Properties

Label 546.2.bi.f.257.3
Level $546$
Weight $2$
Character 546.257
Analytic conductor $4.360$
Analytic rank $0$
Dimension $34$
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(17,546)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(546, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 1, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("546.17");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 546.bi (of order \(6\), degree \(2\), 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: \(34\)
Relative dimension: \(17\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 257.3
Character \(\chi\) \(=\) 546.257
Dual form 546.2.bi.f.17.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} +(-1.63421 - 0.573890i) q^{3} +1.00000 q^{4} +(-1.62172 - 0.936303i) q^{5} +(-1.63421 - 0.573890i) q^{6} +(2.04281 + 1.68135i) q^{7} +1.00000 q^{8} +(2.34130 + 1.87572i) q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +(-1.63421 - 0.573890i) q^{3} +1.00000 q^{4} +(-1.62172 - 0.936303i) q^{5} +(-1.63421 - 0.573890i) q^{6} +(2.04281 + 1.68135i) q^{7} +1.00000 q^{8} +(2.34130 + 1.87572i) q^{9} +(-1.62172 - 0.936303i) q^{10} +(2.54994 - 4.41662i) q^{11} +(-1.63421 - 0.573890i) q^{12} +(-3.20727 - 1.64725i) q^{13} +(2.04281 + 1.68135i) q^{14} +(2.11291 + 2.46081i) q^{15} +1.00000 q^{16} +2.96212 q^{17} +(2.34130 + 1.87572i) q^{18} +(-1.30077 - 2.25300i) q^{19} +(-1.62172 - 0.936303i) q^{20} +(-2.37348 - 3.92003i) q^{21} +(2.54994 - 4.41662i) q^{22} -6.06950i q^{23} +(-1.63421 - 0.573890i) q^{24} +(-0.746672 - 1.29327i) q^{25} +(-3.20727 - 1.64725i) q^{26} +(-2.74973 - 4.40897i) q^{27} +(2.04281 + 1.68135i) q^{28} +(7.30144 - 4.21549i) q^{29} +(2.11291 + 2.46081i) q^{30} +(4.09797 + 7.09789i) q^{31} +1.00000 q^{32} +(-6.70179 + 5.75431i) q^{33} +2.96212 q^{34} +(-1.73863 - 4.63937i) q^{35} +(2.34130 + 1.87572i) q^{36} -6.37656i q^{37} +(-1.30077 - 2.25300i) q^{38} +(4.29602 + 4.53258i) q^{39} +(-1.62172 - 0.936303i) q^{40} +(4.85500 - 2.80304i) q^{41} +(-2.37348 - 3.92003i) q^{42} +(-4.87733 + 8.44778i) q^{43} +(2.54994 - 4.41662i) q^{44} +(-2.04071 - 5.23406i) q^{45} -6.06950i q^{46} +(-2.70708 - 1.56293i) q^{47} +(-1.63421 - 0.573890i) q^{48} +(1.34615 + 6.86934i) q^{49} +(-0.746672 - 1.29327i) q^{50} +(-4.84074 - 1.69993i) q^{51} +(-3.20727 - 1.64725i) q^{52} +(-8.21797 + 4.74465i) q^{53} +(-2.74973 - 4.40897i) q^{54} +(-8.27059 + 4.77503i) q^{55} +(2.04281 + 1.68135i) q^{56} +(0.832761 + 4.42838i) q^{57} +(7.30144 - 4.21549i) q^{58} -2.20283i q^{59} +(2.11291 + 2.46081i) q^{60} +(5.11154 - 2.95115i) q^{61} +(4.09797 + 7.09789i) q^{62} +(1.62910 + 7.76827i) q^{63} +1.00000 q^{64} +(3.65898 + 5.67436i) q^{65} +(-6.70179 + 5.75431i) q^{66} +(9.56582 + 5.52283i) q^{67} +2.96212 q^{68} +(-3.48323 + 9.91886i) q^{69} +(-1.73863 - 4.63937i) q^{70} +(-7.27923 + 12.6080i) q^{71} +(2.34130 + 1.87572i) q^{72} +(1.99779 + 3.46027i) q^{73} -6.37656i q^{74} +(0.478024 + 2.54199i) q^{75} +(-1.30077 - 2.25300i) q^{76} +(12.6349 - 4.73499i) q^{77} +(4.29602 + 4.53258i) q^{78} +(-5.14630 + 8.91365i) q^{79} +(-1.62172 - 0.936303i) q^{80} +(1.96338 + 8.78323i) q^{81} +(4.85500 - 2.80304i) q^{82} +9.63409i q^{83} +(-2.37348 - 3.92003i) q^{84} +(-4.80375 - 2.77345i) q^{85} +(-4.87733 + 8.44778i) q^{86} +(-14.3513 + 2.69878i) q^{87} +(2.54994 - 4.41662i) q^{88} -14.7628i q^{89} +(-2.04071 - 5.23406i) q^{90} +(-3.78224 - 8.75755i) q^{91} -6.06950i q^{92} +(-2.62354 - 13.9512i) q^{93} +(-2.70708 - 1.56293i) q^{94} +4.87167i q^{95} +(-1.63421 - 0.573890i) q^{96} +(5.83860 - 10.1127i) q^{97} +(1.34615 + 6.86934i) q^{98} +(14.2545 - 5.55768i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 34 q + 34 q^{2} + 6 q^{3} + 34 q^{4} + 9 q^{5} + 6 q^{6} + 4 q^{7} + 34 q^{8} + 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 34 q + 34 q^{2} + 6 q^{3} + 34 q^{4} + 9 q^{5} + 6 q^{6} + 4 q^{7} + 34 q^{8} + 4 q^{9} + 9 q^{10} + 9 q^{11} + 6 q^{12} + 8 q^{13} + 4 q^{14} - 17 q^{15} + 34 q^{16} + 12 q^{17} + 4 q^{18} - 5 q^{19} + 9 q^{20} - 7 q^{21} + 9 q^{22} + 6 q^{24} + 16 q^{25} + 8 q^{26} - 18 q^{27} + 4 q^{28} + 27 q^{29} - 17 q^{30} - q^{31} + 34 q^{32} + 12 q^{34} - 3 q^{35} + 4 q^{36} - 5 q^{38} - 10 q^{39} + 9 q^{40} - 3 q^{41} - 7 q^{42} - 3 q^{43} + 9 q^{44} + 9 q^{45} - 27 q^{47} + 6 q^{48} - 2 q^{49} + 16 q^{50} - 36 q^{51} + 8 q^{52} - 21 q^{53} - 18 q^{54} - 57 q^{55} + 4 q^{56} - 17 q^{57} + 27 q^{58} - 17 q^{60} - 51 q^{61} - q^{62} - 24 q^{63} + 34 q^{64} - 21 q^{65} - 21 q^{67} + 12 q^{68} + 30 q^{69} - 3 q^{70} - 15 q^{71} + 4 q^{72} - 19 q^{73} - 54 q^{75} - 5 q^{76} + 9 q^{77} - 10 q^{78} - 9 q^{79} + 9 q^{80} + 28 q^{81} - 3 q^{82} - 7 q^{84} - 42 q^{85} - 3 q^{86} - 81 q^{87} + 9 q^{88} + 9 q^{90} - 72 q^{91} - 17 q^{93} - 27 q^{94} + 6 q^{96} + 19 q^{97} - 2 q^{98} - 27 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(157\) \(365\) \(379\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(-1\) \(e\left(\frac{5}{6}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) −1.63421 0.573890i −0.943513 0.331336i
\(4\) 1.00000 0.500000
\(5\) −1.62172 0.936303i −0.725257 0.418728i 0.0914273 0.995812i \(-0.470857\pi\)
−0.816685 + 0.577084i \(0.804190\pi\)
\(6\) −1.63421 0.573890i −0.667164 0.234290i
\(7\) 2.04281 + 1.68135i 0.772110 + 0.635489i
\(8\) 1.00000 0.353553
\(9\) 2.34130 + 1.87572i 0.780434 + 0.625239i
\(10\) −1.62172 0.936303i −0.512834 0.296085i
\(11\) 2.54994 4.41662i 0.768835 1.33166i −0.169360 0.985554i \(-0.554170\pi\)
0.938195 0.346107i \(-0.112497\pi\)
\(12\) −1.63421 0.573890i −0.471756 0.165668i
\(13\) −3.20727 1.64725i −0.889536 0.456865i
\(14\) 2.04281 + 1.68135i 0.545964 + 0.449359i
\(15\) 2.11291 + 2.46081i 0.545550 + 0.635378i
\(16\) 1.00000 0.250000
\(17\) 2.96212 0.718421 0.359210 0.933257i \(-0.383046\pi\)
0.359210 + 0.933257i \(0.383046\pi\)
\(18\) 2.34130 + 1.87572i 0.551850 + 0.442111i
\(19\) −1.30077 2.25300i −0.298417 0.516874i 0.677357 0.735655i \(-0.263125\pi\)
−0.975774 + 0.218781i \(0.929792\pi\)
\(20\) −1.62172 0.936303i −0.362629 0.209364i
\(21\) −2.37348 3.92003i −0.517935 0.855420i
\(22\) 2.54994 4.41662i 0.543648 0.941627i
\(23\) 6.06950i 1.26558i −0.774324 0.632789i \(-0.781910\pi\)
0.774324 0.632789i \(-0.218090\pi\)
\(24\) −1.63421 0.573890i −0.333582 0.117145i
\(25\) −0.746672 1.29327i −0.149334 0.258655i
\(26\) −3.20727 1.64725i −0.628997 0.323053i
\(27\) −2.74973 4.40897i −0.529185 0.848506i
\(28\) 2.04281 + 1.68135i 0.386055 + 0.317745i
\(29\) 7.30144 4.21549i 1.35584 0.782796i 0.366782 0.930307i \(-0.380459\pi\)
0.989060 + 0.147511i \(0.0471261\pi\)
\(30\) 2.11291 + 2.46081i 0.385762 + 0.449280i
\(31\) 4.09797 + 7.09789i 0.736017 + 1.27482i 0.954276 + 0.298928i \(0.0966291\pi\)
−0.218258 + 0.975891i \(0.570038\pi\)
\(32\) 1.00000 0.176777
\(33\) −6.70179 + 5.75431i −1.16663 + 1.00170i
\(34\) 2.96212 0.508000
\(35\) −1.73863 4.63937i −0.293881 0.784197i
\(36\) 2.34130 + 1.87572i 0.390217 + 0.312619i
\(37\) 6.37656i 1.04830i −0.851626 0.524150i \(-0.824383\pi\)
0.851626 0.524150i \(-0.175617\pi\)
\(38\) −1.30077 2.25300i −0.211013 0.365485i
\(39\) 4.29602 + 4.53258i 0.687913 + 0.725793i
\(40\) −1.62172 0.936303i −0.256417 0.148043i
\(41\) 4.85500 2.80304i 0.758223 0.437761i −0.0704341 0.997516i \(-0.522438\pi\)
0.828658 + 0.559756i \(0.189105\pi\)
\(42\) −2.37348 3.92003i −0.366236 0.604873i
\(43\) −4.87733 + 8.44778i −0.743786 + 1.28827i 0.206974 + 0.978346i \(0.433638\pi\)
−0.950760 + 0.309928i \(0.899695\pi\)
\(44\) 2.54994 4.41662i 0.384417 0.665831i
\(45\) −2.04071 5.23406i −0.304211 0.780248i
\(46\) 6.06950i 0.894899i
\(47\) −2.70708 1.56293i −0.394868 0.227977i 0.289400 0.957208i \(-0.406544\pi\)
−0.684267 + 0.729232i \(0.739878\pi\)
\(48\) −1.63421 0.573890i −0.235878 0.0828339i
\(49\) 1.34615 + 6.86934i 0.192307 + 0.981335i
\(50\) −0.746672 1.29327i −0.105595 0.182897i
\(51\) −4.84074 1.69993i −0.677839 0.238038i
\(52\) −3.20727 1.64725i −0.444768 0.228433i
\(53\) −8.21797 + 4.74465i −1.12883 + 0.651728i −0.943639 0.330976i \(-0.892622\pi\)
−0.185186 + 0.982703i \(0.559289\pi\)
\(54\) −2.74973 4.40897i −0.374191 0.599985i
\(55\) −8.27059 + 4.77503i −1.11521 + 0.643865i
\(56\) 2.04281 + 1.68135i 0.272982 + 0.224679i
\(57\) 0.832761 + 4.42838i 0.110302 + 0.586554i
\(58\) 7.30144 4.21549i 0.958726 0.553520i
\(59\) 2.20283i 0.286784i −0.989666 0.143392i \(-0.954199\pi\)
0.989666 0.143392i \(-0.0458009\pi\)
\(60\) 2.11291 + 2.46081i 0.272775 + 0.317689i
\(61\) 5.11154 2.95115i 0.654466 0.377856i −0.135699 0.990750i \(-0.543328\pi\)
0.790165 + 0.612894i \(0.209995\pi\)
\(62\) 4.09797 + 7.09789i 0.520443 + 0.901433i
\(63\) 1.62910 + 7.76827i 0.205248 + 0.978710i
\(64\) 1.00000 0.125000
\(65\) 3.65898 + 5.67436i 0.453840 + 0.703818i
\(66\) −6.70179 + 5.75431i −0.824934 + 0.708307i
\(67\) 9.56582 + 5.52283i 1.16865 + 0.674721i 0.953362 0.301830i \(-0.0975975\pi\)
0.215289 + 0.976550i \(0.430931\pi\)
\(68\) 2.96212 0.359210
\(69\) −3.48323 + 9.91886i −0.419331 + 1.19409i
\(70\) −1.73863 4.63937i −0.207806 0.554511i
\(71\) −7.27923 + 12.6080i −0.863886 + 1.49629i 0.00426326 + 0.999991i \(0.498643\pi\)
−0.868149 + 0.496303i \(0.834690\pi\)
\(72\) 2.34130 + 1.87572i 0.275925 + 0.221055i
\(73\) 1.99779 + 3.46027i 0.233823 + 0.404994i 0.958930 0.283643i \(-0.0915429\pi\)
−0.725107 + 0.688636i \(0.758210\pi\)
\(74\) 6.37656i 0.741260i
\(75\) 0.478024 + 2.54199i 0.0551975 + 0.293524i
\(76\) −1.30077 2.25300i −0.149209 0.258437i
\(77\) 12.6349 4.73499i 1.43988 0.539602i
\(78\) 4.29602 + 4.53258i 0.486428 + 0.513213i
\(79\) −5.14630 + 8.91365i −0.579004 + 1.00286i 0.416590 + 0.909094i \(0.363225\pi\)
−0.995594 + 0.0937696i \(0.970108\pi\)
\(80\) −1.62172 0.936303i −0.181314 0.104682i
\(81\) 1.96338 + 8.78323i 0.218153 + 0.975915i
\(82\) 4.85500 2.80304i 0.536145 0.309543i
\(83\) 9.63409i 1.05748i 0.848784 + 0.528739i \(0.177335\pi\)
−0.848784 + 0.528739i \(0.822665\pi\)
\(84\) −2.37348 3.92003i −0.258968 0.427710i
\(85\) −4.80375 2.77345i −0.521040 0.300823i
\(86\) −4.87733 + 8.44778i −0.525936 + 0.910948i
\(87\) −14.3513 + 2.69878i −1.53862 + 0.289340i
\(88\) 2.54994 4.41662i 0.271824 0.470813i
\(89\) 14.7628i 1.56486i −0.622741 0.782428i \(-0.713981\pi\)
0.622741 0.782428i \(-0.286019\pi\)
\(90\) −2.04071 5.23406i −0.215109 0.551719i
\(91\) −3.78224 8.75755i −0.396486 0.918041i
\(92\) 6.06950i 0.632789i
\(93\) −2.62354 13.9512i −0.272049 1.44668i
\(94\) −2.70708 1.56293i −0.279214 0.161204i
\(95\) 4.87167i 0.499822i
\(96\) −1.63421 0.573890i −0.166791 0.0585724i
\(97\) 5.83860 10.1127i 0.592820 1.02679i −0.401031 0.916065i \(-0.631348\pi\)
0.993851 0.110729i \(-0.0353187\pi\)
\(98\) 1.34615 + 6.86934i 0.135982 + 0.693909i
\(99\) 14.2545 5.55768i 1.43263 0.558568i
\(100\) −0.746672 1.29327i −0.0746672 0.129327i
\(101\) −3.15026 + 5.45640i −0.313462 + 0.542932i −0.979109 0.203334i \(-0.934822\pi\)
0.665647 + 0.746267i \(0.268156\pi\)
\(102\) −4.84074 1.69993i −0.479305 0.168318i
\(103\) 4.99182 + 2.88203i 0.491859 + 0.283975i 0.725345 0.688385i \(-0.241680\pi\)
−0.233486 + 0.972360i \(0.575013\pi\)
\(104\) −3.20727 1.64725i −0.314498 0.161526i
\(105\) 0.178796 + 8.57950i 0.0174487 + 0.837273i
\(106\) −8.21797 + 4.74465i −0.798200 + 0.460841i
\(107\) 6.14671i 0.594225i −0.954842 0.297113i \(-0.903976\pi\)
0.954842 0.297113i \(-0.0960237\pi\)
\(108\) −2.74973 4.40897i −0.264593 0.424253i
\(109\) −10.8967 + 6.29124i −1.04372 + 0.602591i −0.920884 0.389836i \(-0.872532\pi\)
−0.122834 + 0.992427i \(0.539198\pi\)
\(110\) −8.27059 + 4.77503i −0.788570 + 0.455281i
\(111\) −3.65944 + 10.4207i −0.347339 + 0.989084i
\(112\) 2.04281 + 1.68135i 0.193027 + 0.158872i
\(113\) 1.92741 + 1.11279i 0.181316 + 0.104683i 0.587911 0.808926i \(-0.299951\pi\)
−0.406595 + 0.913609i \(0.633284\pi\)
\(114\) 0.832761 + 4.42838i 0.0779953 + 0.414756i
\(115\) −5.68289 + 9.84306i −0.529933 + 0.917870i
\(116\) 7.30144 4.21549i 0.677921 0.391398i
\(117\) −4.41940 9.87263i −0.408574 0.912725i
\(118\) 2.20283i 0.202787i
\(119\) 6.05106 + 4.98036i 0.554700 + 0.456549i
\(120\) 2.11291 + 2.46081i 0.192881 + 0.224640i
\(121\) −7.50436 12.9979i −0.682214 1.18163i
\(122\) 5.11154 2.95115i 0.462777 0.267185i
\(123\) −9.54273 + 1.79452i −0.860439 + 0.161806i
\(124\) 4.09797 + 7.09789i 0.368009 + 0.637410i
\(125\) 12.1595i 1.08758i
\(126\) 1.62910 + 7.76827i 0.145132 + 0.692052i
\(127\) −3.67232 6.36064i −0.325866 0.564416i 0.655822 0.754916i \(-0.272322\pi\)
−0.981687 + 0.190500i \(0.938989\pi\)
\(128\) 1.00000 0.0883883
\(129\) 12.8187 11.0064i 1.12862 0.969061i
\(130\) 3.65898 + 5.67436i 0.320914 + 0.497675i
\(131\) −0.465541 + 0.806340i −0.0406745 + 0.0704503i −0.885646 0.464361i \(-0.846284\pi\)
0.844971 + 0.534811i \(0.179617\pi\)
\(132\) −6.70179 + 5.75431i −0.583316 + 0.500849i
\(133\) 1.13085 6.78950i 0.0980569 0.588725i
\(134\) 9.56582 + 5.52283i 0.826361 + 0.477100i
\(135\) 0.331171 + 9.72471i 0.0285027 + 0.836970i
\(136\) 2.96212 0.254000
\(137\) 2.15714 0.184297 0.0921483 0.995745i \(-0.470627\pi\)
0.0921483 + 0.995745i \(0.470627\pi\)
\(138\) −3.48323 + 9.91886i −0.296512 + 0.844349i
\(139\) 7.18997 + 4.15113i 0.609845 + 0.352094i 0.772905 0.634522i \(-0.218803\pi\)
−0.163060 + 0.986616i \(0.552136\pi\)
\(140\) −1.73863 4.63937i −0.146941 0.392098i
\(141\) 3.52699 + 4.10772i 0.297026 + 0.345933i
\(142\) −7.27923 + 12.6080i −0.610860 + 1.05804i
\(143\) −15.4536 + 9.96490i −1.29230 + 0.833307i
\(144\) 2.34130 + 1.87572i 0.195108 + 0.156310i
\(145\) −15.7879 −1.31111
\(146\) 1.99779 + 3.46027i 0.165338 + 0.286374i
\(147\) 1.74235 11.9985i 0.143707 0.989620i
\(148\) 6.37656i 0.524150i
\(149\) −1.97912 3.42793i −0.162136 0.280827i 0.773499 0.633798i \(-0.218505\pi\)
−0.935634 + 0.352971i \(0.885172\pi\)
\(150\) 0.478024 + 2.54199i 0.0390305 + 0.207553i
\(151\) 4.82241 2.78422i 0.392442 0.226576i −0.290776 0.956791i \(-0.593913\pi\)
0.683218 + 0.730215i \(0.260580\pi\)
\(152\) −1.30077 2.25300i −0.105506 0.182743i
\(153\) 6.93522 + 5.55610i 0.560680 + 0.449184i
\(154\) 12.6349 4.73499i 1.01815 0.381556i
\(155\) 15.3478i 1.23276i
\(156\) 4.29602 + 4.53258i 0.343957 + 0.362897i
\(157\) 6.31098 3.64365i 0.503671 0.290795i −0.226557 0.973998i \(-0.572747\pi\)
0.730228 + 0.683203i \(0.239414\pi\)
\(158\) −5.14630 + 8.91365i −0.409418 + 0.709132i
\(159\) 16.1528 3.03755i 1.28100 0.240894i
\(160\) −1.62172 0.936303i −0.128209 0.0740213i
\(161\) 10.2049 12.3988i 0.804262 0.977166i
\(162\) 1.96338 + 8.78323i 0.154257 + 0.690076i
\(163\) −17.1552 + 9.90456i −1.34370 + 0.775785i −0.987348 0.158567i \(-0.949313\pi\)
−0.356351 + 0.934352i \(0.615979\pi\)
\(164\) 4.85500 2.80304i 0.379112 0.218880i
\(165\) 16.2562 3.05700i 1.26555 0.237987i
\(166\) 9.63409i 0.747750i
\(167\) −13.0891 + 7.55698i −1.01286 + 0.584777i −0.912029 0.410126i \(-0.865485\pi\)
−0.100834 + 0.994903i \(0.532151\pi\)
\(168\) −2.37348 3.92003i −0.183118 0.302437i
\(169\) 7.57313 + 10.5663i 0.582548 + 0.812796i
\(170\) −4.80375 2.77345i −0.368431 0.212714i
\(171\) 1.18050 7.71483i 0.0902748 0.589968i
\(172\) −4.87733 + 8.44778i −0.371893 + 0.644137i
\(173\) −9.62713 16.6747i −0.731937 1.26775i −0.956054 0.293190i \(-0.905283\pi\)
0.224117 0.974562i \(-0.428050\pi\)
\(174\) −14.3513 + 2.69878i −1.08797 + 0.204594i
\(175\) 0.649132 3.89733i 0.0490698 0.294610i
\(176\) 2.54994 4.41662i 0.192209 0.332915i
\(177\) −1.26418 + 3.59989i −0.0950217 + 0.270584i
\(178\) 14.7628i 1.10652i
\(179\) 4.65318 + 2.68651i 0.347795 + 0.200800i 0.663714 0.747987i \(-0.268979\pi\)
−0.315919 + 0.948786i \(0.602313\pi\)
\(180\) −2.04071 5.23406i −0.152105 0.390124i
\(181\) 11.3131i 0.840893i −0.907317 0.420446i \(-0.861874\pi\)
0.907317 0.420446i \(-0.138126\pi\)
\(182\) −3.78224 8.75755i −0.280358 0.649153i
\(183\) −10.0470 + 1.88934i −0.742694 + 0.139664i
\(184\) 6.06950i 0.447450i
\(185\) −5.97039 + 10.3410i −0.438952 + 0.760287i
\(186\) −2.62354 13.9512i −0.192368 1.02296i
\(187\) 7.55323 13.0826i 0.552347 0.956693i
\(188\) −2.70708 1.56293i −0.197434 0.113988i
\(189\) 1.79583 13.6299i 0.130627 0.991432i
\(190\) 4.87167i 0.353428i
\(191\) 2.74863 1.58692i 0.198884 0.114826i −0.397251 0.917710i \(-0.630036\pi\)
0.596135 + 0.802884i \(0.296702\pi\)
\(192\) −1.63421 0.573890i −0.117939 0.0414169i
\(193\) 0.181273 + 0.104658i 0.0130483 + 0.00753344i 0.506510 0.862234i \(-0.330935\pi\)
−0.493462 + 0.869768i \(0.664269\pi\)
\(194\) 5.83860 10.1127i 0.419187 0.726053i
\(195\) −2.72309 11.3730i −0.195004 0.814435i
\(196\) 1.34615 + 6.86934i 0.0961535 + 0.490667i
\(197\) 9.71998 + 16.8355i 0.692520 + 1.19948i 0.971010 + 0.239040i \(0.0768328\pi\)
−0.278490 + 0.960439i \(0.589834\pi\)
\(198\) 14.2545 5.55768i 1.01302 0.394967i
\(199\) 14.4539i 1.02461i 0.858803 + 0.512306i \(0.171209\pi\)
−0.858803 + 0.512306i \(0.828791\pi\)
\(200\) −0.746672 1.29327i −0.0527977 0.0914483i
\(201\) −12.4631 14.5152i −0.879078 1.02382i
\(202\) −3.15026 + 5.45640i −0.221651 + 0.383911i
\(203\) 22.0031 + 3.66480i 1.54432 + 0.257219i
\(204\) −4.84074 1.69993i −0.338920 0.119019i
\(205\) −10.4980 −0.733210
\(206\) 4.99182 + 2.88203i 0.347797 + 0.200801i
\(207\) 11.3847 14.2105i 0.791289 0.987700i
\(208\) −3.20727 1.64725i −0.222384 0.114216i
\(209\) −13.2675 −0.917735
\(210\) 0.178796 + 8.57950i 0.0123381 + 0.592042i
\(211\) 5.78954 + 10.0278i 0.398568 + 0.690341i 0.993550 0.113399i \(-0.0361738\pi\)
−0.594981 + 0.803740i \(0.702840\pi\)
\(212\) −8.21797 + 4.74465i −0.564413 + 0.325864i
\(213\) 19.1314 16.4267i 1.31086 1.12554i
\(214\) 6.14671i 0.420181i
\(215\) 15.8194 9.13332i 1.07887 0.622887i
\(216\) −2.74973 4.40897i −0.187095 0.299992i
\(217\) −3.56264 + 21.3898i −0.241848 + 1.45203i
\(218\) −10.8967 + 6.29124i −0.738020 + 0.426096i
\(219\) −1.27900 6.80132i −0.0864265 0.459591i
\(220\) −8.27059 + 4.77503i −0.557603 + 0.321932i
\(221\) −9.50032 4.87936i −0.639061 0.328221i
\(222\) −3.65944 + 10.4207i −0.245606 + 0.699388i
\(223\) −3.33759 5.78088i −0.223502 0.387116i 0.732367 0.680910i \(-0.238416\pi\)
−0.955869 + 0.293794i \(0.905082\pi\)
\(224\) 2.04281 + 1.68135i 0.136491 + 0.112340i
\(225\) 0.677631 4.42849i 0.0451754 0.295233i
\(226\) 1.92741 + 1.11279i 0.128210 + 0.0740219i
\(227\) 18.4820i 1.22669i 0.789814 + 0.613346i \(0.210177\pi\)
−0.789814 + 0.613346i \(0.789823\pi\)
\(228\) 0.832761 + 4.42838i 0.0551510 + 0.293277i
\(229\) −0.100542 + 0.174145i −0.00664403 + 0.0115078i −0.869328 0.494235i \(-0.835448\pi\)
0.862684 + 0.505743i \(0.168782\pi\)
\(230\) −5.68289 + 9.84306i −0.374719 + 0.649032i
\(231\) −23.3655 + 0.486935i −1.53734 + 0.0320380i
\(232\) 7.30144 4.21549i 0.479363 0.276760i
\(233\) −11.1073 6.41280i −0.727663 0.420116i 0.0899037 0.995950i \(-0.471344\pi\)
−0.817567 + 0.575834i \(0.804677\pi\)
\(234\) −4.41940 9.87263i −0.288905 0.645394i
\(235\) 2.92675 + 5.06929i 0.190920 + 0.330684i
\(236\) 2.20283i 0.143392i
\(237\) 13.5256 11.6134i 0.878582 0.754371i
\(238\) 6.05106 + 4.98036i 0.392232 + 0.322829i
\(239\) 30.2795 1.95862 0.979311 0.202363i \(-0.0648621\pi\)
0.979311 + 0.202363i \(0.0648621\pi\)
\(240\) 2.11291 + 2.46081i 0.136388 + 0.158845i
\(241\) 8.34511 0.537556 0.268778 0.963202i \(-0.413380\pi\)
0.268778 + 0.963202i \(0.413380\pi\)
\(242\) −7.50436 12.9979i −0.482398 0.835538i
\(243\) 1.83203 15.4804i 0.117525 0.993070i
\(244\) 5.11154 2.95115i 0.327233 0.188928i
\(245\) 4.24871 12.4006i 0.271440 0.792245i
\(246\) −9.54273 + 1.79452i −0.608422 + 0.114414i
\(247\) 0.460662 + 9.36868i 0.0293112 + 0.596115i
\(248\) 4.09797 + 7.09789i 0.260221 + 0.450717i
\(249\) 5.52891 15.7441i 0.350380 0.997745i
\(250\) 12.1595i 0.769033i
\(251\) 0.325183 0.563233i 0.0205253 0.0355509i −0.855580 0.517670i \(-0.826799\pi\)
0.876106 + 0.482119i \(0.160133\pi\)
\(252\) 1.62910 + 7.76827i 0.102624 + 0.489355i
\(253\) −26.8067 15.4768i −1.68532 0.973021i
\(254\) −3.67232 6.36064i −0.230422 0.399102i
\(255\) 6.25870 + 7.28922i 0.391935 + 0.456469i
\(256\) 1.00000 0.0625000
\(257\) −7.41850 −0.462753 −0.231377 0.972864i \(-0.574323\pi\)
−0.231377 + 0.972864i \(0.574323\pi\)
\(258\) 12.8187 11.0064i 0.798057 0.685230i
\(259\) 10.7212 13.0261i 0.666183 0.809403i
\(260\) 3.65898 + 5.67436i 0.226920 + 0.351909i
\(261\) 25.0019 + 3.82570i 1.54758 + 0.236805i
\(262\) −0.465541 + 0.806340i −0.0287612 + 0.0498159i
\(263\) −17.3650 10.0257i −1.07077 0.618209i −0.142378 0.989812i \(-0.545475\pi\)
−0.928392 + 0.371603i \(0.878808\pi\)
\(264\) −6.70179 + 5.75431i −0.412467 + 0.354153i
\(265\) 17.7697 1.09159
\(266\) 1.13085 6.78950i 0.0693367 0.416291i
\(267\) −8.47223 + 24.1256i −0.518492 + 1.47646i
\(268\) 9.56582 + 5.52283i 0.584325 + 0.337360i
\(269\) 12.4850 0.761225 0.380612 0.924735i \(-0.375713\pi\)
0.380612 + 0.924735i \(0.375713\pi\)
\(270\) 0.331171 + 9.72471i 0.0201544 + 0.591827i
\(271\) −2.87931 −0.174906 −0.0874530 0.996169i \(-0.527873\pi\)
−0.0874530 + 0.996169i \(0.527873\pi\)
\(272\) 2.96212 0.179605
\(273\) 1.15511 + 16.4823i 0.0699107 + 0.997553i
\(274\) 2.15714 0.130317
\(275\) −7.61587 −0.459254
\(276\) −3.48323 + 9.91886i −0.209666 + 0.597045i
\(277\) 8.00292 0.480849 0.240424 0.970668i \(-0.422713\pi\)
0.240424 + 0.970668i \(0.422713\pi\)
\(278\) 7.18997 + 4.15113i 0.431226 + 0.248968i
\(279\) −3.71905 + 24.3049i −0.222654 + 1.45510i
\(280\) −1.73863 4.63937i −0.103903 0.277255i
\(281\) −6.16209 −0.367599 −0.183800 0.982964i \(-0.558840\pi\)
−0.183800 + 0.982964i \(0.558840\pi\)
\(282\) 3.52699 + 4.10772i 0.210029 + 0.244611i
\(283\) −11.9016 6.87141i −0.707478 0.408463i 0.102648 0.994718i \(-0.467268\pi\)
−0.810127 + 0.586255i \(0.800602\pi\)
\(284\) −7.27923 + 12.6080i −0.431943 + 0.748147i
\(285\) 2.79580 7.96134i 0.165609 0.471589i
\(286\) −15.4536 + 9.96490i −0.913791 + 0.589237i
\(287\) 14.6307 + 2.43687i 0.863624 + 0.143844i
\(288\) 2.34130 + 1.87572i 0.137962 + 0.110528i
\(289\) −8.22582 −0.483872
\(290\) −15.7879 −0.927097
\(291\) −15.3451 + 13.1757i −0.899546 + 0.772371i
\(292\) 1.99779 + 3.46027i 0.116912 + 0.202497i
\(293\) −4.43117 2.55834i −0.258872 0.149460i 0.364948 0.931028i \(-0.381087\pi\)
−0.623820 + 0.781568i \(0.714420\pi\)
\(294\) 1.74235 11.9985i 0.101616 0.699767i
\(295\) −2.06252 + 3.57238i −0.120084 + 0.207992i
\(296\) 6.37656i 0.370630i
\(297\) −26.4844 + 0.901915i −1.53678 + 0.0523344i
\(298\) −1.97912 3.42793i −0.114647 0.198575i
\(299\) −9.99799 + 19.4665i −0.578199 + 1.12578i
\(300\) 0.478024 + 2.54199i 0.0275987 + 0.146762i
\(301\) −24.1671 + 9.05674i −1.39297 + 0.522022i
\(302\) 4.82241 2.78422i 0.277498 0.160214i
\(303\) 8.27956 7.10902i 0.475648 0.408403i
\(304\) −1.30077 2.25300i −0.0746044 0.129219i
\(305\) −11.0527 −0.632875
\(306\) 6.93522 + 5.55610i 0.396460 + 0.317621i
\(307\) 1.12751 0.0643502 0.0321751 0.999482i \(-0.489757\pi\)
0.0321751 + 0.999482i \(0.489757\pi\)
\(308\) 12.6349 4.73499i 0.719941 0.269801i
\(309\) −6.50373 7.57461i −0.369984 0.430904i
\(310\) 15.3478i 0.871695i
\(311\) −5.59744 9.69505i −0.317402 0.549756i 0.662543 0.749023i \(-0.269477\pi\)
−0.979945 + 0.199268i \(0.936144\pi\)
\(312\) 4.29602 + 4.53258i 0.243214 + 0.256607i
\(313\) 28.1564 + 16.2561i 1.59150 + 0.918850i 0.993051 + 0.117686i \(0.0375475\pi\)
0.598444 + 0.801165i \(0.295786\pi\)
\(314\) 6.31098 3.64365i 0.356149 0.205623i
\(315\) 4.63150 14.1233i 0.260955 0.795760i
\(316\) −5.14630 + 8.91365i −0.289502 + 0.501432i
\(317\) −12.7161 + 22.0249i −0.714206 + 1.23704i 0.249058 + 0.968488i \(0.419879\pi\)
−0.963265 + 0.268553i \(0.913454\pi\)
\(318\) 16.1528 3.03755i 0.905805 0.170337i
\(319\) 42.9969i 2.40736i
\(320\) −1.62172 0.936303i −0.0906572 0.0523409i
\(321\) −3.52754 + 10.0450i −0.196888 + 0.560659i
\(322\) 10.2049 12.3988i 0.568699 0.690960i
\(323\) −3.85305 6.67367i −0.214389 0.371333i
\(324\) 1.96338 + 8.78323i 0.109077 + 0.487957i
\(325\) 0.264430 + 5.37783i 0.0146680 + 0.298309i
\(326\) −17.1552 + 9.90456i −0.950139 + 0.548563i
\(327\) 21.4181 4.02769i 1.18442 0.222732i
\(328\) 4.85500 2.80304i 0.268072 0.154772i
\(329\) −2.90221 7.74430i −0.160004 0.426957i
\(330\) 16.2562 3.05700i 0.894877 0.168282i
\(331\) −6.22337 + 3.59306i −0.342067 + 0.197493i −0.661186 0.750222i \(-0.729947\pi\)
0.319119 + 0.947715i \(0.396613\pi\)
\(332\) 9.63409i 0.528739i
\(333\) 11.9606 14.9294i 0.655438 0.818128i
\(334\) −13.0891 + 7.55698i −0.716202 + 0.413500i
\(335\) −10.3421 17.9130i −0.565048 0.978692i
\(336\) −2.37348 3.92003i −0.129484 0.213855i
\(337\) 19.2711 1.04976 0.524882 0.851175i \(-0.324109\pi\)
0.524882 + 0.851175i \(0.324109\pi\)
\(338\) 7.57313 + 10.5663i 0.411924 + 0.574734i
\(339\) −2.51118 2.92466i −0.136389 0.158846i
\(340\) −4.80375 2.77345i −0.260520 0.150411i
\(341\) 41.7983 2.26350
\(342\) 1.18050 7.71483i 0.0638339 0.417170i
\(343\) −8.79982 + 16.2961i −0.475146 + 0.879907i
\(344\) −4.87733 + 8.44778i −0.262968 + 0.455474i
\(345\) 14.9359 12.8243i 0.804121 0.690437i
\(346\) −9.62713 16.6747i −0.517558 0.896436i
\(347\) 7.79589i 0.418505i −0.977862 0.209253i \(-0.932897\pi\)
0.977862 0.209253i \(-0.0671031\pi\)
\(348\) −14.3513 + 2.69878i −0.769312 + 0.144670i
\(349\) 7.17103 + 12.4206i 0.383857 + 0.664859i 0.991610 0.129267i \(-0.0412623\pi\)
−0.607753 + 0.794126i \(0.707929\pi\)
\(350\) 0.649132 3.89733i 0.0346976 0.208321i
\(351\) 1.55644 + 18.6702i 0.0830764 + 0.996543i
\(352\) 2.54994 4.41662i 0.135912 0.235407i
\(353\) 22.0306 + 12.7194i 1.17257 + 0.676985i 0.954285 0.298900i \(-0.0966196\pi\)
0.218288 + 0.975884i \(0.429953\pi\)
\(354\) −1.26418 + 3.59989i −0.0671905 + 0.191332i
\(355\) 23.6098 13.6311i 1.25308 0.723466i
\(356\) 14.7628i 0.782428i
\(357\) −7.03054 11.6116i −0.372096 0.614551i
\(358\) 4.65318 + 2.68651i 0.245928 + 0.141987i
\(359\) 4.87490 8.44358i 0.257288 0.445635i −0.708227 0.705985i \(-0.750505\pi\)
0.965514 + 0.260350i \(0.0838379\pi\)
\(360\) −2.04071 5.23406i −0.107555 0.275859i
\(361\) 6.11599 10.5932i 0.321894 0.557537i
\(362\) 11.3131i 0.594601i
\(363\) 4.80433 + 25.5481i 0.252162 + 1.34092i
\(364\) −3.78224 8.75755i −0.198243 0.459020i
\(365\) 7.48214i 0.391633i
\(366\) −10.0470 + 1.88934i −0.525164 + 0.0987576i
\(367\) −12.5943 7.27133i −0.657418 0.379560i 0.133875 0.990998i \(-0.457258\pi\)
−0.791292 + 0.611438i \(0.790591\pi\)
\(368\) 6.06950i 0.316395i
\(369\) 16.6247 + 2.54385i 0.865448 + 0.132428i
\(370\) −5.97039 + 10.3410i −0.310386 + 0.537604i
\(371\) −24.7652 4.12484i −1.28574 0.214151i
\(372\) −2.62354 13.9512i −0.136024 0.723339i
\(373\) 6.87679 + 11.9109i 0.356067 + 0.616725i 0.987300 0.158868i \(-0.0507843\pi\)
−0.631233 + 0.775593i \(0.717451\pi\)
\(374\) 7.55323 13.0826i 0.390568 0.676484i
\(375\) 6.97820 19.8712i 0.360353 1.02614i
\(376\) −2.70708 1.56293i −0.139607 0.0806020i
\(377\) −30.3616 + 1.49289i −1.56370 + 0.0768879i
\(378\) 1.79583 13.6299i 0.0923675 0.701048i
\(379\) 25.1138 14.4995i 1.29001 0.744788i 0.311355 0.950294i \(-0.399217\pi\)
0.978656 + 0.205505i \(0.0658838\pi\)
\(380\) 4.87167i 0.249911i
\(381\) 2.35104 + 12.5022i 0.120447 + 0.640505i
\(382\) 2.74863 1.58692i 0.140632 0.0811939i
\(383\) −4.84882 + 2.79947i −0.247763 + 0.143046i −0.618740 0.785596i \(-0.712356\pi\)
0.370977 + 0.928642i \(0.379023\pi\)
\(384\) −1.63421 0.573890i −0.0833956 0.0292862i
\(385\) −24.9237 4.15125i −1.27023 0.211567i
\(386\) 0.181273 + 0.104658i 0.00922654 + 0.00532695i
\(387\) −27.2649 + 10.6303i −1.38595 + 0.540369i
\(388\) 5.83860 10.1127i 0.296410 0.513397i
\(389\) −4.31018 + 2.48848i −0.218535 + 0.126171i −0.605272 0.796019i \(-0.706935\pi\)
0.386737 + 0.922190i \(0.373602\pi\)
\(390\) −2.72309 11.3730i −0.137889 0.575892i
\(391\) 17.9786i 0.909218i
\(392\) 1.34615 + 6.86934i 0.0679908 + 0.346954i
\(393\) 1.22354 1.05056i 0.0617196 0.0529938i
\(394\) 9.71998 + 16.8355i 0.489685 + 0.848160i
\(395\) 16.6918 9.63699i 0.839854 0.484890i
\(396\) 14.2545 5.55768i 0.716315 0.279284i
\(397\) 8.11912 + 14.0627i 0.407487 + 0.705788i 0.994607 0.103711i \(-0.0330718\pi\)
−0.587120 + 0.809500i \(0.699738\pi\)
\(398\) 14.4539i 0.724510i
\(399\) −5.74447 + 10.4465i −0.287583 + 0.522980i
\(400\) −0.746672 1.29327i −0.0373336 0.0646637i
\(401\) −6.92045 −0.345591 −0.172795 0.984958i \(-0.555280\pi\)
−0.172795 + 0.984958i \(0.555280\pi\)
\(402\) −12.4631 14.5152i −0.621602 0.723952i
\(403\) −1.45128 29.5152i −0.0722932 1.47026i
\(404\) −3.15026 + 5.45640i −0.156731 + 0.271466i
\(405\) 5.03971 16.0823i 0.250425 0.799136i
\(406\) 22.0031 + 3.66480i 1.09200 + 0.181881i
\(407\) −28.1628 16.2598i −1.39598 0.805970i
\(408\) −4.84074 1.69993i −0.239652 0.0841592i
\(409\) 11.3829 0.562849 0.281425 0.959583i \(-0.409193\pi\)
0.281425 + 0.959583i \(0.409193\pi\)
\(410\) −10.4980 −0.518457
\(411\) −3.52522 1.23796i −0.173886 0.0610640i
\(412\) 4.99182 + 2.88203i 0.245930 + 0.141987i
\(413\) 3.70372 4.49996i 0.182248 0.221429i
\(414\) 11.3847 14.2105i 0.559526 0.698409i
\(415\) 9.02043 15.6238i 0.442795 0.766944i
\(416\) −3.20727 1.64725i −0.157249 0.0807631i
\(417\) −9.36764 10.9101i −0.458735 0.534269i
\(418\) −13.2675 −0.648937
\(419\) 4.51941 + 7.82784i 0.220788 + 0.382415i 0.955047 0.296453i \(-0.0958039\pi\)
−0.734260 + 0.678869i \(0.762471\pi\)
\(420\) 0.178796 + 8.57950i 0.00872436 + 0.418637i
\(421\) 3.07453i 0.149844i −0.997189 0.0749218i \(-0.976129\pi\)
0.997189 0.0749218i \(-0.0238707\pi\)
\(422\) 5.78954 + 10.0278i 0.281830 + 0.488145i
\(423\) −3.40646 8.73700i −0.165628 0.424807i
\(424\) −8.21797 + 4.74465i −0.399100 + 0.230421i
\(425\) −2.21174 3.83084i −0.107285 0.185823i
\(426\) 19.1314 16.4267i 0.926920 0.795875i
\(427\) 15.4038 + 2.56563i 0.745443 + 0.124160i
\(428\) 6.14671i 0.297113i
\(429\) 30.9732 7.41609i 1.49540 0.358052i
\(430\) 15.8194 9.13332i 0.762878 0.440448i
\(431\) −11.6404 + 20.1618i −0.560700 + 0.971160i 0.436736 + 0.899590i \(0.356134\pi\)
−0.997436 + 0.0715705i \(0.977199\pi\)
\(432\) −2.74973 4.40897i −0.132296 0.212127i
\(433\) −23.9459 13.8252i −1.15077 0.664396i −0.201693 0.979449i \(-0.564644\pi\)
−0.949074 + 0.315053i \(0.897978\pi\)
\(434\) −3.56264 + 21.3898i −0.171012 + 1.02674i
\(435\) 25.8008 + 9.06051i 1.23705 + 0.434418i
\(436\) −10.8967 + 6.29124i −0.521859 + 0.301296i
\(437\) −13.6746 + 7.89503i −0.654145 + 0.377671i
\(438\) −1.27900 6.80132i −0.0611128 0.324980i
\(439\) 4.37253i 0.208690i −0.994541 0.104345i \(-0.966725\pi\)
0.994541 0.104345i \(-0.0332746\pi\)
\(440\) −8.27059 + 4.77503i −0.394285 + 0.227641i
\(441\) −9.73320 + 18.6082i −0.463486 + 0.886104i
\(442\) −9.50032 4.87936i −0.451884 0.232088i
\(443\) 2.31071 + 1.33409i 0.109785 + 0.0633846i 0.553887 0.832592i \(-0.313144\pi\)
−0.444102 + 0.895976i \(0.646477\pi\)
\(444\) −3.65944 + 10.4207i −0.173669 + 0.494542i
\(445\) −13.8225 + 23.9412i −0.655248 + 1.13492i
\(446\) −3.33759 5.78088i −0.158040 0.273733i
\(447\) 1.26704 + 6.73777i 0.0599291 + 0.318685i
\(448\) 2.04281 + 1.68135i 0.0965137 + 0.0794361i
\(449\) 7.64162 13.2357i 0.360630 0.624630i −0.627434 0.778670i \(-0.715895\pi\)
0.988065 + 0.154039i \(0.0492282\pi\)
\(450\) 0.677631 4.42849i 0.0319439 0.208761i
\(451\) 28.5903i 1.34626i
\(452\) 1.92741 + 1.11279i 0.0906580 + 0.0523414i
\(453\) −9.47867 + 1.78247i −0.445347 + 0.0837478i
\(454\) 18.4820i 0.867402i
\(455\) −2.06597 + 17.7437i −0.0968541 + 0.831835i
\(456\) 0.832761 + 4.42838i 0.0389976 + 0.207378i
\(457\) 6.93705i 0.324502i −0.986750 0.162251i \(-0.948125\pi\)
0.986750 0.162251i \(-0.0518754\pi\)
\(458\) −0.100542 + 0.174145i −0.00469804 + 0.00813724i
\(459\) −8.14504 13.0599i −0.380178 0.609584i
\(460\) −5.68289 + 9.84306i −0.264966 + 0.458935i
\(461\) 17.6491 + 10.1897i 0.822001 + 0.474582i 0.851106 0.524994i \(-0.175932\pi\)
−0.0291053 + 0.999576i \(0.509266\pi\)
\(462\) −23.3655 + 0.486935i −1.08706 + 0.0226543i
\(463\) 22.4244i 1.04215i 0.853511 + 0.521075i \(0.174469\pi\)
−0.853511 + 0.521075i \(0.825531\pi\)
\(464\) 7.30144 4.21549i 0.338961 0.195699i
\(465\) −8.80793 + 25.0815i −0.408458 + 1.16313i
\(466\) −11.1073 6.41280i −0.514535 0.297067i
\(467\) −9.83436 + 17.0336i −0.455080 + 0.788221i −0.998693 0.0511146i \(-0.983723\pi\)
0.543613 + 0.839336i \(0.317056\pi\)
\(468\) −4.41940 9.87263i −0.204287 0.456363i
\(469\) 10.2554 + 27.3655i 0.473549 + 1.26362i
\(470\) 2.92675 + 5.06929i 0.135001 + 0.233829i
\(471\) −12.4045 + 2.33268i −0.571571 + 0.107484i
\(472\) 2.20283i 0.101393i
\(473\) 24.8738 + 43.0826i 1.14370 + 1.98094i
\(474\) 13.5256 11.6134i 0.621251 0.533421i
\(475\) −1.94250 + 3.36451i −0.0891280 + 0.154374i
\(476\) 6.05106 + 4.98036i 0.277350 + 0.228274i
\(477\) −28.1404 4.30594i −1.28846 0.197155i
\(478\) 30.2795 1.38495
\(479\) −16.4723 9.51026i −0.752637 0.434535i 0.0740090 0.997258i \(-0.476421\pi\)
−0.826646 + 0.562722i \(0.809754\pi\)
\(480\) 2.11291 + 2.46081i 0.0964406 + 0.112320i
\(481\) −10.5038 + 20.4513i −0.478932 + 0.932500i
\(482\) 8.34511 0.380109
\(483\) −23.7926 + 14.4058i −1.08260 + 0.655488i
\(484\) −7.50436 12.9979i −0.341107 0.590815i
\(485\) −18.9372 + 10.9334i −0.859894 + 0.496460i
\(486\) 1.83203 15.4804i 0.0831027 0.702206i
\(487\) 22.4738i 1.01838i 0.860653 + 0.509192i \(0.170056\pi\)
−0.860653 + 0.509192i \(0.829944\pi\)
\(488\) 5.11154 2.95115i 0.231389 0.133592i
\(489\) 33.7194 6.34096i 1.52484 0.286748i
\(490\) 4.24871 12.4006i 0.191937 0.560201i
\(491\) 25.7148 14.8464i 1.16049 0.670010i 0.209069 0.977901i \(-0.432957\pi\)
0.951422 + 0.307891i \(0.0996233\pi\)
\(492\) −9.54273 + 1.79452i −0.430220 + 0.0809032i
\(493\) 21.6278 12.4868i 0.974065 0.562377i
\(494\) 0.460662 + 9.36868i 0.0207261 + 0.421517i
\(495\) −28.3205 4.33351i −1.27291 0.194777i
\(496\) 4.09797 + 7.09789i 0.184004 + 0.318705i
\(497\) −36.0685 + 13.5168i −1.61789 + 0.606313i
\(498\) 5.52891 15.7441i 0.247756 0.705512i
\(499\) 6.50477 + 3.75553i 0.291193 + 0.168121i 0.638480 0.769638i \(-0.279564\pi\)
−0.347287 + 0.937759i \(0.612897\pi\)
\(500\) 12.1595i 0.543788i
\(501\) 25.7272 4.83802i 1.14941 0.216147i
\(502\) 0.325183 0.563233i 0.0145136 0.0251383i
\(503\) −14.6024 + 25.2921i −0.651089 + 1.12772i 0.331770 + 0.943360i \(0.392354\pi\)
−0.982859 + 0.184358i \(0.940979\pi\)
\(504\) 1.62910 + 7.76827i 0.0725661 + 0.346026i
\(505\) 10.2177 5.89919i 0.454682 0.262511i
\(506\) −26.8067 15.4768i −1.19170 0.688030i
\(507\) −6.31218 21.6138i −0.280334 0.959903i
\(508\) −3.67232 6.36064i −0.162933 0.282208i
\(509\) 38.2320i 1.69460i 0.531113 + 0.847301i \(0.321774\pi\)
−0.531113 + 0.847301i \(0.678226\pi\)
\(510\) 6.25870 + 7.28922i 0.277140 + 0.322772i
\(511\) −1.73681 + 10.4276i −0.0768320 + 0.461292i
\(512\) 1.00000 0.0441942
\(513\) −6.35665 + 11.9302i −0.280653 + 0.526731i
\(514\) −7.41850 −0.327216
\(515\) −5.39691 9.34772i −0.237816 0.411910i
\(516\) 12.8187 11.0064i 0.564311 0.484531i
\(517\) −13.8057 + 7.97075i −0.607176 + 0.350553i
\(518\) 10.7212 13.0261i 0.471063 0.572334i
\(519\) 6.16335 + 32.7749i 0.270541 + 1.43866i
\(520\) 3.65898 + 5.67436i 0.160457 + 0.248837i
\(521\) 1.01347 + 1.75537i 0.0444008 + 0.0769044i 0.887372 0.461055i \(-0.152529\pi\)
−0.842971 + 0.537959i \(0.819195\pi\)
\(522\) 25.0019 + 3.82570i 1.09430 + 0.167446i
\(523\) 14.9844i 0.655221i −0.944813 0.327610i \(-0.893757\pi\)
0.944813 0.327610i \(-0.106243\pi\)
\(524\) −0.465541 + 0.806340i −0.0203372 + 0.0352251i
\(525\) −3.29746 + 5.99653i −0.143913 + 0.261710i
\(526\) −17.3650 10.0257i −0.757149 0.437140i
\(527\) 12.1387 + 21.0248i 0.528770 + 0.915856i
\(528\) −6.70179 + 5.75431i −0.291658 + 0.250424i
\(529\) −13.8389 −0.601690
\(530\) 17.7697 0.771867
\(531\) 4.13188 5.15748i 0.179308 0.223816i
\(532\) 1.13085 6.78950i 0.0490285 0.294362i
\(533\) −20.1886 + 0.992681i −0.874465 + 0.0429978i
\(534\) −8.47223 + 24.1256i −0.366629 + 1.04402i
\(535\) −5.75519 + 9.96828i −0.248818 + 0.430966i
\(536\) 9.56582 + 5.52283i 0.413180 + 0.238550i
\(537\) −6.06252 7.06075i −0.261617 0.304694i
\(538\) 12.4850 0.538267
\(539\) 33.7719 + 11.5710i 1.45466 + 0.498397i
\(540\) 0.331171 + 9.72471i 0.0142513 + 0.418485i
\(541\) −0.930484 0.537215i −0.0400046 0.0230967i 0.479864 0.877343i \(-0.340686\pi\)
−0.519869 + 0.854246i \(0.674019\pi\)
\(542\) −2.87931 −0.123677
\(543\) −6.49245 + 18.4879i −0.278618 + 0.793393i
\(544\) 2.96212 0.127000
\(545\) 23.5620 1.00929
\(546\) 1.15511 + 16.4823i 0.0494343 + 0.705377i
\(547\) −26.8765 −1.14916 −0.574578 0.818450i \(-0.694834\pi\)
−0.574578 + 0.818450i \(0.694834\pi\)
\(548\) 2.15714 0.0921483
\(549\) 17.5032 + 2.67827i 0.747017 + 0.114306i
\(550\) −7.61587 −0.324742
\(551\) −18.9950 10.9668i −0.809214 0.467200i
\(552\) −3.48323 + 9.91886i −0.148256 + 0.422175i
\(553\) −25.4998 + 9.55619i −1.08436 + 0.406370i
\(554\) 8.00292 0.340011
\(555\) 15.6915 13.4731i 0.666067 0.571900i
\(556\) 7.18997 + 4.15113i 0.304922 + 0.176047i
\(557\) −13.5744 + 23.5116i −0.575167 + 0.996219i 0.420856 + 0.907127i \(0.361730\pi\)
−0.996023 + 0.0890918i \(0.971604\pi\)
\(558\) −3.71905 + 24.3049i −0.157440 + 1.02891i
\(559\) 29.5585 19.0601i 1.25019 0.806157i
\(560\) −1.73863 4.63937i −0.0734704 0.196049i
\(561\) −19.8515 + 17.0450i −0.838133 + 0.719640i
\(562\) −6.16209 −0.259932
\(563\) 16.3087 0.687329 0.343664 0.939093i \(-0.388332\pi\)
0.343664 + 0.939093i \(0.388332\pi\)
\(564\) 3.52699 + 4.10772i 0.148513 + 0.172966i
\(565\) −2.08382 3.60929i −0.0876671 0.151844i
\(566\) −11.9016 6.87141i −0.500263 0.288827i
\(567\) −10.7568 + 21.2436i −0.451745 + 0.892147i
\(568\) −7.27923 + 12.6080i −0.305430 + 0.529020i
\(569\) 26.1439i 1.09601i −0.836475 0.548005i \(-0.815388\pi\)
0.836475 0.548005i \(-0.184612\pi\)
\(570\) 2.79580 7.96134i 0.117103 0.333464i
\(571\) −0.114124 0.197668i −0.00477593 0.00827215i 0.863628 0.504130i \(-0.168187\pi\)
−0.868403 + 0.495858i \(0.834854\pi\)
\(572\) −15.4536 + 9.96490i −0.646148 + 0.416653i
\(573\) −5.40256 + 1.01596i −0.225695 + 0.0424422i
\(574\) 14.6307 + 2.43687i 0.610674 + 0.101713i
\(575\) −7.84953 + 4.53193i −0.327348 + 0.188995i
\(576\) 2.34130 + 1.87572i 0.0975542 + 0.0781548i
\(577\) −8.82331 15.2824i −0.367319 0.636215i 0.621826 0.783155i \(-0.286391\pi\)
−0.989145 + 0.146940i \(0.953058\pi\)
\(578\) −8.22582 −0.342149
\(579\) −0.236176 0.275064i −0.00981514 0.0114313i
\(580\) −15.7879 −0.655557
\(581\) −16.1982 + 19.6806i −0.672016 + 0.816490i
\(582\) −15.3451 + 13.1757i −0.636075 + 0.546149i
\(583\) 48.3942i 2.00428i
\(584\) 1.99779 + 3.46027i 0.0826690 + 0.143187i
\(585\) −2.07673 + 20.1486i −0.0858620 + 0.833042i
\(586\) −4.43117 2.55834i −0.183050 0.105684i
\(587\) 13.2115 7.62767i 0.545298 0.314828i −0.201926 0.979401i \(-0.564720\pi\)
0.747223 + 0.664573i \(0.231387\pi\)
\(588\) 1.74235 11.9985i 0.0718535 0.494810i
\(589\) 10.6610 18.4655i 0.439281 0.760857i
\(590\) −2.06252 + 3.57238i −0.0849124 + 0.147073i
\(591\) −6.22279 33.0910i −0.255971 1.36118i
\(592\) 6.37656i 0.262075i
\(593\) 0.0222995 + 0.0128746i 0.000915730 + 0.000528697i 0.500458 0.865761i \(-0.333165\pi\)
−0.499542 + 0.866290i \(0.666498\pi\)
\(594\) −26.4844 + 0.901915i −1.08667 + 0.0370060i
\(595\) −5.15003 13.7424i −0.211131 0.563383i
\(596\) −1.97912 3.42793i −0.0810678 0.140414i
\(597\) 8.29496 23.6208i 0.339490 0.966734i
\(598\) −9.99799 + 19.4665i −0.408848 + 0.796045i
\(599\) 21.8300 12.6035i 0.891949 0.514967i 0.0173692 0.999849i \(-0.494471\pi\)
0.874579 + 0.484882i \(0.161138\pi\)
\(600\) 0.478024 + 2.54199i 0.0195153 + 0.103776i
\(601\) −15.4945 + 8.94574i −0.632033 + 0.364904i −0.781539 0.623856i \(-0.785565\pi\)
0.149506 + 0.988761i \(0.452232\pi\)
\(602\) −24.1671 + 9.05674i −0.984978 + 0.369125i
\(603\) 12.0372 + 30.8734i 0.490192 + 1.25726i
\(604\) 4.82241 2.78422i 0.196221 0.113288i
\(605\) 28.1054i 1.14265i
\(606\) 8.27956 7.10902i 0.336334 0.288784i
\(607\) −22.8924 + 13.2169i −0.929175 + 0.536459i −0.886551 0.462632i \(-0.846905\pi\)
−0.0426244 + 0.999091i \(0.513572\pi\)
\(608\) −1.30077 2.25300i −0.0527532 0.0913713i
\(609\) −33.8546 18.6165i −1.37186 0.754377i
\(610\) −11.0527 −0.447510
\(611\) 6.10778 + 9.47197i 0.247094 + 0.383195i
\(612\) 6.93522 + 5.55610i 0.280340 + 0.224592i
\(613\) −7.14521 4.12529i −0.288593 0.166619i 0.348714 0.937229i \(-0.386618\pi\)
−0.637307 + 0.770610i \(0.719952\pi\)
\(614\) 1.12751 0.0455024
\(615\) 17.1559 + 6.02468i 0.691793 + 0.242938i
\(616\) 12.6349 4.73499i 0.509075 0.190778i
\(617\) 2.53770 4.39542i 0.102164 0.176953i −0.810412 0.585860i \(-0.800757\pi\)
0.912576 + 0.408907i \(0.134090\pi\)
\(618\) −6.50373 7.57461i −0.261619 0.304695i
\(619\) 14.6995 + 25.4603i 0.590822 + 1.02333i 0.994122 + 0.108266i \(0.0345298\pi\)
−0.403300 + 0.915068i \(0.632137\pi\)
\(620\) 15.3478i 0.616381i
\(621\) −26.7602 + 16.6895i −1.07385 + 0.669726i
\(622\) −5.59744 9.69505i −0.224437 0.388736i
\(623\) 24.8214 30.1576i 0.994449 1.20824i
\(624\) 4.29602 + 4.53258i 0.171978 + 0.181448i
\(625\) 7.65160 13.2530i 0.306064 0.530118i
\(626\) 28.1564 + 16.2561i 1.12536 + 0.649725i
\(627\) 21.6820 + 7.61411i 0.865895 + 0.304078i
\(628\) 6.31098 3.64365i 0.251836 0.145397i
\(629\) 18.8882i 0.753120i
\(630\) 4.63150 14.1233i 0.184523 0.562687i
\(631\) 31.4596 + 18.1632i 1.25239 + 0.723066i 0.971583 0.236699i \(-0.0760655\pi\)
0.280804 + 0.959765i \(0.409399\pi\)
\(632\) −5.14630 + 8.91365i −0.204709 + 0.354566i
\(633\) −3.70650 19.7101i −0.147320 0.783405i
\(634\) −12.7161 + 22.0249i −0.505020 + 0.874721i
\(635\) 13.7536i 0.545796i
\(636\) 16.1528 3.03755i 0.640501 0.120447i
\(637\) 6.99807 24.2493i 0.277274 0.960791i
\(638\) 42.9969i 1.70226i
\(639\) −40.6919 + 15.8653i −1.60975 + 0.627623i
\(640\) −1.62172 0.936303i −0.0641043 0.0370106i
\(641\) 0.739636i 0.0292139i −0.999893 0.0146069i \(-0.995350\pi\)
0.999893 0.0146069i \(-0.00464970\pi\)
\(642\) −3.52754 + 10.0450i −0.139221 + 0.396446i
\(643\) −2.41482 + 4.18259i −0.0952313 + 0.164945i −0.909705 0.415255i \(-0.863692\pi\)
0.814474 + 0.580200i \(0.197026\pi\)
\(644\) 10.2049 12.3988i 0.402131 0.488583i
\(645\) −31.0937 + 5.84720i −1.22431 + 0.230233i
\(646\) −3.85305 6.67367i −0.151596 0.262572i
\(647\) 2.02071 3.49997i 0.0794422 0.137598i −0.823567 0.567219i \(-0.808019\pi\)
0.903009 + 0.429621i \(0.141353\pi\)
\(648\) 1.96338 + 8.78323i 0.0771287 + 0.345038i
\(649\) −9.72906 5.61707i −0.381899 0.220489i
\(650\) 0.264430 + 5.37783i 0.0103718 + 0.210936i
\(651\) 18.0975 32.9108i 0.709296 1.28988i
\(652\) −17.1552 + 9.90456i −0.671849 + 0.387892i
\(653\) 46.7035i 1.82765i −0.406108 0.913825i \(-0.633114\pi\)
0.406108 0.913825i \(-0.366886\pi\)
\(654\) 21.4181 4.02769i 0.837513 0.157495i
\(655\) 1.50996 0.871775i 0.0589989 0.0340631i
\(656\) 4.85500 2.80304i 0.189556 0.109440i
\(657\) −1.81306 + 11.8488i −0.0707343 + 0.462266i
\(658\) −2.90221 7.74430i −0.113140 0.301904i
\(659\) −40.3288 23.2838i −1.57099 0.907009i −0.996048 0.0888111i \(-0.971693\pi\)
−0.574937 0.818198i \(-0.694973\pi\)
\(660\) 16.2562 3.05700i 0.632773 0.118994i
\(661\) −22.2936 + 38.6137i −0.867122 + 1.50190i −0.00219813 + 0.999998i \(0.500700\pi\)
−0.864924 + 0.501902i \(0.832634\pi\)
\(662\) −6.22337 + 3.59306i −0.241878 + 0.139648i
\(663\) 12.7253 + 13.4261i 0.494211 + 0.521425i
\(664\) 9.63409i 0.373875i
\(665\) −8.19096 + 9.95189i −0.317632 + 0.385918i
\(666\) 11.9606 14.9294i 0.463464 0.578504i
\(667\) −25.5859 44.3161i −0.990690 1.71593i
\(668\) −13.0891 + 7.55698i −0.506432 + 0.292388i
\(669\) 2.13675 + 11.3626i 0.0826114 + 0.439303i
\(670\) −10.3421 17.9130i −0.399549 0.692040i
\(671\) 30.1010i 1.16204i
\(672\) −2.37348 3.92003i −0.0915589 0.151218i
\(673\) −7.92610 13.7284i −0.305529 0.529191i 0.671850 0.740687i \(-0.265500\pi\)
−0.977379 + 0.211496i \(0.932166\pi\)
\(674\) 19.2711 0.742295
\(675\) −3.64886 + 6.84821i −0.140445 + 0.263588i
\(676\) 7.57313 + 10.5663i 0.291274 + 0.406398i
\(677\) −2.65460 + 4.59790i −0.102024 + 0.176711i −0.912519 0.409035i \(-0.865865\pi\)
0.810494 + 0.585747i \(0.199199\pi\)
\(678\) −2.51118 2.92466i −0.0964415 0.112321i
\(679\) 28.9302 10.8417i 1.11024 0.416067i
\(680\) −4.80375 2.77345i −0.184215 0.106357i
\(681\) 10.6066 30.2035i 0.406447 1.15740i
\(682\) 41.7983 1.60054
\(683\) 11.9713 0.458070 0.229035 0.973418i \(-0.426443\pi\)
0.229035 + 0.973418i \(0.426443\pi\)
\(684\) 1.18050 7.71483i 0.0451374 0.294984i
\(685\) −3.49828 2.01973i −0.133662 0.0771701i
\(686\) −8.79982 + 16.2961i −0.335979 + 0.622188i
\(687\) 0.264247 0.226889i 0.0100817 0.00865635i
\(688\) −4.87733 + 8.44778i −0.185946 + 0.322069i
\(689\) 34.1729 1.68029i 1.30188 0.0640141i
\(690\) 14.9359 12.8243i 0.568600 0.488213i
\(691\) 38.9891 1.48322 0.741608 0.670834i \(-0.234064\pi\)
0.741608 + 0.670834i \(0.234064\pi\)
\(692\) −9.62713 16.6747i −0.365969 0.633876i
\(693\) 38.4636 + 12.6135i 1.46111 + 0.479146i
\(694\) 7.79589i 0.295928i
\(695\) −7.77343 13.4640i −0.294863 0.510718i
\(696\) −14.3513 + 2.69878i −0.543986 + 0.102297i
\(697\) 14.3811 8.30294i 0.544723 0.314496i
\(698\) 7.17103 + 12.4206i 0.271428 + 0.470127i
\(699\) 14.4714 + 16.8542i 0.547360 + 0.637486i
\(700\) 0.649132 3.89733i 0.0245349 0.147305i
\(701\) 41.8339i 1.58005i −0.613078 0.790023i \(-0.710069\pi\)
0.613078 0.790023i \(-0.289931\pi\)
\(702\) 1.55644 + 18.6702i 0.0587439 + 0.704662i
\(703\) −14.3664 + 8.29444i −0.541839 + 0.312831i
\(704\) 2.54994 4.41662i 0.0961044 0.166458i
\(705\) −1.87373 9.96393i −0.0705686 0.375263i
\(706\) 22.0306 + 12.7194i 0.829134 + 0.478701i
\(707\) −15.6095 + 5.84973i −0.587055 + 0.220002i
\(708\) −1.26418 + 3.59989i −0.0475108 + 0.135292i
\(709\) 9.91254 5.72301i 0.372273 0.214932i −0.302178 0.953252i \(-0.597714\pi\)
0.674451 + 0.738320i \(0.264380\pi\)
\(710\) 23.6098 13.6311i 0.886061 0.511567i
\(711\) −28.7685 + 11.2165i −1.07890 + 0.420653i
\(712\) 14.7628i 0.553260i
\(713\) 43.0807 24.8726i 1.61338 0.931488i
\(714\) −7.03054 11.6116i −0.263111 0.434553i
\(715\) 34.3917 1.69105i 1.28618 0.0632418i
\(716\) 4.65318 + 2.68651i 0.173897 + 0.100400i
\(717\) −49.4832 17.3771i −1.84798 0.648961i
\(718\) 4.87490 8.44358i 0.181930 0.315112i
\(719\) −16.1498 27.9723i −0.602286 1.04319i −0.992474 0.122455i \(-0.960923\pi\)
0.390188 0.920735i \(-0.372410\pi\)
\(720\) −2.04071 5.23406i −0.0760526 0.195062i
\(721\) 5.35166 + 14.2804i 0.199306 + 0.531831i
\(722\) 6.11599 10.5932i 0.227614 0.394238i
\(723\) −13.6377 4.78917i −0.507191 0.178111i
\(724\) 11.3131i 0.420446i
\(725\) −10.9036 6.29518i −0.404948 0.233797i
\(726\) 4.80433 + 25.5481i 0.178306 + 0.948177i
\(727\) 35.0984i 1.30173i 0.759195 + 0.650863i \(0.225593\pi\)
−0.759195 + 0.650863i \(0.774407\pi\)
\(728\) −3.78224 8.75755i −0.140179 0.324576i
\(729\) −11.8780 + 24.2469i −0.439926 + 0.898034i
\(730\) 7.48214i 0.276926i
\(731\) −14.4473 + 25.0234i −0.534351 + 0.925523i
\(732\) −10.0470 + 1.88934i −0.371347 + 0.0698321i
\(733\) 1.14358 1.98073i 0.0422389 0.0731600i −0.844133 0.536134i \(-0.819884\pi\)
0.886372 + 0.462974i \(0.153218\pi\)
\(734\) −12.5943 7.27133i −0.464864 0.268390i
\(735\) −14.0599 + 17.8269i −0.518606 + 0.657555i
\(736\) 6.06950i 0.223725i
\(737\) 48.7845 28.1657i 1.79700 1.03750i
\(738\) 16.6247 + 2.54385i 0.611964 + 0.0936405i
\(739\) −5.64299 3.25798i −0.207581 0.119847i 0.392606 0.919707i \(-0.371574\pi\)
−0.600186 + 0.799860i \(0.704907\pi\)
\(740\) −5.97039 + 10.3410i −0.219476 + 0.380144i
\(741\) 4.62377 15.5748i 0.169858 0.572154i
\(742\) −24.7652 4.12484i −0.909158 0.151428i
\(743\) 14.5039 + 25.1215i 0.532097 + 0.921620i 0.999298 + 0.0374682i \(0.0119293\pi\)
−0.467201 + 0.884151i \(0.654737\pi\)
\(744\) −2.62354 13.9512i −0.0961838 0.511478i
\(745\) 7.41222i 0.271563i
\(746\) 6.87679 + 11.9109i 0.251777 + 0.436091i
\(747\) −18.0708 + 22.5563i −0.661177 + 0.825292i
\(748\) 7.55323 13.0826i 0.276173 0.478346i
\(749\) 10.3348 12.5566i 0.377624 0.458807i
\(750\) 6.97820 19.8712i 0.254808 0.725593i
\(751\) 30.8433 1.12549 0.562744 0.826631i \(-0.309746\pi\)
0.562744 + 0.826631i \(0.309746\pi\)
\(752\) −2.70708 1.56293i −0.0987169 0.0569942i
\(753\) −0.854651 + 0.733823i −0.0311452 + 0.0267420i
\(754\) −30.3616 + 1.49289i −1.10571 + 0.0543680i
\(755\) −10.4275 −0.379495
\(756\) 1.79583 13.6299i 0.0653137 0.495716i
\(757\) −10.6357 18.4215i −0.386560 0.669542i 0.605424 0.795903i \(-0.293004\pi\)
−0.991984 + 0.126361i \(0.959670\pi\)
\(758\) 25.1138 14.4995i 0.912176 0.526645i
\(759\) 34.9258 + 40.6765i 1.26773 + 1.47647i
\(760\) 4.87167i 0.176714i
\(761\) 21.3492 12.3260i 0.773908 0.446816i −0.0603590 0.998177i \(-0.519225\pi\)
0.834267 + 0.551361i \(0.185891\pi\)
\(762\) 2.35104 + 12.5022i 0.0851692 + 0.452905i
\(763\) −32.8377 5.46939i −1.18881 0.198005i
\(764\) 2.74863 1.58692i 0.0994418 0.0574128i
\(765\) −6.04482 15.5039i −0.218551 0.560546i
\(766\) −4.84882 + 2.79947i −0.175195 + 0.101149i
\(767\) −3.62861 + 7.06506i −0.131022 + 0.255105i
\(768\) −1.63421 0.573890i −0.0589696 0.0207085i
\(769\) 6.30372 + 10.9184i 0.227318 + 0.393726i 0.957012 0.290047i \(-0.0936710\pi\)
−0.729694 + 0.683773i \(0.760338\pi\)
\(770\) −24.9237 4.15125i −0.898189 0.149601i
\(771\) 12.1234 + 4.25740i 0.436614 + 0.153327i
\(772\) 0.181273 + 0.104658i 0.00652415 + 0.00376672i
\(773\) 20.1987i 0.726496i −0.931692 0.363248i \(-0.881668\pi\)
0.931692 0.363248i \(-0.118332\pi\)
\(774\) −27.2649 + 10.6303i −0.980018 + 0.382099i
\(775\) 6.11968 10.5996i 0.219826 0.380749i
\(776\) 5.83860 10.1127i 0.209593 0.363026i
\(777\) −24.9963 + 15.1346i −0.896736 + 0.542952i
\(778\) −4.31018 + 2.48848i −0.154527 + 0.0892164i
\(779\) −12.6305 7.29222i −0.452534 0.261271i
\(780\) −2.72309 11.3730i −0.0975022 0.407217i
\(781\) 37.1232 + 64.2992i 1.32837 + 2.30081i
\(782\) 17.9786i 0.642914i
\(783\) −38.6629 20.6004i −1.38170 0.736197i
\(784\) 1.34615 + 6.86934i 0.0480767 + 0.245334i
\(785\) −13.6462 −0.487055
\(786\) 1.22354 1.05056i 0.0436423 0.0374723i
\(787\) 17.5342 0.625026 0.312513 0.949913i \(-0.398829\pi\)
0.312513 + 0.949913i \(0.398829\pi\)
\(788\) 9.71998 + 16.8355i 0.346260 + 0.599740i
\(789\) 22.6244 + 26.3497i 0.805451 + 0.938073i
\(790\) 16.6918 9.63699i 0.593866 0.342869i
\(791\) 2.06635 + 5.51388i 0.0734710 + 0.196051i
\(792\) 14.2545 5.55768i 0.506511 0.197483i
\(793\) −21.2554 + 1.04513i −0.754800 + 0.0371138i
\(794\) 8.11912 + 14.0627i 0.288137 + 0.499068i
\(795\) −29.0395 10.1979i −1.02992 0.361681i
\(796\) 14.4539i 0.512306i
\(797\) 24.3061 42.0995i 0.860968 1.49124i −0.0100279 0.999950i \(-0.503192\pi\)
0.870996 0.491290i \(-0.163475\pi\)
\(798\) −5.74447 + 10.4465i −0.203352 + 0.369802i
\(799\) −8.01869 4.62959i −0.283681 0.163783i
\(800\) −0.746672 1.29327i −0.0263989 0.0457242i
\(801\) 27.6909 34.5642i 0.978408 1.22127i
\(802\) −6.92045 −0.244370
\(803\) 20.3769 0.719086
\(804\) −12.4631 14.5152i −0.439539 0.511912i
\(805\) −28.1587 + 10.5526i −0.992463 + 0.371930i
\(806\) −1.45128 29.5152i −0.0511190 1.03963i
\(807\) −20.4032 7.16502i −0.718225 0.252221i
\(808\) −3.15026 + 5.45640i −0.110826 + 0.191956i
\(809\) 7.20663 + 4.16075i 0.253372 + 0.146284i 0.621307 0.783567i \(-0.286602\pi\)
−0.367936 + 0.929851i \(0.619935\pi\)
\(810\) 5.03971 16.0823i 0.177077 0.565074i
\(811\) 21.9549 0.770941 0.385470 0.922720i \(-0.374039\pi\)
0.385470 + 0.922720i \(0.374039\pi\)
\(812\) 22.0031 + 3.66480i 0.772159 + 0.128609i
\(813\) 4.70541 + 1.65241i 0.165026 + 0.0579525i
\(814\) −28.1628 16.2598i −0.987107 0.569907i
\(815\) 37.0947 1.29937
\(816\) −4.84074 1.69993i −0.169460 0.0595096i
\(817\) 25.3772 0.887834
\(818\) 11.3829 0.397995
\(819\) 7.57132 27.5985i 0.264563 0.964368i
\(820\) −10.4980 −0.366605
\(821\) −27.3330 −0.953929 −0.476964 0.878923i \(-0.658263\pi\)
−0.476964 + 0.878923i \(0.658263\pi\)
\(822\) −3.52522 1.23796i −0.122956 0.0431788i
\(823\) 12.7593 0.444760 0.222380 0.974960i \(-0.428618\pi\)
0.222380 + 0.974960i \(0.428618\pi\)
\(824\) 4.99182 + 2.88203i 0.173898 + 0.100400i
\(825\) 12.4460 + 4.37067i 0.433312 + 0.152167i
\(826\) 3.70372 4.49996i 0.128869 0.156574i
\(827\) −43.7556 −1.52153 −0.760766 0.649027i \(-0.775176\pi\)
−0.760766 + 0.649027i \(0.775176\pi\)
\(828\) 11.3847 14.2105i 0.395644 0.493850i
\(829\) −35.5899 20.5478i −1.23609 0.713656i −0.267796 0.963476i \(-0.586295\pi\)
−0.968292 + 0.249819i \(0.919629\pi\)
\(830\) 9.02043 15.6238i 0.313104 0.542311i
\(831\) −13.0785 4.59279i −0.453687 0.159322i
\(832\) −3.20727 1.64725i −0.111192 0.0571082i
\(833\) 3.98746 + 20.3478i 0.138157 + 0.705011i
\(834\) −9.36764 10.9101i −0.324375 0.377785i
\(835\) 28.3025 0.979449
\(836\) −13.2675 −0.458867
\(837\) 20.0261 37.5851i 0.692203 1.29913i
\(838\) 4.51941 + 7.82784i 0.156120 + 0.270408i
\(839\) −19.7685 11.4133i −0.682484 0.394032i 0.118306 0.992977i \(-0.462253\pi\)
−0.800790 + 0.598945i \(0.795587\pi\)
\(840\) 0.178796 + 8.57950i 0.00616905 + 0.296021i
\(841\) 21.0407 36.4435i 0.725540 1.25667i
\(842\) 3.07453i 0.105955i
\(843\) 10.0702 + 3.53636i 0.346835 + 0.121799i
\(844\) 5.78954 + 10.0278i 0.199284 + 0.345170i
\(845\) −2.38822 24.2265i −0.0821574 0.833415i
\(846\) −3.40646 8.73700i −0.117117 0.300384i
\(847\) 6.52404 39.1697i 0.224169 1.34589i
\(848\) −8.21797 + 4.74465i −0.282206 + 0.162932i
\(849\) 15.5064 + 18.0596i 0.532177 + 0.619803i
\(850\) −2.21174 3.83084i −0.0758619 0.131397i
\(851\) −38.7025 −1.32671
\(852\) 19.1314 16.4267i 0.655432 0.562769i
\(853\) −4.19858 −0.143757 −0.0718783 0.997413i \(-0.522899\pi\)
−0.0718783 + 0.997413i \(0.522899\pi\)
\(854\) 15.4038 + 2.56563i 0.527108 + 0.0877941i
\(855\) −9.13786 + 11.4060i −0.312508 + 0.390078i
\(856\) 6.14671i 0.210090i
\(857\) −4.09187 7.08733i −0.139776 0.242099i 0.787636 0.616141i \(-0.211305\pi\)
−0.927412 + 0.374042i \(0.877972\pi\)
\(858\) 30.9732 7.41609i 1.05741 0.253181i
\(859\) −42.2454 24.3904i −1.44139 0.832189i −0.443451 0.896299i \(-0.646246\pi\)
−0.997943 + 0.0641096i \(0.979579\pi\)
\(860\) 15.8194 9.13332i 0.539436 0.311444i
\(861\) −22.5112 12.3788i −0.767180 0.421868i
\(862\) −11.6404 + 20.1618i −0.396475 + 0.686714i
\(863\) −0.899862 + 1.55861i −0.0306316 + 0.0530556i −0.880935 0.473238i \(-0.843085\pi\)
0.850303 + 0.526293i \(0.176419\pi\)
\(864\) −2.74973 4.40897i −0.0935476 0.149996i
\(865\) 36.0557i 1.22593i
\(866\) −23.9459 13.8252i −0.813715 0.469799i
\(867\) 13.4427 + 4.72072i 0.456539 + 0.160324i
\(868\) −3.56264 + 21.3898i −0.120924 + 0.726016i
\(869\) 26.2455 + 45.4585i 0.890317 + 1.54207i
\(870\) 25.8008 + 9.06051i 0.874728 + 0.307180i
\(871\) −21.5826 33.4705i −0.731300 1.13410i
\(872\) −10.8967 + 6.29124i −0.369010 + 0.213048i
\(873\) 32.6386 12.7254i 1.10465 0.430691i
\(874\) −13.6746 + 7.89503i −0.462550 + 0.267054i
\(875\) −20.4443 + 24.8395i −0.691143 + 0.839729i
\(876\) −1.27900 6.80132i −0.0432132 0.229795i
\(877\) −34.6606 + 20.0113i −1.17040 + 0.675733i −0.953775 0.300521i \(-0.902839\pi\)
−0.216629 + 0.976254i \(0.569506\pi\)
\(878\) 4.37253i 0.147566i
\(879\) 5.77327 + 6.72387i 0.194728 + 0.226791i
\(880\) −8.27059 + 4.77503i −0.278802 + 0.160966i
\(881\) 1.57402 + 2.72629i 0.0530302 + 0.0918510i 0.891322 0.453371i \(-0.149779\pi\)
−0.838292 + 0.545222i \(0.816445\pi\)
\(882\) −9.73320 + 18.6082i −0.327734 + 0.626570i
\(883\) −5.79510 −0.195021 −0.0975103 0.995235i \(-0.531088\pi\)
−0.0975103 + 0.995235i \(0.531088\pi\)
\(884\) −9.50032 4.87936i −0.319530 0.164111i
\(885\) 5.42074 4.65437i 0.182216 0.156455i
\(886\) 2.31071 + 1.33409i 0.0776299 + 0.0448196i
\(887\) 48.8111 1.63892 0.819458 0.573139i \(-0.194275\pi\)
0.819458 + 0.573139i \(0.194275\pi\)
\(888\) −3.65944 + 10.4207i −0.122803 + 0.349694i
\(889\) 3.19259 19.1680i 0.107076 0.642875i
\(890\) −13.8225 + 23.9412i −0.463330 + 0.802512i
\(891\) 43.7987 + 13.7252i 1.46731 + 0.459811i
\(892\) −3.33759 5.78088i −0.111751 0.193558i
\(893\) 8.13206i 0.272129i
\(894\) 1.26704 + 6.73777i 0.0423763 + 0.225345i
\(895\) −5.03078 8.71357i −0.168161 0.291263i
\(896\) 2.04281 + 1.68135i 0.0682455 + 0.0561698i
\(897\) 27.5105 26.0747i 0.918548 0.870608i
\(898\) 7.64162 13.2357i 0.255004 0.441680i
\(899\) 59.8421 + 34.5499i 1.99585 + 1.15230i
\(900\) 0.677631 4.42849i 0.0225877 0.147616i
\(901\) −24.3427 + 14.0542i −0.810972 + 0.468215i
\(902\) 28.5903i 0.951951i
\(903\) 44.6918 0.931373i 1.48725 0.0309942i
\(904\) 1.92741 + 1.11279i 0.0641049 + 0.0370110i
\(905\) −10.5924 + 18.3467i −0.352105 + 0.609864i
\(906\) −9.47867 + 1.78247i −0.314908 + 0.0592187i
\(907\) 11.9759 20.7429i 0.397653 0.688756i −0.595783 0.803146i \(-0.703158\pi\)
0.993436 + 0.114390i \(0.0364913\pi\)
\(908\) 18.4820i 0.613346i
\(909\) −17.6104 + 6.86609i −0.584099 + 0.227734i
\(910\) −2.06597 + 17.7437i −0.0684862 + 0.588197i
\(911\) 51.9614i 1.72156i −0.508979 0.860779i \(-0.669977\pi\)
0.508979 0.860779i \(-0.330023\pi\)
\(912\) 0.832761 + 4.42838i 0.0275755 + 0.146638i
\(913\) 42.5501 + 24.5663i 1.40820 + 0.813026i
\(914\) 6.93705i 0.229457i
\(915\) 18.0624 + 6.34302i 0.597126 + 0.209694i
\(916\) −0.100542 + 0.174145i −0.00332201 + 0.00575390i
\(917\) −2.30675 + 0.864465i −0.0761756 + 0.0285471i
\(918\) −8.14504 13.0599i −0.268826 0.431041i
\(919\) 18.8651 + 32.6754i 0.622303 + 1.07786i 0.989056 + 0.147542i \(0.0471363\pi\)
−0.366753 + 0.930319i \(0.619530\pi\)
\(920\) −5.68289 + 9.84306i −0.187359 + 0.324516i
\(921\) −1.84258 0.647064i −0.0607152 0.0213215i
\(922\) 17.6491 + 10.1897i 0.581242 + 0.335580i
\(923\) 44.1150 28.4465i 1.45206 0.936328i
\(924\) −23.3655 + 0.486935i −0.768668 + 0.0160190i
\(925\) −8.24664 + 4.76120i −0.271148 + 0.156547i
\(926\) 22.4244i 0.736912i
\(927\) 6.28149 + 16.1109i 0.206311 + 0.529153i
\(928\) 7.30144 4.21549i 0.239681 0.138380i
\(929\) −20.9701 + 12.1071i −0.688006 + 0.397220i −0.802865 0.596162i \(-0.796692\pi\)
0.114859 + 0.993382i \(0.463358\pi\)
\(930\) −8.80793 + 25.0815i −0.288823 + 0.822455i
\(931\) 13.7256 11.9683i 0.449839 0.392246i
\(932\) −11.1073 6.41280i −0.363831 0.210058i
\(933\) 3.58351 + 19.0561i 0.117319 + 0.623868i
\(934\) −9.83436 + 17.0336i −0.321790 + 0.557357i
\(935\) −24.4985 + 14.1442i −0.801187 + 0.462566i
\(936\) −4.41940 9.87263i −0.144453 0.322697i
\(937\) 25.9178i 0.846698i −0.905967 0.423349i \(-0.860854\pi\)
0.905967 0.423349i \(-0.139146\pi\)
\(938\) 10.2554 + 27.3655i 0.334849 + 0.893516i
\(939\) −36.6844 42.7246i −1.19715 1.39427i
\(940\) 2.92675 + 5.06929i 0.0954602 + 0.165342i
\(941\) −51.6878 + 29.8420i −1.68498 + 0.972821i −0.726709 + 0.686946i \(0.758951\pi\)
−0.958267 + 0.285875i \(0.907716\pi\)
\(942\) −12.4045 + 2.33268i −0.404162 + 0.0760030i
\(943\) −17.0130 29.4674i −0.554020 0.959592i
\(944\) 2.20283i 0.0716960i
\(945\) −15.6741 + 20.4226i −0.509878 + 0.664346i
\(946\) 24.8738 + 43.0826i 0.808716 + 1.40074i
\(947\) 21.8964 0.711538 0.355769 0.934574i \(-0.384219\pi\)
0.355769 + 0.934574i \(0.384219\pi\)
\(948\) 13.5256 11.6134i 0.439291 0.377185i
\(949\) −0.707506 14.3889i −0.0229666 0.467082i
\(950\) −1.94250 + 3.36451i −0.0630230 + 0.109159i
\(951\) 33.4207 28.6957i 1.08374 0.930523i
\(952\) 6.05106 + 4.98036i 0.196116 + 0.161414i
\(953\) −5.23975 3.02517i −0.169732 0.0979949i 0.412727 0.910855i \(-0.364576\pi\)
−0.582459 + 0.812860i \(0.697910\pi\)
\(954\) −28.1404 4.30594i −0.911078 0.139410i
\(955\) −5.94335 −0.192322
\(956\) 30.2795 0.979311
\(957\) −24.6755 + 70.2661i −0.797645 + 2.27138i
\(958\) −16.4723 9.51026i −0.532195 0.307263i
\(959\) 4.40662 + 3.62689i 0.142297 + 0.117119i
\(960\) 2.11291 + 2.46081i 0.0681938 + 0.0794223i
\(961\) −18.0867 + 31.3271i −0.583443 + 1.01055i
\(962\) −10.5038 + 20.4513i −0.338656 + 0.659377i
\(963\) 11.5295 14.3913i 0.371533 0.463753i
\(964\) 8.34511 0.268778
\(965\) −0.195983 0.339453i −0.00630892 0.0109274i
\(966\) −23.7926 + 14.4058i −0.765515 + 0.463500i
\(967\) 17.1921i 0.552862i 0.961034 + 0.276431i \(0.0891518\pi\)
−0.961034 + 0.276431i \(0.910848\pi\)
\(968\) −7.50436 12.9979i −0.241199 0.417769i
\(969\) 2.46674 + 13.1174i 0.0792432 + 0.421392i
\(970\) −18.9372 + 10.9334i −0.608037 + 0.351050i
\(971\) 20.6939 + 35.8429i 0.664100 + 1.15025i 0.979529 + 0.201305i \(0.0645183\pi\)
−0.315429 + 0.948949i \(0.602148\pi\)
\(972\) 1.83203 15.4804i 0.0587625 0.496535i
\(973\) 7.70825 + 20.5688i 0.247115 + 0.659405i
\(974\) 22.4738i 0.720107i
\(975\) 2.65415 8.94028i 0.0850008 0.286318i
\(976\) 5.11154 2.95115i 0.163616 0.0944640i
\(977\) 19.9713 34.5912i 0.638937 1.10667i −0.346729 0.937965i \(-0.612708\pi\)
0.985666 0.168706i \(-0.0539589\pi\)
\(978\) 33.7194 6.34096i 1.07823 0.202761i
\(979\) −65.2018 37.6443i −2.08386 1.20312i
\(980\) 4.24871 12.4006i 0.135720 0.396122i
\(981\) −37.3131 5.70952i −1.19132 0.182291i
\(982\) 25.7148 14.8464i 0.820591 0.473768i
\(983\) 3.96116 2.28698i 0.126342 0.0729433i −0.435497 0.900190i \(-0.643427\pi\)
0.561839 + 0.827247i \(0.310094\pi\)
\(984\) −9.54273 + 1.79452i −0.304211 + 0.0572072i
\(985\) 36.4034i 1.15991i
\(986\) 21.6278 12.4868i 0.688768 0.397661i
\(987\) 0.298457 + 14.3214i 0.00949998 + 0.455855i
\(988\) 0.460662 + 9.36868i 0.0146556 + 0.298057i
\(989\) 51.2738 + 29.6030i 1.63041 + 0.941319i
\(990\) −28.3205 4.33351i −0.900086 0.137728i
\(991\) 9.02683 15.6349i 0.286747 0.496660i −0.686285 0.727333i \(-0.740760\pi\)
0.973031 + 0.230673i \(0.0740929\pi\)
\(992\) 4.09797 + 7.09789i 0.130111 + 0.225358i
\(993\) 12.2323 2.30030i 0.388181 0.0729978i
\(994\) −36.0685 + 13.5168i −1.14402 + 0.428728i
\(995\) 13.5333 23.4403i 0.429033 0.743107i
\(996\) 5.52891 15.7441i 0.175190 0.498872i
\(997\) 42.3940i 1.34263i 0.741171 + 0.671316i \(0.234271\pi\)
−0.741171 + 0.671316i \(0.765729\pi\)
\(998\) 6.50477 + 3.75553i 0.205905 + 0.118879i
\(999\) −28.1140 + 17.5338i −0.889489 + 0.554745i
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.bi.f.257.3 yes 34
3.2 odd 2 546.2.bi.e.257.4 yes 34
7.3 odd 6 546.2.bn.e.101.8 yes 34
13.4 even 6 546.2.bn.f.173.10 yes 34
21.17 even 6 546.2.bn.f.101.10 yes 34
39.17 odd 6 546.2.bn.e.173.8 yes 34
91.17 odd 6 546.2.bi.e.17.4 34
273.17 even 6 inner 546.2.bi.f.17.3 yes 34
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
546.2.bi.e.17.4 34 91.17 odd 6
546.2.bi.e.257.4 yes 34 3.2 odd 2
546.2.bi.f.17.3 yes 34 273.17 even 6 inner
546.2.bi.f.257.3 yes 34 1.1 even 1 trivial
546.2.bn.e.101.8 yes 34 7.3 odd 6
546.2.bn.e.173.8 yes 34 39.17 odd 6
546.2.bn.f.101.10 yes 34 21.17 even 6
546.2.bn.f.173.10 yes 34 13.4 even 6