Properties

Label 546.2.p.d.239.8
Level $546$
Weight $2$
Character 546.239
Analytic conductor $4.360$
Analytic rank $0$
Dimension $20$
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(239,546)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(546, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 0, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("546.239");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 546.p (of order \(4\), 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: \(20\)
Relative dimension: \(10\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{20} - 4 x^{19} + 8 x^{18} - 20 x^{17} + 56 x^{16} - 140 x^{15} + 288 x^{14} - 532 x^{13} + 1065 x^{12} - 2080 x^{11} + 3712 x^{10} - 6240 x^{9} + 9585 x^{8} - 14364 x^{7} + \cdots + 59049 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 239.8
Root \(-1.01577 - 1.40293i\) of defining polynomial
Character \(\chi\) \(=\) 546.239
Dual form 546.2.p.d.281.8

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.707107 + 0.707107i) q^{2} +(0.273767 + 1.71028i) q^{3} +1.00000i q^{4} +(1.75112 + 1.75112i) q^{5} +(-1.01577 + 1.40293i) q^{6} +(0.707107 + 0.707107i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-2.85010 + 0.936434i) q^{9} +O(q^{10})\) \(q+(0.707107 + 0.707107i) q^{2} +(0.273767 + 1.71028i) q^{3} +1.00000i q^{4} +(1.75112 + 1.75112i) q^{5} +(-1.01577 + 1.40293i) q^{6} +(0.707107 + 0.707107i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-2.85010 + 0.936434i) q^{9} +2.47645i q^{10} +(2.12300 - 2.12300i) q^{11} +(-1.71028 + 0.273767i) q^{12} +(-3.47808 + 0.950237i) q^{13} +1.00000i q^{14} +(-2.51550 + 3.47430i) q^{15} -1.00000 q^{16} +3.03575 q^{17} +(-2.67749 - 1.35317i) q^{18} +(2.63603 - 2.63603i) q^{19} +(-1.75112 + 1.75112i) q^{20} +(-1.01577 + 1.40293i) q^{21} +3.00237 q^{22} +0.478247 q^{23} +(-1.40293 - 1.01577i) q^{24} +1.13282i q^{25} +(-3.13129 - 1.78746i) q^{26} +(-2.38183 - 4.61811i) q^{27} +(-0.707107 + 0.707107i) q^{28} -6.03691i q^{29} +(-4.23543 + 0.677971i) q^{30} +(-2.07156 + 2.07156i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(4.21213 + 3.04971i) q^{33} +(2.14660 + 2.14660i) q^{34} +2.47645i q^{35} +(-0.936434 - 2.85010i) q^{36} +(-4.21400 - 4.21400i) q^{37} +3.72791 q^{38} +(-2.57735 - 5.68834i) q^{39} -2.47645 q^{40} +(4.84049 + 4.84049i) q^{41} +(-1.71028 + 0.273767i) q^{42} +4.59522i q^{43} +(2.12300 + 2.12300i) q^{44} +(-6.63067 - 3.35106i) q^{45} +(0.338172 + 0.338172i) q^{46} +(-6.97225 + 6.97225i) q^{47} +(-0.273767 - 1.71028i) q^{48} +1.00000i q^{49} +(-0.801028 + 0.801028i) q^{50} +(0.831086 + 5.19197i) q^{51} +(-0.950237 - 3.47808i) q^{52} -5.90009i q^{53} +(1.58129 - 4.94970i) q^{54} +7.43524 q^{55} -1.00000 q^{56} +(5.23000 + 3.78669i) q^{57} +(4.26874 - 4.26874i) q^{58} +(3.76763 - 3.76763i) q^{59} +(-3.47430 - 2.51550i) q^{60} +13.2619 q^{61} -2.92963 q^{62} +(-2.67749 - 1.35317i) q^{63} -1.00000i q^{64} +(-7.75451 - 4.42655i) q^{65} +(0.821950 + 5.13490i) q^{66} +(-6.61080 + 6.61080i) q^{67} +3.03575i q^{68} +(0.130928 + 0.817936i) q^{69} +(-1.75112 + 1.75112i) q^{70} +(7.36537 + 7.36537i) q^{71} +(1.35317 - 2.67749i) q^{72} +(-8.06119 - 8.06119i) q^{73} -5.95950i q^{74} +(-1.93745 + 0.310130i) q^{75} +(2.63603 + 2.63603i) q^{76} +3.00237 q^{77} +(2.19980 - 5.84473i) q^{78} -11.6022 q^{79} +(-1.75112 - 1.75112i) q^{80} +(7.24618 - 5.33787i) q^{81} +6.84548i q^{82} +(9.96904 + 9.96904i) q^{83} +(-1.40293 - 1.01577i) q^{84} +(5.31595 + 5.31595i) q^{85} +(-3.24931 + 3.24931i) q^{86} +(10.3248 - 1.65271i) q^{87} +3.00237i q^{88} +(10.9270 - 10.9270i) q^{89} +(-2.31904 - 7.05815i) q^{90} +(-3.13129 - 1.78746i) q^{91} +0.478247i q^{92} +(-4.11007 - 2.97582i) q^{93} -9.86025 q^{94} +9.23199 q^{95} +(1.01577 - 1.40293i) q^{96} +(10.7186 - 10.7186i) q^{97} +(-0.707107 + 0.707107i) q^{98} +(-4.06272 + 8.03882i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q + 4 q^{5} + 4 q^{6} - 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 20 q + 4 q^{5} + 4 q^{6} - 8 q^{9} + 16 q^{11} + 8 q^{12} + 4 q^{13} - 4 q^{15} - 20 q^{16} - 12 q^{17} - 16 q^{18} + 12 q^{19} - 4 q^{20} + 4 q^{21} - 12 q^{22} + 4 q^{23} - 4 q^{24} + 24 q^{27} - 12 q^{30} - 8 q^{31} + 16 q^{33} - 4 q^{34} + 32 q^{37} + 4 q^{38} + 8 q^{39} - 4 q^{40} - 8 q^{41} + 8 q^{42} + 16 q^{44} - 32 q^{45} - 8 q^{46} - 32 q^{50} + 8 q^{51} - 8 q^{52} + 20 q^{54} + 28 q^{55} - 20 q^{56} + 36 q^{57} - 4 q^{58} - 20 q^{59} - 4 q^{60} - 4 q^{61} - 48 q^{62} - 16 q^{63} - 52 q^{65} - 36 q^{67} - 68 q^{69} - 4 q^{70} + 28 q^{71} - 8 q^{72} - 24 q^{73} + 76 q^{75} + 12 q^{76} - 12 q^{77} + 56 q^{78} - 64 q^{79} - 4 q^{80} + 32 q^{81} + 24 q^{83} - 4 q^{84} + 24 q^{85} - 4 q^{86} + 4 q^{87} + 4 q^{89} + 8 q^{90} + 16 q^{93} - 40 q^{94} + 76 q^{95} - 4 q^{96} + 32 q^{97} - 36 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(157\) \(365\) \(379\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{3}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.707107 + 0.707107i 0.500000 + 0.500000i
\(3\) 0.273767 + 1.71028i 0.158059 + 0.987430i
\(4\) 1.00000i 0.500000i
\(5\) 1.75112 + 1.75112i 0.783124 + 0.783124i 0.980357 0.197233i \(-0.0631956\pi\)
−0.197233 + 0.980357i \(0.563196\pi\)
\(6\) −1.01577 + 1.40293i −0.414685 + 0.572744i
\(7\) 0.707107 + 0.707107i 0.267261 + 0.267261i
\(8\) −0.707107 + 0.707107i −0.250000 + 0.250000i
\(9\) −2.85010 + 0.936434i −0.950035 + 0.312145i
\(10\) 2.47645i 0.783124i
\(11\) 2.12300 2.12300i 0.640108 0.640108i −0.310474 0.950582i \(-0.600488\pi\)
0.950582 + 0.310474i \(0.100488\pi\)
\(12\) −1.71028 + 0.273767i −0.493715 + 0.0790296i
\(13\) −3.47808 + 0.950237i −0.964646 + 0.263548i
\(14\) 1.00000i 0.267261i
\(15\) −2.51550 + 3.47430i −0.649499 + 0.897059i
\(16\) −1.00000 −0.250000
\(17\) 3.03575 0.736277 0.368138 0.929771i \(-0.379995\pi\)
0.368138 + 0.929771i \(0.379995\pi\)
\(18\) −2.67749 1.35317i −0.631090 0.318945i
\(19\) 2.63603 2.63603i 0.604747 0.604747i −0.336822 0.941568i \(-0.609352\pi\)
0.941568 + 0.336822i \(0.109352\pi\)
\(20\) −1.75112 + 1.75112i −0.391562 + 0.391562i
\(21\) −1.01577 + 1.40293i −0.221659 + 0.306145i
\(22\) 3.00237 0.640108
\(23\) 0.478247 0.0997215 0.0498607 0.998756i \(-0.484122\pi\)
0.0498607 + 0.998756i \(0.484122\pi\)
\(24\) −1.40293 1.01577i −0.286372 0.207343i
\(25\) 1.13282i 0.226565i
\(26\) −3.13129 1.78746i −0.614097 0.350549i
\(27\) −2.38183 4.61811i −0.458383 0.888755i
\(28\) −0.707107 + 0.707107i −0.133631 + 0.133631i
\(29\) 6.03691i 1.12103i −0.828145 0.560513i \(-0.810604\pi\)
0.828145 0.560513i \(-0.189396\pi\)
\(30\) −4.23543 + 0.677971i −0.773279 + 0.123780i
\(31\) −2.07156 + 2.07156i −0.372064 + 0.372064i −0.868228 0.496165i \(-0.834741\pi\)
0.496165 + 0.868228i \(0.334741\pi\)
\(32\) −0.707107 0.707107i −0.125000 0.125000i
\(33\) 4.21213 + 3.04971i 0.733237 + 0.530887i
\(34\) 2.14660 + 2.14660i 0.368138 + 0.368138i
\(35\) 2.47645i 0.418597i
\(36\) −0.936434 2.85010i −0.156072 0.475017i
\(37\) −4.21400 4.21400i −0.692778 0.692778i 0.270064 0.962842i \(-0.412955\pi\)
−0.962842 + 0.270064i \(0.912955\pi\)
\(38\) 3.72791 0.604747
\(39\) −2.57735 5.68834i −0.412707 0.910864i
\(40\) −2.47645 −0.391562
\(41\) 4.84049 + 4.84049i 0.755957 + 0.755957i 0.975584 0.219627i \(-0.0704840\pi\)
−0.219627 + 0.975584i \(0.570484\pi\)
\(42\) −1.71028 + 0.273767i −0.263902 + 0.0422431i
\(43\) 4.59522i 0.700764i 0.936607 + 0.350382i \(0.113948\pi\)
−0.936607 + 0.350382i \(0.886052\pi\)
\(44\) 2.12300 + 2.12300i 0.320054 + 0.320054i
\(45\) −6.63067 3.35106i −0.988442 0.499546i
\(46\) 0.338172 + 0.338172i 0.0498607 + 0.0498607i
\(47\) −6.97225 + 6.97225i −1.01701 + 1.01701i −0.0171544 + 0.999853i \(0.505461\pi\)
−0.999853 + 0.0171544i \(0.994539\pi\)
\(48\) −0.273767 1.71028i −0.0395148 0.246857i
\(49\) 1.00000i 0.142857i
\(50\) −0.801028 + 0.801028i −0.113282 + 0.113282i
\(51\) 0.831086 + 5.19197i 0.116375 + 0.727021i
\(52\) −0.950237 3.47808i −0.131774 0.482323i
\(53\) 5.90009i 0.810440i −0.914219 0.405220i \(-0.867195\pi\)
0.914219 0.405220i \(-0.132805\pi\)
\(54\) 1.58129 4.94970i 0.215186 0.673569i
\(55\) 7.43524 1.00257
\(56\) −1.00000 −0.133631
\(57\) 5.23000 + 3.78669i 0.692730 + 0.501559i
\(58\) 4.26874 4.26874i 0.560513 0.560513i
\(59\) 3.76763 3.76763i 0.490504 0.490504i −0.417961 0.908465i \(-0.637255\pi\)
0.908465 + 0.417961i \(0.137255\pi\)
\(60\) −3.47430 2.51550i −0.448530 0.324750i
\(61\) 13.2619 1.69801 0.849007 0.528382i \(-0.177201\pi\)
0.849007 + 0.528382i \(0.177201\pi\)
\(62\) −2.92963 −0.372064
\(63\) −2.67749 1.35317i −0.337332 0.170483i
\(64\) 1.00000i 0.125000i
\(65\) −7.75451 4.42655i −0.961828 0.549046i
\(66\) 0.821950 + 5.13490i 0.101175 + 0.632062i
\(67\) −6.61080 + 6.61080i −0.807638 + 0.807638i −0.984276 0.176638i \(-0.943478\pi\)
0.176638 + 0.984276i \(0.443478\pi\)
\(68\) 3.03575i 0.368138i
\(69\) 0.130928 + 0.817936i 0.0157619 + 0.0984680i
\(70\) −1.75112 + 1.75112i −0.209299 + 0.209299i
\(71\) 7.36537 + 7.36537i 0.874109 + 0.874109i 0.992917 0.118808i \(-0.0379073\pi\)
−0.118808 + 0.992917i \(0.537907\pi\)
\(72\) 1.35317 2.67749i 0.159472 0.315545i
\(73\) −8.06119 8.06119i −0.943491 0.943491i 0.0549955 0.998487i \(-0.482486\pi\)
−0.998487 + 0.0549955i \(0.982486\pi\)
\(74\) 5.95950i 0.692778i
\(75\) −1.93745 + 0.310130i −0.223717 + 0.0358107i
\(76\) 2.63603 + 2.63603i 0.302373 + 0.302373i
\(77\) 3.00237 0.342152
\(78\) 2.19980 5.84473i 0.249079 0.661785i
\(79\) −11.6022 −1.30535 −0.652673 0.757640i \(-0.726353\pi\)
−0.652673 + 0.757640i \(0.726353\pi\)
\(80\) −1.75112 1.75112i −0.195781 0.195781i
\(81\) 7.24618 5.33787i 0.805131 0.593097i
\(82\) 6.84548i 0.755957i
\(83\) 9.96904 + 9.96904i 1.09424 + 1.09424i 0.995070 + 0.0991748i \(0.0316203\pi\)
0.0991748 + 0.995070i \(0.468380\pi\)
\(84\) −1.40293 1.01577i −0.153072 0.110829i
\(85\) 5.31595 + 5.31595i 0.576596 + 0.576596i
\(86\) −3.24931 + 3.24931i −0.350382 + 0.350382i
\(87\) 10.3248 1.65271i 1.10694 0.177189i
\(88\) 3.00237i 0.320054i
\(89\) 10.9270 10.9270i 1.15826 1.15826i 0.173415 0.984849i \(-0.444520\pi\)
0.984849 0.173415i \(-0.0554803\pi\)
\(90\) −2.31904 7.05815i −0.244448 0.743994i
\(91\) −3.13129 1.78746i −0.328249 0.187376i
\(92\) 0.478247i 0.0498607i
\(93\) −4.11007 2.97582i −0.426195 0.308579i
\(94\) −9.86025 −1.01701
\(95\) 9.23199 0.947182
\(96\) 1.01577 1.40293i 0.103671 0.143186i
\(97\) 10.7186 10.7186i 1.08831 1.08831i 0.0926043 0.995703i \(-0.470481\pi\)
0.995703 0.0926043i \(-0.0295192\pi\)
\(98\) −0.707107 + 0.707107i −0.0714286 + 0.0714286i
\(99\) −4.06272 + 8.03882i −0.408319 + 0.807932i
\(100\) −1.13282 −0.113282
\(101\) −5.04608 −0.502103 −0.251052 0.967974i \(-0.580776\pi\)
−0.251052 + 0.967974i \(0.580776\pi\)
\(102\) −3.08361 + 4.25894i −0.305323 + 0.421698i
\(103\) 17.3260i 1.70718i −0.520944 0.853591i \(-0.674420\pi\)
0.520944 0.853591i \(-0.325580\pi\)
\(104\) 1.78746 3.13129i 0.175274 0.307049i
\(105\) −4.23543 + 0.677971i −0.413335 + 0.0661632i
\(106\) 4.17199 4.17199i 0.405220 0.405220i
\(107\) 7.64785i 0.739345i 0.929162 + 0.369673i \(0.120530\pi\)
−0.929162 + 0.369673i \(0.879470\pi\)
\(108\) 4.61811 2.38183i 0.444377 0.229191i
\(109\) 2.94969 2.94969i 0.282529 0.282529i −0.551588 0.834117i \(-0.685978\pi\)
0.834117 + 0.551588i \(0.185978\pi\)
\(110\) 5.25751 + 5.25751i 0.501284 + 0.501284i
\(111\) 6.05346 8.36077i 0.574569 0.793569i
\(112\) −0.707107 0.707107i −0.0668153 0.0668153i
\(113\) 4.99755i 0.470130i 0.971980 + 0.235065i \(0.0755303\pi\)
−0.971980 + 0.235065i \(0.924470\pi\)
\(114\) 1.02058 + 6.37576i 0.0955858 + 0.597145i
\(115\) 0.837467 + 0.837467i 0.0780942 + 0.0780942i
\(116\) 6.03691 0.560513
\(117\) 9.02306 5.96527i 0.834182 0.551489i
\(118\) 5.32824 0.490504
\(119\) 2.14660 + 2.14660i 0.196778 + 0.196778i
\(120\) −0.677971 4.23543i −0.0618900 0.386640i
\(121\) 1.98575i 0.180522i
\(122\) 9.37758 + 9.37758i 0.849007 + 0.849007i
\(123\) −6.95342 + 9.60374i −0.626968 + 0.865940i
\(124\) −2.07156 2.07156i −0.186032 0.186032i
\(125\) 6.77188 6.77188i 0.605695 0.605695i
\(126\) −0.936434 2.85010i −0.0834242 0.253907i
\(127\) 0.521751i 0.0462979i 0.999732 + 0.0231490i \(0.00736920\pi\)
−0.999732 + 0.0231490i \(0.992631\pi\)
\(128\) 0.707107 0.707107i 0.0625000 0.0625000i
\(129\) −7.85910 + 1.25802i −0.691956 + 0.110762i
\(130\) −2.35322 8.61331i −0.206391 0.755437i
\(131\) 10.1350i 0.885497i 0.896646 + 0.442748i \(0.145997\pi\)
−0.896646 + 0.442748i \(0.854003\pi\)
\(132\) −3.04971 + 4.21213i −0.265443 + 0.366619i
\(133\) 3.72791 0.323251
\(134\) −9.34908 −0.807638
\(135\) 3.91599 12.2577i 0.337034 1.05498i
\(136\) −2.14660 + 2.14660i −0.184069 + 0.184069i
\(137\) −4.06995 + 4.06995i −0.347720 + 0.347720i −0.859259 0.511540i \(-0.829075\pi\)
0.511540 + 0.859259i \(0.329075\pi\)
\(138\) −0.485788 + 0.670949i −0.0413530 + 0.0571149i
\(139\) 0.173766 0.0147387 0.00736933 0.999973i \(-0.497654\pi\)
0.00736933 + 0.999973i \(0.497654\pi\)
\(140\) −2.47645 −0.209299
\(141\) −13.8333 10.0157i −1.16497 0.843476i
\(142\) 10.4162i 0.874109i
\(143\) −5.36661 + 9.40132i −0.448779 + 0.786178i
\(144\) 2.85010 0.936434i 0.237509 0.0780362i
\(145\) 10.5713 10.5713i 0.877903 0.877903i
\(146\) 11.4002i 0.943491i
\(147\) −1.71028 + 0.273767i −0.141061 + 0.0225799i
\(148\) 4.21400 4.21400i 0.346389 0.346389i
\(149\) 4.13899 + 4.13899i 0.339079 + 0.339079i 0.856021 0.516941i \(-0.172929\pi\)
−0.516941 + 0.856021i \(0.672929\pi\)
\(150\) −1.58928 1.15069i −0.129764 0.0939531i
\(151\) −6.75083 6.75083i −0.549375 0.549375i 0.376885 0.926260i \(-0.376995\pi\)
−0.926260 + 0.376885i \(0.876995\pi\)
\(152\) 3.72791i 0.302373i
\(153\) −8.65219 + 2.84278i −0.699488 + 0.229825i
\(154\) 2.12300 + 2.12300i 0.171076 + 0.171076i
\(155\) −7.25510 −0.582744
\(156\) 5.68834 2.57735i 0.455432 0.206353i
\(157\) −4.14765 −0.331018 −0.165509 0.986208i \(-0.552927\pi\)
−0.165509 + 0.986208i \(0.552927\pi\)
\(158\) −8.20397 8.20397i −0.652673 0.652673i
\(159\) 10.0908 1.61525i 0.800252 0.128098i
\(160\) 2.47645i 0.195781i
\(161\) 0.338172 + 0.338172i 0.0266517 + 0.0266517i
\(162\) 8.89827 + 1.34938i 0.699114 + 0.106017i
\(163\) −13.3414 13.3414i −1.04498 1.04498i −0.998940 0.0460395i \(-0.985340\pi\)
−0.0460395 0.998940i \(-0.514660\pi\)
\(164\) −4.84049 + 4.84049i −0.377979 + 0.377979i
\(165\) 2.03552 + 12.7163i 0.158465 + 0.989965i
\(166\) 14.0984i 1.09424i
\(167\) −6.44717 + 6.44717i −0.498897 + 0.498897i −0.911095 0.412197i \(-0.864761\pi\)
0.412197 + 0.911095i \(0.364761\pi\)
\(168\) −0.273767 1.71028i −0.0211216 0.131951i
\(169\) 11.1941 6.61000i 0.861085 0.508462i
\(170\) 7.51789i 0.576596i
\(171\) −5.04449 + 9.98142i −0.385762 + 0.763299i
\(172\) −4.59522 −0.350382
\(173\) 2.65682 0.201994 0.100997 0.994887i \(-0.467797\pi\)
0.100997 + 0.994887i \(0.467797\pi\)
\(174\) 8.46938 + 6.13210i 0.642062 + 0.464873i
\(175\) −0.801028 + 0.801028i −0.0605520 + 0.0605520i
\(176\) −2.12300 + 2.12300i −0.160027 + 0.160027i
\(177\) 7.47515 + 5.41225i 0.561867 + 0.406809i
\(178\) 15.4532 1.15826
\(179\) 3.64878 0.272723 0.136361 0.990659i \(-0.456459\pi\)
0.136361 + 0.990659i \(0.456459\pi\)
\(180\) 3.35106 6.63067i 0.249773 0.494221i
\(181\) 19.5037i 1.44970i 0.688909 + 0.724848i \(0.258090\pi\)
−0.688909 + 0.724848i \(0.741910\pi\)
\(182\) −0.950237 3.47808i −0.0704362 0.257813i
\(183\) 3.63067 + 22.6815i 0.268387 + 1.67667i
\(184\) −0.338172 + 0.338172i −0.0249304 + 0.0249304i
\(185\) 14.7584i 1.08506i
\(186\) −0.802036 5.01049i −0.0588081 0.367387i
\(187\) 6.44489 6.44489i 0.471297 0.471297i
\(188\) −6.97225 6.97225i −0.508504 0.508504i
\(189\) 1.58129 4.94970i 0.115022 0.360038i
\(190\) 6.52800 + 6.52800i 0.473591 + 0.473591i
\(191\) 0.854794i 0.0618508i −0.999522 0.0309254i \(-0.990155\pi\)
0.999522 0.0309254i \(-0.00984542\pi\)
\(192\) 1.71028 0.273767i 0.123429 0.0197574i
\(193\) −16.3246 16.3246i −1.17507 1.17507i −0.980985 0.194083i \(-0.937827\pi\)
−0.194083 0.980985i \(-0.562173\pi\)
\(194\) 15.1584 1.08831
\(195\) 5.44771 14.4742i 0.390119 1.03652i
\(196\) −1.00000 −0.0714286
\(197\) −7.45721 7.45721i −0.531304 0.531304i 0.389656 0.920960i \(-0.372594\pi\)
−0.920960 + 0.389656i \(0.872594\pi\)
\(198\) −8.55708 + 2.81153i −0.608125 + 0.199807i
\(199\) 0.778109i 0.0551587i −0.999620 0.0275793i \(-0.991220\pi\)
0.999620 0.0275793i \(-0.00877989\pi\)
\(200\) −0.801028 0.801028i −0.0566412 0.0566412i
\(201\) −13.1161 9.49649i −0.925140 0.669831i
\(202\) −3.56811 3.56811i −0.251052 0.251052i
\(203\) 4.26874 4.26874i 0.299607 0.299607i
\(204\) −5.19197 + 0.831086i −0.363511 + 0.0581877i
\(205\) 16.9525i 1.18402i
\(206\) 12.2513 12.2513i 0.853591 0.853591i
\(207\) −1.36305 + 0.447847i −0.0947389 + 0.0311275i
\(208\) 3.47808 0.950237i 0.241162 0.0658871i
\(209\) 11.1926i 0.774207i
\(210\) −3.47430 2.51550i −0.239749 0.173586i
\(211\) −4.51239 −0.310646 −0.155323 0.987864i \(-0.549642\pi\)
−0.155323 + 0.987864i \(0.549642\pi\)
\(212\) 5.90009 0.405220
\(213\) −10.5804 + 14.6132i −0.724960 + 1.00128i
\(214\) −5.40784 + 5.40784i −0.369673 + 0.369673i
\(215\) −8.04677 + 8.04677i −0.548785 + 0.548785i
\(216\) 4.94970 + 1.58129i 0.336784 + 0.107593i
\(217\) −2.92963 −0.198876
\(218\) 4.17149 0.282529
\(219\) 11.5800 15.9938i 0.782504 1.08076i
\(220\) 7.43524i 0.501284i
\(221\) −10.5586 + 2.88468i −0.710246 + 0.194044i
\(222\) 10.1924 1.63151i 0.684069 0.109500i
\(223\) −3.08394 + 3.08394i −0.206516 + 0.206516i −0.802785 0.596269i \(-0.796649\pi\)
0.596269 + 0.802785i \(0.296649\pi\)
\(224\) 1.00000i 0.0668153i
\(225\) −1.06082 3.22867i −0.0707211 0.215245i
\(226\) −3.53380 + 3.53380i −0.235065 + 0.235065i
\(227\) −18.9348 18.9348i −1.25675 1.25675i −0.952637 0.304109i \(-0.901641\pi\)
−0.304109 0.952637i \(-0.598359\pi\)
\(228\) −3.78669 + 5.23000i −0.250779 + 0.346365i
\(229\) 12.2479 + 12.2479i 0.809366 + 0.809366i 0.984538 0.175172i \(-0.0560482\pi\)
−0.175172 + 0.984538i \(0.556048\pi\)
\(230\) 1.18436i 0.0780942i
\(231\) 0.821950 + 5.13490i 0.0540804 + 0.337851i
\(232\) 4.26874 + 4.26874i 0.280257 + 0.280257i
\(233\) −15.4793 −1.01408 −0.507041 0.861922i \(-0.669261\pi\)
−0.507041 + 0.861922i \(0.669261\pi\)
\(234\) 10.5983 + 2.16218i 0.692836 + 0.141346i
\(235\) −24.4185 −1.59288
\(236\) 3.76763 + 3.76763i 0.245252 + 0.245252i
\(237\) −3.17629 19.8429i −0.206322 1.28894i
\(238\) 3.03575i 0.196778i
\(239\) −11.2898 11.2898i −0.730278 0.730278i 0.240397 0.970675i \(-0.422722\pi\)
−0.970675 + 0.240397i \(0.922722\pi\)
\(240\) 2.51550 3.47430i 0.162375 0.224265i
\(241\) −3.14172 3.14172i −0.202376 0.202376i 0.598641 0.801017i \(-0.295707\pi\)
−0.801017 + 0.598641i \(0.795707\pi\)
\(242\) −1.40413 + 1.40413i −0.0902612 + 0.0902612i
\(243\) 11.1130 + 10.9317i 0.712900 + 0.701266i
\(244\) 13.2619i 0.849007i
\(245\) −1.75112 + 1.75112i −0.111875 + 0.111875i
\(246\) −11.7077 + 1.87406i −0.746454 + 0.119486i
\(247\) −6.66347 + 11.6732i −0.423987 + 0.742746i
\(248\) 2.92963i 0.186032i
\(249\) −14.3206 + 19.7790i −0.907534 + 1.25345i
\(250\) 9.57688 0.605695
\(251\) 18.4294 1.16326 0.581628 0.813455i \(-0.302416\pi\)
0.581628 + 0.813455i \(0.302416\pi\)
\(252\) 1.35317 2.67749i 0.0852416 0.168666i
\(253\) 1.01532 1.01532i 0.0638326 0.0638326i
\(254\) −0.368934 + 0.368934i −0.0231490 + 0.0231490i
\(255\) −7.63642 + 10.5471i −0.478211 + 0.660484i
\(256\) 1.00000 0.0625000
\(257\) −4.35687 −0.271774 −0.135887 0.990724i \(-0.543388\pi\)
−0.135887 + 0.990724i \(0.543388\pi\)
\(258\) −6.44678 4.66767i −0.401359 0.290597i
\(259\) 5.95950i 0.370305i
\(260\) 4.42655 7.75451i 0.274523 0.480914i
\(261\) 5.65317 + 17.2058i 0.349923 + 1.06501i
\(262\) −7.16651 + 7.16651i −0.442748 + 0.442748i
\(263\) 1.49647i 0.0922762i −0.998935 0.0461381i \(-0.985309\pi\)
0.998935 0.0461381i \(-0.0146914\pi\)
\(264\) −5.13490 + 0.821950i −0.316031 + 0.0505875i
\(265\) 10.3318 10.3318i 0.634674 0.634674i
\(266\) 2.63603 + 2.63603i 0.161625 + 0.161625i
\(267\) 21.6797 + 15.6968i 1.32678 + 0.960630i
\(268\) −6.61080 6.61080i −0.403819 0.403819i
\(269\) 11.0765i 0.675349i −0.941263 0.337674i \(-0.890360\pi\)
0.941263 0.337674i \(-0.109640\pi\)
\(270\) 11.4365 5.89849i 0.696005 0.358970i
\(271\) −9.41699 9.41699i −0.572042 0.572042i 0.360657 0.932699i \(-0.382553\pi\)
−0.932699 + 0.360657i \(0.882553\pi\)
\(272\) −3.03575 −0.184069
\(273\) 2.19980 5.84473i 0.133138 0.353739i
\(274\) −5.75578 −0.347720
\(275\) 2.40499 + 2.40499i 0.145026 + 0.145026i
\(276\) −0.817936 + 0.130928i −0.0492340 + 0.00788095i
\(277\) 20.3743i 1.22417i 0.790792 + 0.612085i \(0.209669\pi\)
−0.790792 + 0.612085i \(0.790331\pi\)
\(278\) 0.122871 + 0.122871i 0.00736933 + 0.00736933i
\(279\) 3.96429 7.84405i 0.237336 0.469611i
\(280\) −1.75112 1.75112i −0.104649 0.104649i
\(281\) 14.5729 14.5729i 0.869346 0.869346i −0.123054 0.992400i \(-0.539269\pi\)
0.992400 + 0.123054i \(0.0392690\pi\)
\(282\) −2.69941 16.8638i −0.160747 1.00422i
\(283\) 17.5244i 1.04171i 0.853644 + 0.520857i \(0.174388\pi\)
−0.853644 + 0.520857i \(0.825612\pi\)
\(284\) −7.36537 + 7.36537i −0.437055 + 0.437055i
\(285\) 2.52741 + 15.7893i 0.149711 + 0.935276i
\(286\) −10.4425 + 2.85297i −0.617478 + 0.168699i
\(287\) 6.84548i 0.404076i
\(288\) 2.67749 + 1.35317i 0.157772 + 0.0797362i
\(289\) −7.78425 −0.457897
\(290\) 14.9501 0.877903
\(291\) 21.2662 + 15.3974i 1.24664 + 0.902610i
\(292\) 8.06119 8.06119i 0.471746 0.471746i
\(293\) −22.5588 + 22.5588i −1.31790 + 1.31790i −0.402466 + 0.915435i \(0.631847\pi\)
−0.915435 + 0.402466i \(0.868153\pi\)
\(294\) −1.40293 1.01577i −0.0818206 0.0592407i
\(295\) 13.1951 0.768250
\(296\) 5.95950 0.346389
\(297\) −14.8609 4.74762i −0.862314 0.275485i
\(298\) 5.85342i 0.339079i
\(299\) −1.66338 + 0.454448i −0.0961960 + 0.0262814i
\(300\) −0.310130 1.93745i −0.0179053 0.111858i
\(301\) −3.24931 + 3.24931i −0.187287 + 0.187287i
\(302\) 9.54712i 0.549375i
\(303\) −1.38145 8.63019i −0.0793621 0.495792i
\(304\) −2.63603 + 2.63603i −0.151187 + 0.151187i
\(305\) 23.2232 + 23.2232i 1.32975 + 1.32975i
\(306\) −8.12817 4.10788i −0.464657 0.234832i
\(307\) 15.0145 + 15.0145i 0.856921 + 0.856921i 0.990974 0.134053i \(-0.0427992\pi\)
−0.134053 + 0.990974i \(0.542799\pi\)
\(308\) 3.00237i 0.171076i
\(309\) 29.6323 4.74328i 1.68572 0.269836i
\(310\) −5.13013 5.13013i −0.291372 0.291372i
\(311\) −10.7272 −0.608283 −0.304142 0.952627i \(-0.598370\pi\)
−0.304142 + 0.952627i \(0.598370\pi\)
\(312\) 5.84473 + 2.19980i 0.330893 + 0.124539i
\(313\) −17.3350 −0.979834 −0.489917 0.871769i \(-0.662973\pi\)
−0.489917 + 0.871769i \(0.662973\pi\)
\(314\) −2.93283 2.93283i −0.165509 0.165509i
\(315\) −2.31904 7.05815i −0.130663 0.397682i
\(316\) 11.6022i 0.652673i
\(317\) −19.6716 19.6716i −1.10487 1.10487i −0.993814 0.111055i \(-0.964577\pi\)
−0.111055 0.993814i \(-0.535423\pi\)
\(318\) 8.27742 + 5.99312i 0.464175 + 0.336077i
\(319\) −12.8164 12.8164i −0.717579 0.717579i
\(320\) 1.75112 1.75112i 0.0978904 0.0978904i
\(321\) −13.0799 + 2.09373i −0.730051 + 0.116860i
\(322\) 0.478247i 0.0266517i
\(323\) 8.00231 8.00231i 0.445261 0.445261i
\(324\) 5.33787 + 7.24618i 0.296548 + 0.402566i
\(325\) −1.07645 3.94006i −0.0597108 0.218555i
\(326\) 18.8676i 1.04498i
\(327\) 5.85232 + 4.23726i 0.323634 + 0.234321i
\(328\) −6.84548 −0.377979
\(329\) −9.86025 −0.543613
\(330\) −7.55248 + 10.4311i −0.415750 + 0.574215i
\(331\) 4.17896 4.17896i 0.229697 0.229697i −0.582869 0.812566i \(-0.698070\pi\)
0.812566 + 0.582869i \(0.198070\pi\)
\(332\) −9.96904 + 9.96904i −0.547122 + 0.547122i
\(333\) 15.9565 + 8.06421i 0.874410 + 0.441916i
\(334\) −9.11768 −0.498897
\(335\) −23.1526 −1.26496
\(336\) 1.01577 1.40293i 0.0554146 0.0765362i
\(337\) 7.79284i 0.424503i −0.977215 0.212251i \(-0.931920\pi\)
0.977215 0.212251i \(-0.0680796\pi\)
\(338\) 12.5894 + 3.24145i 0.684773 + 0.176311i
\(339\) −8.54720 + 1.36816i −0.464220 + 0.0743084i
\(340\) −5.31595 + 5.31595i −0.288298 + 0.288298i
\(341\) 8.79586i 0.476322i
\(342\) −10.6249 + 3.49094i −0.574530 + 0.188768i
\(343\) −0.707107 + 0.707107i −0.0381802 + 0.0381802i
\(344\) −3.24931 3.24931i −0.175191 0.175191i
\(345\) −1.20303 + 1.66157i −0.0647691 + 0.0894561i
\(346\) 1.87865 + 1.87865i 0.100997 + 0.100997i
\(347\) 10.9288i 0.586690i 0.956007 + 0.293345i \(0.0947684\pi\)
−0.956007 + 0.293345i \(0.905232\pi\)
\(348\) 1.65271 + 10.3248i 0.0885944 + 0.553468i
\(349\) −23.3039 23.3039i −1.24743 1.24743i −0.956850 0.290581i \(-0.906151\pi\)
−0.290581 0.956850i \(-0.593849\pi\)
\(350\) −1.13282 −0.0605520
\(351\) 12.6725 + 13.7988i 0.676407 + 0.736528i
\(352\) −3.00237 −0.160027
\(353\) −17.4264 17.4264i −0.927516 0.927516i 0.0700290 0.997545i \(-0.477691\pi\)
−0.997545 + 0.0700290i \(0.977691\pi\)
\(354\) 1.45869 + 9.11277i 0.0775287 + 0.484338i
\(355\) 25.7953i 1.36907i
\(356\) 10.9270 + 10.9270i 0.579132 + 0.579132i
\(357\) −3.08361 + 4.25894i −0.163202 + 0.225407i
\(358\) 2.58008 + 2.58008i 0.136361 + 0.136361i
\(359\) −13.3523 + 13.3523i −0.704707 + 0.704707i −0.965417 0.260710i \(-0.916043\pi\)
0.260710 + 0.965417i \(0.416043\pi\)
\(360\) 7.05815 2.31904i 0.371997 0.122224i
\(361\) 5.10270i 0.268563i
\(362\) −13.7912 + 13.7912i −0.724848 + 0.724848i
\(363\) −3.39618 + 0.543631i −0.178253 + 0.0285332i
\(364\) 1.78746 3.13129i 0.0936882 0.164124i
\(365\) 28.2322i 1.47774i
\(366\) −13.4710 + 18.6055i −0.704141 + 0.972528i
\(367\) 23.3338 1.21801 0.609006 0.793165i \(-0.291568\pi\)
0.609006 + 0.793165i \(0.291568\pi\)
\(368\) −0.478247 −0.0249304
\(369\) −18.3287 9.26309i −0.954153 0.482217i
\(370\) 10.4358 10.4358i 0.542531 0.542531i
\(371\) 4.17199 4.17199i 0.216599 0.216599i
\(372\) 2.97582 4.11007i 0.154289 0.213097i
\(373\) 6.26271 0.324271 0.162135 0.986769i \(-0.448162\pi\)
0.162135 + 0.986769i \(0.448162\pi\)
\(374\) 9.11445 0.471297
\(375\) 13.4357 + 9.72788i 0.693817 + 0.502346i
\(376\) 9.86025i 0.508504i
\(377\) 5.73650 + 20.9969i 0.295445 + 1.08139i
\(378\) 4.61811 2.38183i 0.237530 0.122508i
\(379\) −23.9024 + 23.9024i −1.22779 + 1.22779i −0.262986 + 0.964800i \(0.584707\pi\)
−0.964800 + 0.262986i \(0.915293\pi\)
\(380\) 9.23199i 0.473591i
\(381\) −0.892340 + 0.142838i −0.0457160 + 0.00731782i
\(382\) 0.604431 0.604431i 0.0309254 0.0309254i
\(383\) 6.96614 + 6.96614i 0.355953 + 0.355953i 0.862319 0.506366i \(-0.169011\pi\)
−0.506366 + 0.862319i \(0.669011\pi\)
\(384\) 1.40293 + 1.01577i 0.0715931 + 0.0518356i
\(385\) 5.25751 + 5.25751i 0.267948 + 0.267948i
\(386\) 23.0864i 1.17507i
\(387\) −4.30312 13.0969i −0.218740 0.665750i
\(388\) 10.7186 + 10.7186i 0.544154 + 0.544154i
\(389\) −33.8785 −1.71771 −0.858854 0.512220i \(-0.828823\pi\)
−0.858854 + 0.512220i \(0.828823\pi\)
\(390\) 14.0869 6.38269i 0.713319 0.323200i
\(391\) 1.45184 0.0734226
\(392\) −0.707107 0.707107i −0.0357143 0.0357143i
\(393\) −17.3336 + 2.77462i −0.874366 + 0.139961i
\(394\) 10.5461i 0.531304i
\(395\) −20.3168 20.3168i −1.02225 1.02225i
\(396\) −8.03882 4.06272i −0.403966 0.204159i
\(397\) 1.28835 + 1.28835i 0.0646606 + 0.0646606i 0.738698 0.674037i \(-0.235441\pi\)
−0.674037 + 0.738698i \(0.735441\pi\)
\(398\) 0.550206 0.550206i 0.0275793 0.0275793i
\(399\) 1.02058 + 6.37576i 0.0510928 + 0.319187i
\(400\) 1.13282i 0.0566412i
\(401\) 17.5817 17.5817i 0.877988 0.877988i −0.115339 0.993326i \(-0.536795\pi\)
0.993326 + 0.115339i \(0.0367953\pi\)
\(402\) −2.55947 15.9895i −0.127655 0.797486i
\(403\) 5.23659 9.17354i 0.260853 0.456967i
\(404\) 5.04608i 0.251052i
\(405\) 22.0362 + 3.34168i 1.09499 + 0.166049i
\(406\) 6.03691 0.299607
\(407\) −17.8927 −0.886906
\(408\) −4.25894 3.08361i −0.210849 0.152661i
\(409\) 21.1765 21.1765i 1.04711 1.04711i 0.0482783 0.998834i \(-0.484627\pi\)
0.998834 0.0482783i \(-0.0153735\pi\)
\(410\) −11.9872 + 11.9872i −0.592008 + 0.592008i
\(411\) −8.07497 5.84653i −0.398309 0.288388i
\(412\) 17.3260 0.853591
\(413\) 5.32824 0.262185
\(414\) −1.28050 0.647149i −0.0629332 0.0318057i
\(415\) 34.9139i 1.71386i
\(416\) 3.13129 + 1.78746i 0.153524 + 0.0876372i
\(417\) 0.0475714 + 0.297189i 0.00232958 + 0.0145534i
\(418\) 7.91435 7.91435i 0.387103 0.387103i
\(419\) 31.9709i 1.56188i 0.624607 + 0.780939i \(0.285259\pi\)
−0.624607 + 0.780939i \(0.714741\pi\)
\(420\) −0.677971 4.23543i −0.0330816 0.206668i
\(421\) 11.0977 11.0977i 0.540869 0.540869i −0.382915 0.923784i \(-0.625080\pi\)
0.923784 + 0.382915i \(0.125080\pi\)
\(422\) −3.19074 3.19074i −0.155323 0.155323i
\(423\) 13.3426 26.4007i 0.648738 1.28365i
\(424\) 4.17199 + 4.17199i 0.202610 + 0.202610i
\(425\) 3.43897i 0.166814i
\(426\) −17.8146 + 2.85161i −0.863121 + 0.138161i
\(427\) 9.37758 + 9.37758i 0.453813 + 0.453813i
\(428\) −7.64785 −0.369673
\(429\) −17.5481 6.60463i −0.847229 0.318875i
\(430\) −11.3798 −0.548785
\(431\) 0.127561 + 0.127561i 0.00614442 + 0.00614442i 0.710172 0.704028i \(-0.248617\pi\)
−0.704028 + 0.710172i \(0.748617\pi\)
\(432\) 2.38183 + 4.61811i 0.114596 + 0.222189i
\(433\) 10.1128i 0.485988i 0.970028 + 0.242994i \(0.0781296\pi\)
−0.970028 + 0.242994i \(0.921870\pi\)
\(434\) −2.07156 2.07156i −0.0994382 0.0994382i
\(435\) 20.9740 + 15.1859i 1.00563 + 0.728106i
\(436\) 2.94969 + 2.94969i 0.141265 + 0.141265i
\(437\) 1.26067 1.26067i 0.0603062 0.0603062i
\(438\) 19.4976 3.12101i 0.931631 0.149128i
\(439\) 22.8399i 1.09009i −0.838408 0.545043i \(-0.816513\pi\)
0.838408 0.545043i \(-0.183487\pi\)
\(440\) −5.25751 + 5.25751i −0.250642 + 0.250642i
\(441\) −0.936434 2.85010i −0.0445921 0.135719i
\(442\) −9.50581 5.42626i −0.452145 0.258101i
\(443\) 8.91535i 0.423581i −0.977315 0.211791i \(-0.932071\pi\)
0.977315 0.211791i \(-0.0679295\pi\)
\(444\) 8.36077 + 6.05346i 0.396785 + 0.287285i
\(445\) 38.2691 1.81413
\(446\) −4.36135 −0.206516
\(447\) −5.94571 + 8.21195i −0.281222 + 0.388412i
\(448\) 0.707107 0.707107i 0.0334077 0.0334077i
\(449\) 19.3368 19.3368i 0.912558 0.912558i −0.0839148 0.996473i \(-0.526742\pi\)
0.996473 + 0.0839148i \(0.0267424\pi\)
\(450\) 1.53290 3.03312i 0.0722617 0.142983i
\(451\) 20.5527 0.967789
\(452\) −4.99755 −0.235065
\(453\) 9.69765 13.3940i 0.455635 0.629303i
\(454\) 26.7778i 1.25675i
\(455\) −2.35322 8.61331i −0.110321 0.403798i
\(456\) −6.37576 + 1.02058i −0.298572 + 0.0477929i
\(457\) 6.87890 6.87890i 0.321781 0.321781i −0.527669 0.849450i \(-0.676934\pi\)
0.849450 + 0.527669i \(0.176934\pi\)
\(458\) 17.3212i 0.809366i
\(459\) −7.23062 14.0194i −0.337497 0.654369i
\(460\) −0.837467 + 0.837467i −0.0390471 + 0.0390471i
\(461\) −5.37847 5.37847i −0.250500 0.250500i 0.570675 0.821176i \(-0.306681\pi\)
−0.821176 + 0.570675i \(0.806681\pi\)
\(462\) −3.04971 + 4.21213i −0.141886 + 0.195966i
\(463\) −1.71052 1.71052i −0.0794944 0.0794944i 0.666242 0.745736i \(-0.267902\pi\)
−0.745736 + 0.666242i \(0.767902\pi\)
\(464\) 6.03691i 0.280257i
\(465\) −1.98621 12.4082i −0.0921081 0.575418i
\(466\) −10.9455 10.9455i −0.507041 0.507041i
\(467\) 12.1098 0.560375 0.280188 0.959945i \(-0.409603\pi\)
0.280188 + 0.959945i \(0.409603\pi\)
\(468\) 5.96527 + 9.02306i 0.275745 + 0.417091i
\(469\) −9.34908 −0.431701
\(470\) −17.2665 17.2665i −0.796442 0.796442i
\(471\) −1.13549 7.09363i −0.0523205 0.326857i
\(472\) 5.32824i 0.245252i
\(473\) 9.75565 + 9.75565i 0.448565 + 0.448565i
\(474\) 11.7851 16.2771i 0.541308 0.747630i
\(475\) 2.98616 + 2.98616i 0.137014 + 0.137014i
\(476\) −2.14660 + 2.14660i −0.0983891 + 0.0983891i
\(477\) 5.52505 + 16.8159i 0.252975 + 0.769946i
\(478\) 15.9662i 0.730278i
\(479\) 0.535810 0.535810i 0.0244818 0.0244818i −0.694760 0.719242i \(-0.744489\pi\)
0.719242 + 0.694760i \(0.244489\pi\)
\(480\) 4.23543 0.677971i 0.193320 0.0309450i
\(481\) 18.6609 + 10.6523i 0.850866 + 0.485705i
\(482\) 4.44306i 0.202376i
\(483\) −0.485788 + 0.670949i −0.0221041 + 0.0305292i
\(484\) −1.98575 −0.0902612
\(485\) 37.5390 1.70456
\(486\) 0.128235 + 15.5879i 0.00581687 + 0.707083i
\(487\) 5.52429 5.52429i 0.250329 0.250329i −0.570776 0.821106i \(-0.693358\pi\)
0.821106 + 0.570776i \(0.193358\pi\)
\(488\) −9.37758 + 9.37758i −0.424503 + 0.424503i
\(489\) 19.1651 26.4699i 0.866675 1.19701i
\(490\) −2.47645 −0.111875
\(491\) 32.2992 1.45764 0.728821 0.684704i \(-0.240068\pi\)
0.728821 + 0.684704i \(0.240068\pi\)
\(492\) −9.60374 6.95342i −0.432970 0.313484i
\(493\) 18.3265i 0.825386i
\(494\) −12.9660 + 3.54240i −0.583366 + 0.159380i
\(495\) −21.1912 + 6.96262i −0.952474 + 0.312946i
\(496\) 2.07156 2.07156i 0.0930159 0.0930159i
\(497\) 10.4162i 0.467231i
\(498\) −24.1121 + 3.85966i −1.08049 + 0.172956i
\(499\) 24.5090 24.5090i 1.09717 1.09717i 0.102433 0.994740i \(-0.467337\pi\)
0.994740 0.102433i \(-0.0326627\pi\)
\(500\) 6.77188 + 6.77188i 0.302848 + 0.302848i
\(501\) −12.7915 9.26144i −0.571481 0.413771i
\(502\) 13.0316 + 13.0316i 0.581628 + 0.581628i
\(503\) 22.3557i 0.996792i 0.866949 + 0.498396i \(0.166077\pi\)
−0.866949 + 0.498396i \(0.833923\pi\)
\(504\) 2.85010 0.936434i 0.126954 0.0417121i
\(505\) −8.83627 8.83627i −0.393209 0.393209i
\(506\) 1.43588 0.0638326
\(507\) 14.3695 + 17.3354i 0.638173 + 0.769893i
\(508\) −0.521751 −0.0231490
\(509\) −2.91721 2.91721i −0.129303 0.129303i 0.639493 0.768797i \(-0.279144\pi\)
−0.768797 + 0.639493i \(0.779144\pi\)
\(510\) −12.8577 + 2.05815i −0.569347 + 0.0911363i
\(511\) 11.4002i 0.504317i
\(512\) 0.707107 + 0.707107i 0.0312500 + 0.0312500i
\(513\) −18.4520 5.89490i −0.814677 0.260266i
\(514\) −3.08077 3.08077i −0.135887 0.135887i
\(515\) 30.3399 30.3399i 1.33693 1.33693i
\(516\) −1.25802 7.85910i −0.0553812 0.345978i
\(517\) 29.6042i 1.30199i
\(518\) 4.21400 4.21400i 0.185153 0.185153i
\(519\) 0.727347 + 4.54389i 0.0319270 + 0.199455i
\(520\) 8.61331 2.35322i 0.377719 0.103195i
\(521\) 20.6947i 0.906651i 0.891345 + 0.453325i \(0.149762\pi\)
−0.891345 + 0.453325i \(0.850238\pi\)
\(522\) −8.16896 + 16.1638i −0.357546 + 0.707469i
\(523\) −22.5537 −0.986202 −0.493101 0.869972i \(-0.664137\pi\)
−0.493101 + 0.869972i \(0.664137\pi\)
\(524\) −10.1350 −0.442748
\(525\) −1.58928 1.15069i −0.0693617 0.0502201i
\(526\) 1.05816 1.05816i 0.0461381 0.0461381i
\(527\) −6.28874 + 6.28874i −0.273942 + 0.273942i
\(528\) −4.21213 3.04971i −0.183309 0.132722i
\(529\) −22.7713 −0.990056
\(530\) 14.6113 0.634674
\(531\) −7.21000 + 14.2663i −0.312887 + 0.619104i
\(532\) 3.72791i 0.161625i
\(533\) −21.4352 12.2360i −0.928462 0.530000i
\(534\) 4.23056 + 26.4292i 0.183074 + 1.14370i
\(535\) −13.3923 + 13.3923i −0.578999 + 0.578999i
\(536\) 9.34908i 0.403819i
\(537\) 0.998915 + 6.24043i 0.0431063 + 0.269294i
\(538\) 7.83230 7.83230i 0.337674 0.337674i
\(539\) 2.12300 + 2.12300i 0.0914441 + 0.0914441i
\(540\) 12.2577 + 3.91599i 0.527488 + 0.168517i
\(541\) −0.860954 0.860954i −0.0370153 0.0370153i 0.688357 0.725372i \(-0.258332\pi\)
−0.725372 + 0.688357i \(0.758332\pi\)
\(542\) 13.3176i 0.572042i
\(543\) −33.3567 + 5.33945i −1.43147 + 0.229138i
\(544\) −2.14660 2.14660i −0.0920346 0.0920346i
\(545\) 10.3305 0.442510
\(546\) 5.68834 2.57735i 0.243439 0.110300i
\(547\) 38.4468 1.64387 0.821934 0.569582i \(-0.192895\pi\)
0.821934 + 0.569582i \(0.192895\pi\)
\(548\) −4.06995 4.06995i −0.173860 0.173860i
\(549\) −37.7978 + 12.4189i −1.61317 + 0.530026i
\(550\) 3.40116i 0.145026i
\(551\) −15.9135 15.9135i −0.677937 0.677937i
\(552\) −0.670949 0.485788i −0.0285575 0.0206765i
\(553\) −8.20397 8.20397i −0.348868 0.348868i
\(554\) −14.4068 + 14.4068i −0.612085 + 0.612085i
\(555\) 25.2410 4.04037i 1.07142 0.171504i
\(556\) 0.173766i 0.00736933i
\(557\) 0.845111 0.845111i 0.0358085 0.0358085i −0.688976 0.724784i \(-0.741939\pi\)
0.724784 + 0.688976i \(0.241939\pi\)
\(558\) 8.34976 2.74341i 0.353473 0.116138i
\(559\) −4.36655 15.9825i −0.184685 0.675990i
\(560\) 2.47645i 0.104649i
\(561\) 12.7869 + 9.25816i 0.539865 + 0.390880i
\(562\) 20.6092 0.869346
\(563\) 42.4619 1.78955 0.894777 0.446513i \(-0.147334\pi\)
0.894777 + 0.446513i \(0.147334\pi\)
\(564\) 10.0157 13.8333i 0.421738 0.582485i
\(565\) −8.75130 + 8.75130i −0.368170 + 0.368170i
\(566\) −12.3916 + 12.3916i −0.520857 + 0.520857i
\(567\) 8.89827 + 1.34938i 0.373692 + 0.0566686i
\(568\) −10.4162 −0.437055
\(569\) −13.1702 −0.552122 −0.276061 0.961140i \(-0.589029\pi\)
−0.276061 + 0.961140i \(0.589029\pi\)
\(570\) −9.37755 + 12.9519i −0.392783 + 0.542493i
\(571\) 22.7843i 0.953494i −0.879041 0.476747i \(-0.841816\pi\)
0.879041 0.476747i \(-0.158184\pi\)
\(572\) −9.40132 5.36661i −0.393089 0.224389i
\(573\) 1.46194 0.234014i 0.0610733 0.00977609i
\(574\) −4.84049 + 4.84049i −0.202038 + 0.202038i
\(575\) 0.541771i 0.0225934i
\(576\) 0.936434 + 2.85010i 0.0390181 + 0.118754i
\(577\) 17.2984 17.2984i 0.720142 0.720142i −0.248492 0.968634i \(-0.579935\pi\)
0.968634 + 0.248492i \(0.0799350\pi\)
\(578\) −5.50429 5.50429i −0.228948 0.228948i
\(579\) 23.4504 32.3887i 0.974567 1.34603i
\(580\) 10.5713 + 10.5713i 0.438951 + 0.438951i
\(581\) 14.0984i 0.584898i
\(582\) 4.14986 + 25.9250i 0.172017 + 1.07463i
\(583\) −12.5259 12.5259i −0.518769 0.518769i
\(584\) 11.4002 0.471746
\(585\) 26.2463 + 5.35455i 1.08515 + 0.221383i
\(586\) −31.9030 −1.31790
\(587\) 21.3846 + 21.3846i 0.882638 + 0.882638i 0.993802 0.111164i \(-0.0354580\pi\)
−0.111164 + 0.993802i \(0.535458\pi\)
\(588\) −0.273767 1.71028i −0.0112899 0.0705307i
\(589\) 10.9214i 0.450009i
\(590\) 9.33037 + 9.33037i 0.384125 + 0.384125i
\(591\) 10.7124 14.7954i 0.440648 0.608603i
\(592\) 4.21400 + 4.21400i 0.173194 + 0.173194i
\(593\) 0.343278 0.343278i 0.0140968 0.0140968i −0.700023 0.714120i \(-0.746827\pi\)
0.714120 + 0.700023i \(0.246827\pi\)
\(594\) −7.15114 13.8653i −0.293415 0.568900i
\(595\) 7.51789i 0.308203i
\(596\) −4.13899 + 4.13899i −0.169540 + 0.169540i
\(597\) 1.33078 0.213020i 0.0544653 0.00871834i
\(598\) −1.49753 0.854846i −0.0612387 0.0349573i
\(599\) 36.3142i 1.48376i −0.670534 0.741879i \(-0.733935\pi\)
0.670534 0.741879i \(-0.266065\pi\)
\(600\) 1.15069 1.58928i 0.0469766 0.0648819i
\(601\) −21.1337 −0.862061 −0.431031 0.902337i \(-0.641850\pi\)
−0.431031 + 0.902337i \(0.641850\pi\)
\(602\) −4.59522 −0.187287
\(603\) 12.6509 25.0320i 0.515184 1.01938i
\(604\) 6.75083 6.75083i 0.274687 0.274687i
\(605\) −3.47727 + 3.47727i −0.141371 + 0.141371i
\(606\) 5.12564 7.07930i 0.208215 0.287577i
\(607\) −5.09736 −0.206896 −0.103448 0.994635i \(-0.532987\pi\)
−0.103448 + 0.994635i \(0.532987\pi\)
\(608\) −3.72791 −0.151187
\(609\) 8.46938 + 6.13210i 0.343197 + 0.248485i
\(610\) 32.8425i 1.32975i
\(611\) 17.6248 30.8753i 0.713022 1.24908i
\(612\) −2.84278 8.65219i −0.114912 0.349744i
\(613\) 28.8407 28.8407i 1.16486 1.16486i 0.181467 0.983397i \(-0.441915\pi\)
0.983397 0.181467i \(-0.0580845\pi\)
\(614\) 21.2337i 0.856921i
\(615\) −28.9935 + 4.64104i −1.16913 + 0.187145i
\(616\) −2.12300 + 2.12300i −0.0855381 + 0.0855381i
\(617\) 29.3917 + 29.3917i 1.18327 + 1.18327i 0.978893 + 0.204373i \(0.0655155\pi\)
0.204373 + 0.978893i \(0.434485\pi\)
\(618\) 24.3072 + 17.5992i 0.977779 + 0.707943i
\(619\) −2.81364 2.81364i −0.113090 0.113090i 0.648298 0.761387i \(-0.275481\pi\)
−0.761387 + 0.648298i \(0.775481\pi\)
\(620\) 7.25510i 0.291372i
\(621\) −1.13910 2.20860i −0.0457106 0.0886280i
\(622\) −7.58527 7.58527i −0.304142 0.304142i
\(623\) 15.4532 0.619118
\(624\) 2.57735 + 5.68834i 0.103177 + 0.227716i
\(625\) 29.3808 1.17523
\(626\) −12.2577 12.2577i −0.489917 0.489917i
\(627\) 19.1424 3.06415i 0.764475 0.122371i
\(628\) 4.14765i 0.165509i
\(629\) −12.7926 12.7926i −0.510076 0.510076i
\(630\) 3.35106 6.63067i 0.133509 0.264172i
\(631\) −22.1341 22.1341i −0.881143 0.881143i 0.112507 0.993651i \(-0.464112\pi\)
−0.993651 + 0.112507i \(0.964112\pi\)
\(632\) 8.20397 8.20397i 0.326337 0.326337i
\(633\) −1.23534 7.71744i −0.0491004 0.306741i
\(634\) 27.8199i 1.10487i
\(635\) −0.913648 + 0.913648i −0.0362570 + 0.0362570i
\(636\) 1.61525 + 10.0908i 0.0640488 + 0.400126i
\(637\) −0.950237 3.47808i −0.0376498 0.137807i
\(638\) 18.1251i 0.717579i
\(639\) −27.8893 14.0949i −1.10328 0.557585i
\(640\) 2.47645 0.0978904
\(641\) −22.5807 −0.891885 −0.445943 0.895062i \(-0.647131\pi\)
−0.445943 + 0.895062i \(0.647131\pi\)
\(642\) −10.7294 7.76843i −0.423456 0.306595i
\(643\) −11.9697 + 11.9697i −0.472039 + 0.472039i −0.902574 0.430535i \(-0.858325\pi\)
0.430535 + 0.902574i \(0.358325\pi\)
\(644\) −0.338172 + 0.338172i −0.0133258 + 0.0133258i
\(645\) −15.9652 11.5593i −0.628627 0.455146i
\(646\) 11.3170 0.445261
\(647\) −49.1692 −1.93304 −0.966521 0.256586i \(-0.917402\pi\)
−0.966521 + 0.256586i \(0.917402\pi\)
\(648\) −1.34938 + 8.89827i −0.0530086 + 0.349557i
\(649\) 15.9974i 0.627951i
\(650\) 2.02487 3.54721i 0.0794221 0.139133i
\(651\) −0.802036 5.01049i −0.0314343 0.196376i
\(652\) 13.3414 13.3414i 0.522490 0.522490i
\(653\) 34.8066i 1.36209i 0.732242 + 0.681044i \(0.238474\pi\)
−0.732242 + 0.681044i \(0.761526\pi\)
\(654\) 1.14202 + 7.13441i 0.0446563 + 0.278978i
\(655\) −17.7475 + 17.7475i −0.693453 + 0.693453i
\(656\) −4.84049 4.84049i −0.188989 0.188989i
\(657\) 30.5240 + 15.4265i 1.19085 + 0.601843i
\(658\) −6.97225 6.97225i −0.271807 0.271807i
\(659\) 12.0404i 0.469029i −0.972113 0.234514i \(-0.924650\pi\)
0.972113 0.234514i \(-0.0753500\pi\)
\(660\) −12.7163 + 2.03552i −0.494983 + 0.0792326i
\(661\) 27.1053 + 27.1053i 1.05427 + 1.05427i 0.998440 + 0.0558331i \(0.0177815\pi\)
0.0558331 + 0.998440i \(0.482219\pi\)
\(662\) 5.90994 0.229697
\(663\) −7.82419 17.2684i −0.303866 0.670648i
\(664\) −14.0984 −0.547122
\(665\) 6.52800 + 6.52800i 0.253145 + 0.253145i
\(666\) 5.58068 + 16.9852i 0.216247 + 0.658163i
\(667\) 2.88714i 0.111790i
\(668\) −6.44717 6.44717i −0.249449 0.249449i
\(669\) −6.11867 4.43011i −0.236561 0.171278i
\(670\) −16.3713 16.3713i −0.632480 0.632480i
\(671\) 28.1550 28.1550i 1.08691 1.08691i
\(672\) 1.71028 0.273767i 0.0659754 0.0105608i
\(673\) 17.0132i 0.655809i 0.944711 + 0.327905i \(0.106342\pi\)
−0.944711 + 0.327905i \(0.893658\pi\)
\(674\) 5.51037 5.51037i 0.212251 0.212251i
\(675\) 5.23150 2.69819i 0.201361 0.103853i
\(676\) 6.61000 + 11.1941i 0.254231 + 0.430542i
\(677\) 2.58605i 0.0993901i −0.998764 0.0496950i \(-0.984175\pi\)
0.998764 0.0496950i \(-0.0158249\pi\)
\(678\) −7.01122 5.07635i −0.269264 0.194956i
\(679\) 15.1584 0.581725
\(680\) −7.51789 −0.288298
\(681\) 27.2001 37.5675i 1.04231 1.43959i
\(682\) −6.21961 + 6.21961i −0.238161 + 0.238161i
\(683\) 25.9379 25.9379i 0.992486 0.992486i −0.00748557 0.999972i \(-0.502383\pi\)
0.999972 + 0.00748557i \(0.00238275\pi\)
\(684\) −9.98142 5.04449i −0.381649 0.192881i
\(685\) −14.2539 −0.544615
\(686\) −1.00000 −0.0381802
\(687\) −17.5943 + 24.3004i −0.671264 + 0.927119i
\(688\) 4.59522i 0.175191i
\(689\) 5.60648 + 20.5210i 0.213590 + 0.781788i
\(690\) −2.02558 + 0.324238i −0.0771126 + 0.0123435i
\(691\) −35.6892 + 35.6892i −1.35768 + 1.35768i −0.480914 + 0.876768i \(0.659695\pi\)
−0.876768 + 0.480914i \(0.840305\pi\)
\(692\) 2.65682i 0.100997i
\(693\) −8.55708 + 2.81153i −0.325057 + 0.106801i
\(694\) −7.72784 + 7.72784i −0.293345 + 0.293345i
\(695\) 0.304285 + 0.304285i 0.0115422 + 0.0115422i
\(696\) −6.13210 + 8.46938i −0.232437 + 0.321031i
\(697\) 14.6945 + 14.6945i 0.556593 + 0.556593i
\(698\) 32.9568i 1.24743i
\(699\) −4.23771 26.4739i −0.160285 1.00133i
\(700\) −0.801028 0.801028i −0.0302760 0.0302760i
\(701\) −28.4715 −1.07535 −0.537676 0.843151i \(-0.680698\pi\)
−0.537676 + 0.843151i \(0.680698\pi\)
\(702\) −0.796461 + 18.7181i −0.0300605 + 0.706468i
\(703\) −22.2165 −0.837910
\(704\) −2.12300 2.12300i −0.0800136 0.0800136i
\(705\) −6.68496 41.7624i −0.251770 1.57286i
\(706\) 24.6447i 0.927516i
\(707\) −3.56811 3.56811i −0.134193 0.134193i
\(708\) −5.41225 + 7.47515i −0.203405 + 0.280933i
\(709\) 34.7099 + 34.7099i 1.30356 + 1.30356i 0.925975 + 0.377584i \(0.123245\pi\)
0.377584 + 0.925975i \(0.376755\pi\)
\(710\) −18.2400 + 18.2400i −0.684535 + 0.684535i
\(711\) 33.0674 10.8647i 1.24012 0.407457i
\(712\) 15.4532i 0.579132i
\(713\) −0.990720 + 0.990720i −0.0371028 + 0.0371028i
\(714\) −5.19197 + 0.831086i −0.194305 + 0.0311026i
\(715\) −25.8604 + 7.06524i −0.967123 + 0.264225i
\(716\) 3.64878i 0.136361i
\(717\) 16.2180 22.3995i 0.605671 0.836525i
\(718\) −18.8830 −0.704707
\(719\) −3.99422 −0.148959 −0.0744797 0.997223i \(-0.523730\pi\)
−0.0744797 + 0.997223i \(0.523730\pi\)
\(720\) 6.63067 + 3.35106i 0.247111 + 0.124887i
\(721\) 12.2513 12.2513i 0.456263 0.456263i
\(722\) −3.60816 + 3.60816i −0.134282 + 0.134282i
\(723\) 4.51311 6.23331i 0.167844 0.231819i
\(724\) −19.5037 −0.724848
\(725\) 6.83877 0.253985
\(726\) −2.78587 2.01705i −0.103393 0.0748599i
\(727\) 31.5807i 1.17126i 0.810577 + 0.585632i \(0.199154\pi\)
−0.810577 + 0.585632i \(0.800846\pi\)
\(728\) 3.47808 0.950237i 0.128906 0.0352181i
\(729\) −15.6538 + 21.9991i −0.579770 + 0.814780i
\(730\) 19.9632 19.9632i 0.738870 0.738870i
\(731\) 13.9499i 0.515956i
\(732\) −22.6815 + 3.63067i −0.838334 + 0.134193i
\(733\) −3.05349 + 3.05349i −0.112783 + 0.112783i −0.761246 0.648463i \(-0.775412\pi\)
0.648463 + 0.761246i \(0.275412\pi\)
\(734\) 16.4995 + 16.4995i 0.609006 + 0.609006i
\(735\) −3.47430 2.51550i −0.128151 0.0927856i
\(736\) −0.338172 0.338172i −0.0124652 0.0124652i
\(737\) 28.0695i 1.03395i
\(738\) −6.41035 19.5103i −0.235968 0.718185i
\(739\) 5.30152 + 5.30152i 0.195020 + 0.195020i 0.797861 0.602841i \(-0.205965\pi\)
−0.602841 + 0.797861i \(0.705965\pi\)
\(740\) 14.7584 0.542531
\(741\) −21.7886 8.20066i −0.800425 0.301259i
\(742\) 5.90009 0.216599
\(743\) 21.0757 + 21.0757i 0.773191 + 0.773191i 0.978663 0.205472i \(-0.0658728\pi\)
−0.205472 + 0.978663i \(0.565873\pi\)
\(744\) 5.01049 0.802036i 0.183693 0.0294041i
\(745\) 14.4957i 0.531082i
\(746\) 4.42841 + 4.42841i 0.162135 + 0.162135i
\(747\) −37.7482 19.0775i −1.38113 0.698007i
\(748\) 6.44489 + 6.44489i 0.235648 + 0.235648i
\(749\) −5.40784 + 5.40784i −0.197598 + 0.197598i
\(750\) 2.62183 + 16.3791i 0.0957357 + 0.598081i
\(751\) 52.4292i 1.91317i 0.291454 + 0.956585i \(0.405861\pi\)
−0.291454 + 0.956585i \(0.594139\pi\)
\(752\) 6.97225 6.97225i 0.254252 0.254252i
\(753\) 5.04536 + 31.5195i 0.183863 + 1.14863i
\(754\) −10.7907 + 18.9034i −0.392975 + 0.688420i
\(755\) 23.6430i 0.860457i
\(756\) 4.94970 + 1.58129i 0.180019 + 0.0575109i
\(757\) −37.6352 −1.36787 −0.683937 0.729541i \(-0.739734\pi\)
−0.683937 + 0.729541i \(0.739734\pi\)
\(758\) −33.8031 −1.22779
\(759\) 2.01444 + 1.45852i 0.0731195 + 0.0529408i
\(760\) −6.52800 + 6.52800i −0.236796 + 0.236796i
\(761\) 4.70073 4.70073i 0.170401 0.170401i −0.616754 0.787156i \(-0.711553\pi\)
0.787156 + 0.616754i \(0.211553\pi\)
\(762\) −0.731981 0.529978i −0.0265169 0.0191991i
\(763\) 4.17149 0.151018
\(764\) 0.854794 0.0309254
\(765\) −20.1290 10.1730i −0.727767 0.367804i
\(766\) 9.85161i 0.355953i
\(767\) −9.52399 + 16.6843i −0.343891 + 0.602434i
\(768\) 0.273767 + 1.71028i 0.00987870 + 0.0617144i
\(769\) −11.5981 + 11.5981i −0.418239 + 0.418239i −0.884596 0.466358i \(-0.845566\pi\)
0.466358 + 0.884596i \(0.345566\pi\)
\(770\) 7.43524i 0.267948i
\(771\) −1.19277 7.45146i −0.0429564 0.268358i
\(772\) 16.3246 16.3246i 0.587534 0.587534i
\(773\) 21.5154 + 21.5154i 0.773854 + 0.773854i 0.978778 0.204924i \(-0.0656947\pi\)
−0.204924 + 0.978778i \(0.565695\pi\)
\(774\) 6.21811 12.3036i 0.223505 0.442245i
\(775\) −2.34672 2.34672i −0.0842966 0.0842966i
\(776\) 15.1584i 0.544154i
\(777\) 10.1924 1.63151i 0.365650 0.0585302i
\(778\) −23.9557 23.9557i −0.858854 0.858854i
\(779\) 25.5193 0.914325
\(780\) 14.4742 + 5.44771i 0.518260 + 0.195059i
\(781\) 31.2734 1.11905
\(782\) 1.02660 + 1.02660i 0.0367113 + 0.0367113i
\(783\) −27.8791 + 14.3789i −0.996318 + 0.513859i
\(784\) 1.00000i 0.0357143i
\(785\) −7.26302 7.26302i −0.259228 0.259228i
\(786\) −14.2187 10.2948i −0.507163 0.367202i
\(787\) −16.1871 16.1871i −0.577009 0.577009i 0.357069 0.934078i \(-0.383776\pi\)
−0.934078 + 0.357069i \(0.883776\pi\)
\(788\) 7.45721 7.45721i 0.265652 0.265652i
\(789\) 2.55938 0.409683i 0.0911163 0.0145851i
\(790\) 28.7322i 1.02225i
\(791\) −3.53380 + 3.53380i −0.125648 + 0.125648i
\(792\) −2.81153 8.55708i −0.0999033 0.304063i
\(793\) −46.1260 + 12.6020i −1.63798 + 0.447508i
\(794\) 1.82201i 0.0646606i
\(795\) 20.4987 + 14.8417i 0.727013 + 0.526380i
\(796\) 0.778109 0.0275793
\(797\) 39.4250 1.39651 0.698253 0.715851i \(-0.253961\pi\)
0.698253 + 0.715851i \(0.253961\pi\)
\(798\) −3.78669 + 5.23000i −0.134047 + 0.185140i
\(799\) −21.1660 + 21.1660i −0.748799 + 0.748799i
\(800\) 0.801028 0.801028i 0.0283206 0.0283206i
\(801\) −20.9107 + 41.3757i −0.738845 + 1.46194i
\(802\) 24.8643 0.877988
\(803\) −34.2278 −1.20787
\(804\) 9.49649 13.1161i 0.334915 0.462570i
\(805\) 1.18436i 0.0417431i
\(806\) 10.1895 2.78385i 0.358910 0.0980568i
\(807\) 18.9440 3.03239i 0.666860 0.106745i
\(808\) 3.56811 3.56811i 0.125526 0.125526i
\(809\) 0.405681i 0.0142630i −0.999975 0.00713149i \(-0.997730\pi\)
0.999975 0.00713149i \(-0.00227004\pi\)
\(810\) 13.2190 + 17.9448i 0.464468 + 0.630517i
\(811\) −26.4050 + 26.4050i −0.927206 + 0.927206i −0.997525 0.0703186i \(-0.977598\pi\)
0.0703186 + 0.997525i \(0.477598\pi\)
\(812\) 4.26874 + 4.26874i 0.149804 + 0.149804i
\(813\) 13.5276 18.6837i 0.474434 0.655267i
\(814\) −12.6520 12.6520i −0.443453 0.443453i
\(815\) 46.7247i 1.63670i
\(816\) −0.831086 5.19197i −0.0290938 0.181755i
\(817\) 12.1131 + 12.1131i 0.423785 + 0.423785i
\(818\) 29.9481 1.04711
\(819\) 10.5983 + 2.16218i 0.370336 + 0.0755528i
\(820\) −16.9525 −0.592008
\(821\) 31.8342 + 31.8342i 1.11102 + 1.11102i 0.993012 + 0.118010i \(0.0376513\pi\)
0.118010 + 0.993012i \(0.462349\pi\)
\(822\) −1.57574 9.84399i −0.0549603 0.343349i
\(823\) 29.9746i 1.04485i 0.852685 + 0.522425i \(0.174973\pi\)
−0.852685 + 0.522425i \(0.825027\pi\)
\(824\) 12.2513 + 12.2513i 0.426795 + 0.426795i
\(825\) −3.45479 + 4.77160i −0.120280 + 0.166126i
\(826\) 3.76763 + 3.76763i 0.131093 + 0.131093i
\(827\) −22.1847 + 22.1847i −0.771436 + 0.771436i −0.978358 0.206921i \(-0.933656\pi\)
0.206921 + 0.978358i \(0.433656\pi\)
\(828\) −0.447847 1.36305i −0.0155638 0.0473694i
\(829\) 25.2640i 0.877455i 0.898620 + 0.438728i \(0.144571\pi\)
−0.898620 + 0.438728i \(0.855429\pi\)
\(830\) −24.6879 + 24.6879i −0.856929 + 0.856929i
\(831\) −34.8457 + 5.57779i −1.20878 + 0.193492i
\(832\) 0.950237 + 3.47808i 0.0329435 + 0.120581i
\(833\) 3.03575i 0.105182i
\(834\) −0.176506 + 0.243782i −0.00611190 + 0.00844148i
\(835\) −22.5795 −0.781396
\(836\) 11.1926 0.387103
\(837\) 14.5008 + 4.63259i 0.501221 + 0.160126i
\(838\) −22.6068 + 22.6068i −0.780939 + 0.780939i
\(839\) −21.9032 + 21.9032i −0.756182 + 0.756182i −0.975625 0.219443i \(-0.929576\pi\)
0.219443 + 0.975625i \(0.429576\pi\)
\(840\) 2.51550 3.47430i 0.0867930 0.119875i
\(841\) −7.44434 −0.256701
\(842\) 15.6945 0.540869
\(843\) 28.9133 + 20.9341i 0.995826 + 0.721009i
\(844\) 4.51239i 0.155323i
\(845\) 31.1771 + 8.02730i 1.07252 + 0.276147i
\(846\) 28.1027 9.23348i 0.966192 0.317454i
\(847\) −1.40413 + 1.40413i −0.0482466 + 0.0482466i
\(848\) 5.90009i 0.202610i
\(849\) −29.9715 + 4.79758i −1.02862 + 0.164653i
\(850\) −2.43172 + 2.43172i −0.0834072 + 0.0834072i
\(851\) −2.01534 2.01534i −0.0690848 0.0690848i
\(852\) −14.6132 10.5804i −0.500641 0.362480i
\(853\) −26.8634 26.8634i −0.919786 0.919786i 0.0772278 0.997013i \(-0.475393\pi\)
−0.997013 + 0.0772278i \(0.975393\pi\)
\(854\) 13.2619i 0.453813i
\(855\) −26.3121 + 8.64516i −0.899856 + 0.295658i
\(856\) −5.40784 5.40784i −0.184836 0.184836i
\(857\) 14.0267 0.479144 0.239572 0.970879i \(-0.422993\pi\)
0.239572 + 0.970879i \(0.422993\pi\)
\(858\) −7.73818 17.0785i −0.264177 0.583052i
\(859\) −8.32911 −0.284185 −0.142093 0.989853i \(-0.545383\pi\)
−0.142093 + 0.989853i \(0.545383\pi\)
\(860\) −8.04677 8.04677i −0.274393 0.274393i
\(861\) −11.7077 + 1.87406i −0.398997 + 0.0638680i
\(862\) 0.180399i 0.00614442i
\(863\) −16.9934 16.9934i −0.578463 0.578463i 0.356017 0.934480i \(-0.384135\pi\)
−0.934480 + 0.356017i \(0.884135\pi\)
\(864\) −1.58129 + 4.94970i −0.0537965 + 0.168392i
\(865\) 4.65240 + 4.65240i 0.158186 + 0.158186i
\(866\) −7.15080 + 7.15080i −0.242994 + 0.242994i
\(867\) −2.13107 13.3132i −0.0723748 0.452141i
\(868\) 2.92963i 0.0994382i
\(869\) −24.6314 + 24.6314i −0.835563 + 0.835563i
\(870\) 4.09285 + 25.5689i 0.138761 + 0.866867i
\(871\) 16.7111 29.2747i 0.566233 0.991936i
\(872\) 4.17149i 0.141265i
\(873\) −20.5118 + 40.5863i −0.694220 + 1.37364i
\(874\) 1.78286 0.0603062
\(875\) 9.57688 0.323758
\(876\) 15.9938 + 11.5800i 0.540379 + 0.391252i
\(877\) −11.7092 + 11.7092i −0.395392 + 0.395392i −0.876604 0.481212i \(-0.840197\pi\)
0.481212 + 0.876604i \(0.340197\pi\)
\(878\) 16.1502 16.1502i 0.545043 0.545043i
\(879\) −44.7577 32.4060i −1.50964 1.09303i
\(880\) −7.43524 −0.250642
\(881\) 34.9545 1.17765 0.588824 0.808261i \(-0.299591\pi\)
0.588824 + 0.808261i \(0.299591\pi\)
\(882\) 1.35317 2.67749i 0.0455636 0.0901557i
\(883\) 38.3261i 1.28978i −0.764277 0.644888i \(-0.776904\pi\)
0.764277 0.644888i \(-0.223096\pi\)
\(884\) −2.88468 10.5586i −0.0970222 0.355123i
\(885\) 3.61239 + 22.5673i 0.121429 + 0.758593i
\(886\) 6.30410 6.30410i 0.211791 0.211791i
\(887\) 35.4423i 1.19004i 0.803712 + 0.595018i \(0.202855\pi\)
−0.803712 + 0.595018i \(0.797145\pi\)
\(888\) 1.63151 + 10.1924i 0.0547500 + 0.342035i
\(889\) −0.368934 + 0.368934i −0.0123736 + 0.0123736i
\(890\) 27.0603 + 27.0603i 0.907064 + 0.907064i
\(891\) 4.05134 26.7159i 0.135725 0.895018i
\(892\) −3.08394 3.08394i −0.103258 0.103258i
\(893\) 36.7581i 1.23006i
\(894\) −10.0110 + 1.60247i −0.334817 + 0.0535947i
\(895\) 6.38944 + 6.38944i 0.213576 + 0.213576i
\(896\) 1.00000 0.0334077
\(897\) −1.23261 2.72044i −0.0411557 0.0908327i
\(898\) 27.3463 0.912558
\(899\) 12.5059 + 12.5059i 0.417093 + 0.417093i
\(900\) 3.22867 1.06082i 0.107622 0.0353605i
\(901\) 17.9112i 0.596708i
\(902\) 14.5330 + 14.5330i 0.483894 + 0.483894i
\(903\) −6.44678 4.66767i −0.214535 0.155330i
\(904\) −3.53380 3.53380i −0.117533 0.117533i
\(905\) −34.1532 + 34.1532i −1.13529 + 1.13529i
\(906\) 16.3282 2.61368i 0.542469 0.0868338i
\(907\) 10.5119i 0.349043i −0.984653 0.174522i \(-0.944162\pi\)
0.984653 0.174522i \(-0.0558379\pi\)
\(908\) 18.9348 18.9348i 0.628373 0.628373i
\(909\) 14.3818 4.72532i 0.477015 0.156729i
\(910\) 4.42655 7.75451i 0.146739 0.257059i
\(911\) 47.2476i 1.56538i −0.622410 0.782691i \(-0.713846\pi\)
0.622410 0.782691i \(-0.286154\pi\)
\(912\) −5.23000 3.78669i −0.173183 0.125390i
\(913\) 42.3286 1.40087
\(914\) 9.72824 0.321781
\(915\) −33.3603 + 46.0758i −1.10286 + 1.52322i
\(916\) −12.2479 + 12.2479i −0.404683 + 0.404683i
\(917\) −7.16651 + 7.16651i −0.236659 + 0.236659i
\(918\) 4.80039 15.0260i 0.158436 0.495933i
\(919\) −55.3266 −1.82506 −0.912529 0.409013i \(-0.865873\pi\)
−0.912529 + 0.409013i \(0.865873\pi\)
\(920\) −1.18436 −0.0390471
\(921\) −21.5685 + 29.7894i −0.710705 + 0.981594i
\(922\) 7.60631i 0.250500i
\(923\) −32.6162 18.6185i −1.07358 0.612836i
\(924\) −5.13490 + 0.821950i −0.168926 + 0.0270402i
\(925\) 4.77373 4.77373i 0.156959 0.156959i
\(926\) 2.41903i 0.0794944i
\(927\) 16.2247 + 49.3809i 0.532888 + 1.62188i
\(928\) −4.26874 + 4.26874i −0.140128 + 0.140128i
\(929\) −15.2981 15.2981i −0.501914 0.501914i 0.410119 0.912032i \(-0.365487\pi\)
−0.912032 + 0.410119i \(0.865487\pi\)
\(930\) 7.36949 10.1784i 0.241655 0.333763i
\(931\) 2.63603 + 2.63603i 0.0863924 + 0.0863924i
\(932\) 15.4793i 0.507041i
\(933\) −2.93675 18.3465i −0.0961448 0.600637i
\(934\) 8.56293 + 8.56293i 0.280188 + 0.280188i
\(935\) 22.5715 0.738167
\(936\) −2.16218 + 10.5983i −0.0706732 + 0.346418i
\(937\) 50.3587 1.64515 0.822574 0.568658i \(-0.192537\pi\)
0.822574 + 0.568658i \(0.192537\pi\)
\(938\) −6.61080 6.61080i −0.215850 0.215850i
\(939\) −4.74576 29.6477i −0.154872 0.967517i
\(940\) 24.4185i 0.796442i
\(941\) −32.9621 32.9621i −1.07453 1.07453i −0.996989 0.0775433i \(-0.975292\pi\)
−0.0775433 0.996989i \(-0.524708\pi\)
\(942\) 4.21304 5.81887i 0.137268 0.189589i
\(943\) 2.31495 + 2.31495i 0.0753852 + 0.0753852i
\(944\) −3.76763 + 3.76763i −0.122626 + 0.122626i
\(945\) 11.4365 5.89849i 0.372030 0.191878i
\(946\) 13.7966i 0.448565i
\(947\) 2.53584 2.53584i 0.0824038 0.0824038i −0.664703 0.747107i \(-0.731442\pi\)
0.747107 + 0.664703i \(0.231442\pi\)
\(948\) 19.8429 3.17629i 0.644469 0.103161i
\(949\) 35.6975 + 20.3774i 1.15879 + 0.661480i
\(950\) 4.22307i 0.137014i
\(951\) 28.2585 39.0294i 0.916346 1.26562i
\(952\) −3.03575 −0.0983891
\(953\) −5.10013 −0.165209 −0.0826047 0.996582i \(-0.526324\pi\)
−0.0826047 + 0.996582i \(0.526324\pi\)
\(954\) −7.98382 + 15.7974i −0.258486 + 0.511460i
\(955\) 1.49685 1.49685i 0.0484368 0.0484368i
\(956\) 11.2898 11.2898i 0.365139 0.365139i
\(957\) 18.4109 25.4282i 0.595139 0.821979i
\(958\) 0.757750 0.0244818
\(959\) −5.75578 −0.185864
\(960\) 3.47430 + 2.51550i 0.112132 + 0.0811874i
\(961\) 22.4173i 0.723137i
\(962\) 5.66294 + 20.7276i 0.182580 + 0.668285i
\(963\) −7.16171 21.7972i −0.230783 0.702403i
\(964\) 3.14172 3.14172i 0.101188 0.101188i
\(965\) 57.1725i 1.84045i
\(966\) −0.817936 + 0.130928i −0.0263167 + 0.00421255i
\(967\) −36.9427 + 36.9427i −1.18800 + 1.18800i −0.210376 + 0.977621i \(0.567469\pi\)
−0.977621 + 0.210376i \(0.932531\pi\)
\(968\) −1.40413 1.40413i −0.0451306 0.0451306i
\(969\) 15.8770 + 11.4954i 0.510041 + 0.369286i
\(970\) 26.5441 + 26.5441i 0.852279 + 0.852279i
\(971\) 57.2866i 1.83842i 0.393773 + 0.919208i \(0.371170\pi\)
−0.393773 + 0.919208i \(0.628830\pi\)
\(972\) −10.9317 + 11.1130i −0.350633 + 0.356450i
\(973\) 0.122871 + 0.122871i 0.00393907 + 0.00393907i
\(974\) 7.81252 0.250329
\(975\) 6.44390 2.91969i 0.206370 0.0935048i
\(976\) −13.2619 −0.424503
\(977\) −24.4879 24.4879i −0.783437 0.783437i 0.196972 0.980409i \(-0.436889\pi\)
−0.980409 + 0.196972i \(0.936889\pi\)
\(978\) 32.2688 5.16532i 1.03184 0.165169i
\(979\) 46.3962i 1.48283i
\(980\) −1.75112 1.75112i −0.0559374 0.0559374i
\(981\) −5.64473 + 11.1691i −0.180222 + 0.356602i
\(982\) 22.8390 + 22.8390i 0.728821 + 0.728821i
\(983\) −10.8336 + 10.8336i −0.345537 + 0.345537i −0.858444 0.512907i \(-0.828568\pi\)
0.512907 + 0.858444i \(0.328568\pi\)
\(984\) −1.87406 11.7077i −0.0597430 0.373227i
\(985\) 26.1169i 0.832154i
\(986\) 12.9588 12.9588i 0.412693 0.412693i
\(987\) −2.69941 16.8638i −0.0859231 0.536780i
\(988\) −11.6732 6.66347i −0.371373 0.211993i
\(989\) 2.19765i 0.0698813i
\(990\) −19.9078 10.0611i −0.632710 0.319764i
\(991\) 49.1490 1.56127 0.780635 0.624988i \(-0.214896\pi\)
0.780635 + 0.624988i \(0.214896\pi\)
\(992\) 2.92963 0.0930159
\(993\) 8.29125 + 6.00313i 0.263115 + 0.190503i
\(994\) −7.36537 + 7.36537i −0.233615 + 0.233615i
\(995\) 1.36256 1.36256i 0.0431961 0.0431961i
\(996\) −19.7790 14.3206i −0.626723 0.453767i
\(997\) −3.17797 −0.100647 −0.0503237 0.998733i \(-0.516025\pi\)
−0.0503237 + 0.998733i \(0.516025\pi\)
\(998\) 34.6609 1.09717
\(999\) −9.42368 + 29.4977i −0.298152 + 0.933267i
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.p.d.239.8 yes 20
3.2 odd 2 546.2.p.c.239.3 20
13.8 odd 4 546.2.p.c.281.3 yes 20
39.8 even 4 inner 546.2.p.d.281.8 yes 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
546.2.p.c.239.3 20 3.2 odd 2
546.2.p.c.281.3 yes 20 13.8 odd 4
546.2.p.d.239.8 yes 20 1.1 even 1 trivial
546.2.p.d.281.8 yes 20 39.8 even 4 inner