317479i \(-0.897164\pi\)
0.749078 + 0.662482i \(0.230497\pi\)
\(798\) 13.3433 + 0.676265i 0.472347 + 0.0239395i
\(799\) −4.19374 15.6513i −0.148364 0.553702i
\(800\) −3.64834 + 0.977571i −0.128988 + 0.0345624i
\(801\) 11.1012 11.1012i 0.392243 0.392243i
\(802\) −7.26512 + 12.5836i −0.256540 + 0.444341i
\(803\) 3.56454 + 6.17397i 0.125790 + 0.217875i
\(804\) 5.76691 + 1.54524i 0.203383 + 0.0544963i
\(805\) −11.4320 12.6527i −0.402925 0.445948i
\(806\) −29.6445 8.91353i −1.04418 0.313966i
\(807\) 5.73658 0.201937
\(808\) −1.89152 + 7.05926i −0.0665435 + 0.248344i
\(809\) −8.95015 15.5021i −0.314671 0.545025i 0.664697 0.747113i \(-0.268561\pi\)
−0.979367 + 0.202088i \(0.935227\pi\)
\(810\) −0.552937 + 0.957714i −0.0194282 + 0.0336507i
\(811\) −2.71012 2.71012i −0.0951653 0.0951653i 0.657921 0.753087i \(-0.271436\pi\)
−0.753087 + 0.657921i \(0.771436\pi\)
\(812\) −12.0358 + 18.6035i −0.422373 + 0.652855i
\(813\) 24.3208 6.51674i 0.852968 0.228552i
\(814\) −8.71299 8.71299i −0.305390 0.305390i
\(815\) −10.8626 6.27150i −0.380499 0.219681i
\(816\) 2.06921 1.19466i 0.0724368 0.0418214i
\(817\) 52.9360 + 14.1841i 1.85199 + 0.496240i
\(818\) −12.9368 −0.452325
\(819\) 3.20571 8.98462i 0.112017 0.313948i
\(820\) −0.301941 −0.0105443
\(821\) 3.31759 + 0.888945i 0.115785 + 0.0310244i 0.316246 0.948677i \(-0.397577\pi\)
−0.200461 + 0.979702i \(0.564244\pi\)
\(822\) −9.66763 + 5.58161i −0.337197 + 0.194681i
\(823\) −28.5856 16.5039i −0.996432 0.575290i −0.0892411 0.996010i \(-0.528444\pi\)
−0.907191 + 0.420720i \(0.861778\pi\)
\(824\) −6.35410 6.35410i −0.221355 0.221355i
\(825\) 4.41107 1.18194i 0.153574 0.0411499i
\(826\) 13.6648 21.1214i 0.475457 0.734907i
\(827\) 39.4736 + 39.4736i 1.37263 + 1.37263i 0.856521 + 0.516112i \(0.172621\pi\)
0.516112 + 0.856521i \(0.327379\pi\)
\(828\) 2.91406 5.04730i 0.101271 0.175406i
\(829\) −26.7186 46.2780i −0.927976 1.60730i −0.786704 0.617331i \(-0.788214\pi\)
−0.141272 0.989971i \(-0.545119\pi\)
\(830\) 0.883663 3.29787i 0.0306724 0.114471i
\(831\) 14.7779 0.512641
\(832\) −2.47115 2.62553i −0.0856717 0.0910240i
\(833\) −16.6395 1.69099i −0.576525 0.0585894i
\(834\) −10.4119 2.78985i −0.360533 0.0966047i
\(835\) −2.89097 5.00730i −0.100046 0.173285i
\(836\) −3.05273 + 5.28749i −0.105581 + 0.182872i
\(837\) 6.07089 6.07089i 0.209841 0.209841i
\(838\) 6.44302 1.72640i 0.222570 0.0596376i
\(839\) −1.84779 6.89605i −0.0637928 0.238078i 0.926666 0.375885i \(-0.122661\pi\)
−0.990459 + 0.137807i \(0.955995\pi\)
\(840\) 0.148099 2.92211i 0.00510989 0.100823i
\(841\) −20.5678 + 35.6246i −0.709236 + 1.22843i
\(842\) −11.3312 + 6.54209i −0.390500 + 0.225455i
\(843\) −14.1043 3.77923i −0.485777 0.130164i
\(844\) 13.7065i 0.471797i
\(845\) 10.7623 9.53169i 0.370233 0.327900i
\(846\) 6.78159i 0.233156i
\(847\) −11.4954 22.4654i −0.394987 0.771919i
\(848\) 1.76292 + 3.05347i 0.0605389 + 0.104856i
\(849\) 5.27810 + 3.04731i 0.181144 + 0.104583i
\(850\) −6.38133 6.38133i −0.218878 0.218878i
\(851\) 15.3730 + 57.3729i 0.526980 + 1.96672i
\(852\) 2.24186 + 8.36673i 0.0768048 + 0.286639i
\(853\) 5.08984 5.08984i 0.174273 0.174273i −0.614581 0.788854i \(-0.710675\pi\)
0.788854 + 0.614581i \(0.210675\pi\)
\(854\) −6.29527 29.3683i −0.215420 1.00496i
\(855\) −4.83623 + 2.79220i −0.165396 + 0.0954912i
\(856\) 3.60059 13.4376i 0.123066 0.459288i
\(857\) −35.4108 −1.20961 −0.604806 0.796373i \(-0.706749\pi\)
−0.604806 + 0.796373i \(0.706749\pi\)
\(858\) 2.98777 + 3.17443i 0.102001 + 0.108373i
\(859\) 14.6378i 0.499435i −0.968319 0.249718i \(-0.919662\pi\)
0.968319 0.249718i \(-0.0803378\pi\)
\(860\) 3.10626 11.5927i 0.105923 0.395308i
\(861\) −0.222045 + 0.687409i −0.00756728 + 0.0234268i
\(862\) 0.491807 + 0.283945i 0.0167510 + 0.00967121i
\(863\) 10.7015 10.7015i 0.364284 0.364284i −0.501104 0.865387i \(-0.667072\pi\)
0.865387 + 0.501104i \(0.167072\pi\)
\(864\) 0.965926 0.258819i 0.0328615 0.00880520i
\(865\) 16.1286 4.32165i 0.548389 0.146940i
\(866\) −0.636227 + 0.636227i −0.0216199 + 0.0216199i
\(867\) −9.77843 5.64558i −0.332093 0.191734i
\(868\) −6.98218 + 21.6155i −0.236991 + 0.733677i
\(869\) 2.31031 8.62218i 0.0783718 0.292487i
\(870\) 9.26136i 0.313990i
\(871\) 18.9597 10.1938i 0.642426 0.345404i
\(872\) 4.56160 0.154475
\(873\) 0.476399 1.77794i 0.0161237 0.0601743i
\(874\) 25.4876 14.7153i 0.862133 0.497752i
\(875\) −25.1100 + 5.38249i −0.848874 + 0.181961i
\(876\) 4.16937 4.16937i 0.140870 0.140870i
\(877\) −2.98564 11.1426i −0.100818 0.376258i 0.897019 0.441991i \(-0.145728\pi\)
−0.997837 + 0.0657339i \(0.979061\pi\)
\(878\) 8.55308 + 31.9205i 0.288652 + 1.07727i
\(879\) 23.3863 + 23.3863i 0.788800 + 0.788800i
\(880\) 1.15793 + 0.668533i 0.0390339 + 0.0225363i
\(881\) −8.02315 13.8965i −0.270307 0.468185i 0.698634 0.715480i \(-0.253792\pi\)
−0.968940 + 0.247295i \(0.920458\pi\)
\(882\) −6.54366 2.48606i −0.220336 0.0837101i
\(883\) 41.4765i 1.39579i 0.716198 + 0.697897i \(0.245881\pi\)
−0.716198 + 0.697897i \(0.754119\pi\)
\(884\) 2.48060 8.24994i 0.0834316 0.277476i
\(885\) 10.5148i 0.353452i
\(886\) −6.99847 1.87523i −0.235118 0.0629997i
\(887\) −46.4648 + 26.8265i −1.56014 + 0.900745i −0.562893 + 0.826530i \(0.690312\pi\)
−0.997242 + 0.0742151i \(0.976355\pi\)
\(888\) −5.09571 + 8.82603i −0.171001 + 0.296182i
\(889\) −29.4555 1.49286i −0.987906 0.0500691i
\(890\) −4.49353 16.7701i −0.150623 0.562134i
\(891\) −1.16786 + 0.312928i −0.0391248 + 0.0104835i
\(892\) 1.29425 1.29425i 0.0433345 0.0433345i
\(893\) 17.1227 29.6574i 0.572989 0.992447i
\(894\) 11.5420 + 19.9913i 0.386021 + 0.668608i
\(895\) 1.88313 + 0.504582i 0.0629460 + 0.0168663i
\(896\) −1.96313 + 1.77373i −0.0655834 + 0.0592563i
\(897\) −4.82166 20.4529i −0.160991 0.682903i
\(898\) −12.2700 −0.409455
\(899\) −18.6094 + 69.4513i −0.620659 + 2.31633i
\(900\) −1.88852 3.27102i −0.0629507 0.109034i
\(901\) −4.21218 + 7.29570i −0.140328 + 0.243055i
\(902\) −0.233426 0.233426i −0.00777225 0.00777225i
\(903\) −24.1080 15.5970i −0.802264 0.519035i
\(904\) 19.3903 5.19562i 0.644912 0.172804i
\(905\) 18.5397 + 18.5397i 0.616280 + 0.616280i
\(906\) 2.83886 + 1.63902i 0.0943147 + 0.0544526i
\(907\) −24.5316 + 14.1633i −0.814558 + 0.470285i −0.848536 0.529138i \(-0.822516\pi\)
0.0339785 + 0.999423i \(0.489182\pi\)
\(908\) 7.87073 + 2.10896i 0.261199 + 0.0699882i
\(909\) −7.30828 −0.242400
\(910\) −6.83214 8.03808i −0.226483 0.266460i
\(911\) −17.1135 −0.566995 −0.283498 0.958973i \(-0.591495\pi\)
−0.283498 + 0.958973i \(0.591495\pi\)
\(912\) 4.87770 + 1.30697i 0.161517 + 0.0432783i
\(913\) 3.23268 1.86639i 0.106986 0.0617685i
\(914\) 28.6171 + 16.5221i 0.946568 + 0.546502i
\(915\) 8.87717 + 8.87717i 0.293470 + 0.293470i
\(916\) −21.1928 + 5.67860i −0.700231 + 0.187626i
\(917\) 5.54967 8.57803i 0.183266 0.283272i
\(918\) 1.68950 + 1.68950i 0.0557619 + 0.0557619i
\(919\) 0.208334 0.360845i 0.00687230 0.0119032i −0.862569 0.505940i \(-0.831146\pi\)
0.869441 + 0.494037i \(0.164479\pi\)
\(920\) −3.22258 5.58167i −0.106245 0.184022i
\(921\) 4.81548 17.9716i 0.158675 0.592185i
\(922\) −7.59275 −0.250054
\(923\) 26.5615 + 16.4272i 0.874282 + 0.540706i
\(924\) 2.37354 2.14455i 0.0780836 0.0705505i
\(925\) 37.1818 + 9.96284i 1.22253 + 0.327576i
\(926\) 3.57857 + 6.19827i 0.117599 + 0.203688i
\(927\) 4.49303 7.78215i 0.147570 0.255599i
\(928\) −5.92181 + 5.92181i −0.194393 + 0.194393i
\(929\) −28.6289 + 7.67108i −0.939283 + 0.251680i −0.695809 0.718227i \(-0.744954\pi\)
−0.243474 + 0.969907i \(0.578287\pi\)
\(930\) −2.45736 9.17099i −0.0805800 0.300729i
\(931\) −22.3399 27.3941i −0.732160 0.897805i
\(932\) 11.4859 19.8942i 0.376234 0.651657i
\(933\) 20.8869 12.0590i 0.683806 0.394795i
\(934\) −37.7538 10.1161i −1.23534 0.331009i
\(935\) 3.19468i 0.104477i
\(936\) 1.89649 3.06648i 0.0619887 0.100231i
\(937\) 35.1676i 1.14888i 0.818548 + 0.574438i \(0.194779\pi\)
−0.818548 + 0.574438i \(0.805221\pi\)
\(938\) −7.19547 14.0620i −0.234940 0.459141i
\(939\) −0.326970 0.566328i −0.0106703 0.0184814i
\(940\) −6.49482 3.74979i −0.211838 0.122305i
\(941\) −18.3694 18.3694i −0.598825 0.598825i 0.341175 0.940000i \(-0.389175\pi\)
−0.940000 + 0.341175i \(0.889175\pi\)
\(942\) 0.722048 + 2.69472i 0.0235256 + 0.0877987i
\(943\) 0.411853 + 1.53705i 0.0134118 + 0.0500534i
\(944\) 6.72330 6.72330i 0.218825 0.218825i
\(945\) 2.86088 0.613247i 0.0930643 0.0199489i
\(946\) 11.3636 6.56075i 0.369461 0.213308i
\(947\) 2.18485 8.15396i 0.0709980 0.264968i −0.921298 0.388857i \(-0.872870\pi\)
0.992296 + 0.123889i \(0.0395366\pi\)
\(948\) −7.38288 −0.239785
\(949\) 0.643687 21.2500i 0.0208950 0.689803i
\(950\) 19.0732i 0.618816i
\(951\) 5.96082 22.2461i 0.193293 0.721379i
\(952\) −6.01550 1.94311i −0.194963 0.0629766i
\(953\) −39.7256 22.9356i −1.28684 0.742956i −0.308749 0.951144i \(-0.599910\pi\)
−0.978089 + 0.208188i \(0.933244\pi\)
\(954\) −2.49314 + 2.49314i −0.0807185 + 0.0807185i
\(955\) −3.24012 + 0.868187i −0.104848 + 0.0280939i
\(956\) 8.89437 2.38324i 0.287664 0.0770794i
\(957\) 7.15982 7.15982i 0.231444 0.231444i
\(958\) 13.4335 + 7.75581i 0.434016 + 0.250579i
\(959\) 28.1052 + 9.07849i 0.907565 + 0.293160i
\(960\) 0.286221 1.06819i 0.00923774 0.0344757i
\(961\) 42.7113i 1.37778i
\(962\) 8.43147 + 35.7653i 0.271842 + 1.15312i
\(963\) 13.9116 0.448296
\(964\) −2.09265 + 7.80988i −0.0673998 + 0.251539i
\(965\) 10.5971 6.11826i 0.341134 0.196954i
\(966\) −15.0772 + 3.23190i −0.485102 + 0.103985i
\(967\) −10.2351 + 10.2351i −0.329140 + 0.329140i −0.852259 0.523119i \(-0.824768\pi\)
0.523119 + 0.852259i \(0.324768\pi\)
\(968\) −2.46866 9.21317i −0.0793458 0.296122i
\(969\) 3.12278 + 11.6544i 0.100318 + 0.374392i
\(970\) −1.43934 1.43934i −0.0462146 0.0462146i
\(971\) 30.0710 + 17.3615i 0.965024 + 0.557157i 0.897716 0.440575i \(-0.145225\pi\)
0.0673086 + 0.997732i \(0.478559\pi\)
\(972\) 0.500000 + 0.866025i 0.0160375 + 0.0277778i
\(973\) 12.9911 + 25.3883i 0.416474 + 0.813910i
\(974\) 4.90883i 0.157289i
\(975\) −13.0415 3.92134i −0.417664 0.125583i
\(976\) 11.3523i 0.363379i
\(977\) 29.7442 + 7.96992i 0.951600 + 0.254980i 0.701041 0.713121i \(-0.252719\pi\)
0.250559 + 0.968101i \(0.419386\pi\)
\(978\) −9.82260 + 5.67108i −0.314092 + 0.181341i
\(979\) 9.49082 16.4386i 0.303328 0.525379i
\(980\) −5.99917 + 4.89232i −0.191636 + 0.156279i
\(981\) 1.18063 + 4.40617i 0.0376946 + 0.140678i
\(982\) −12.7914 + 3.42743i −0.408189 + 0.109374i
\(983\) 41.7064 41.7064i 1.33023 1.33023i 0.425067 0.905162i \(-0.360251\pi\)
0.905162 0.425067i \(-0.139749\pi\)
\(984\) −0.136517 + 0.236455i −0.00435201 + 0.00753790i
\(985\) −11.0584 19.1537i −0.352349 0.610287i
\(986\) −19.3280 5.17893i −0.615529 0.164931i
\(987\) −13.3131 + 12.0287i −0.423761 + 0.382879i
\(988\) 16.0363 8.62201i 0.510182 0.274303i
\(989\) −63.2505 −2.01125
\(990\) −0.346058 + 1.29151i −0.0109985 + 0.0410468i
\(991\) 26.9472 + 46.6739i 0.856006 + 1.48265i 0.875709 + 0.482840i \(0.160395\pi\)
−0.0197025 + 0.999806i \(0.506272\pi\)
\(992\) −4.29276 + 7.43529i −0.136295 + 0.236071i
\(993\) 10.0679 + 10.0679i 0.319494 + 0.319494i
\(994\) 12.4485 19.2414i 0.394842 0.610300i
\(995\) −7.99756 + 2.14294i −0.253540 + 0.0679358i
\(996\) −2.18308 2.18308i −0.0691736 0.0691736i
\(997\) 2.09912 + 1.21193i 0.0664799 + 0.0383822i 0.532872 0.846196i \(-0.321113\pi\)
−0.466392 + 0.884578i \(0.654446\pi\)
\(998\) −3.76402 + 2.17316i −0.119148 + 0.0687901i
\(999\) −9.84416 2.63773i −0.311455 0.0834542i
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 546.2.bx.b.223.3 yes 40
7.6 odd 2 546.2.bx.a.223.3 40
13.7 odd 12 546.2.bx.a.475.3 yes 40
91.20 even 12 inner 546.2.bx.b.475.3 yes 40
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
546.2.bx.a.223.3 40 7.6 odd 2
546.2.bx.a.475.3 yes 40 13.7 odd 12
546.2.bx.b.223.3 yes 40 1.1 even 1 trivial
546.2.bx.b.475.3 yes 40 91.20 even 12 inner