Properties

Label 273.2.bl.c.88.6
Level $273$
Weight $2$
Character 273.88
Analytic conductor $2.180$
Analytic rank $0$
Dimension $12$
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] = [273,2,Mod(88,273)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(273, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 4, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("273.88");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 273 = 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 273.bl (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: \(2.17991597518\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: 12.0.2346760387617129.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 3 x^{11} + x^{10} + 10 x^{9} - 15 x^{8} - 10 x^{7} + 45 x^{6} - 20 x^{5} - 60 x^{4} + 80 x^{3} + 16 x^{2} - 96 x + 64 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 88.6
Root \(0.874681 - 1.11128i\) of defining polynomial
Character \(\chi\) \(=\) 273.88
Dual form 273.2.bl.c.121.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.92478 + 1.11128i) q^{2} +1.00000 q^{3} +(1.46986 + 2.54588i) q^{4} +(0.701414 - 0.404962i) q^{5} +(1.92478 + 1.11128i) q^{6} +(-2.09638 - 1.61406i) q^{7} +2.08860i q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+(1.92478 + 1.11128i) q^{2} +1.00000 q^{3} +(1.46986 + 2.54588i) q^{4} +(0.701414 - 0.404962i) q^{5} +(1.92478 + 1.11128i) q^{6} +(-2.09638 - 1.61406i) q^{7} +2.08860i q^{8} +1.00000 q^{9} +1.80010 q^{10} +3.07728i q^{11} +(1.46986 + 2.54588i) q^{12} +(-3.01583 + 1.97606i) q^{13} +(-2.24141 - 5.43638i) q^{14} +(0.701414 - 0.404962i) q^{15} +(0.618725 - 1.07166i) q^{16} +(-1.39973 - 2.42441i) q^{17} +(1.92478 + 1.11128i) q^{18} -4.31115i q^{19} +(2.06197 + 1.19048i) q^{20} +(-2.09638 - 1.61406i) q^{21} +(-3.41970 + 5.92310i) q^{22} +(-2.47614 + 4.28881i) q^{23} +2.08860i q^{24} +(-2.17201 + 3.76204i) q^{25} +(-8.00076 + 0.452072i) q^{26} +1.00000 q^{27} +(1.02782 - 7.70958i) q^{28} +(-2.84837 - 4.93353i) q^{29} +1.80010 q^{30} +(-2.93282 - 1.69327i) q^{31} +(5.99938 - 3.46374i) q^{32} +3.07728i q^{33} -6.22195i q^{34} +(-2.12406 - 0.283173i) q^{35} +(1.46986 + 2.54588i) q^{36} +(8.42267 + 4.86283i) q^{37} +(4.79087 - 8.29803i) q^{38} +(-3.01583 + 1.97606i) q^{39} +(0.845801 + 1.46497i) q^{40} +(8.48708 - 4.90002i) q^{41} +(-2.24141 - 5.43638i) q^{42} +(-2.85083 + 4.93777i) q^{43} +(-7.83438 + 4.52318i) q^{44} +(0.701414 - 0.404962i) q^{45} +(-9.53209 + 5.50335i) q^{46} +(5.31465 - 3.06841i) q^{47} +(0.618725 - 1.07166i) q^{48} +(1.78961 + 6.76737i) q^{49} +(-8.36131 + 4.82741i) q^{50} +(-1.39973 - 2.42441i) q^{51} +(-9.46366 - 4.77339i) q^{52} +(2.83659 - 4.91312i) q^{53} +(1.92478 + 1.11128i) q^{54} +(1.24618 + 2.15845i) q^{55} +(3.37112 - 4.37849i) q^{56} -4.31115i q^{57} -12.6613i q^{58} +(-4.27457 + 2.46792i) q^{59} +(2.06197 + 1.19048i) q^{60} -3.03483 q^{61} +(-3.76337 - 6.51834i) q^{62} +(-2.09638 - 1.61406i) q^{63} +12.9218 q^{64} +(-1.31512 + 2.60733i) q^{65} +(-3.41970 + 5.92310i) q^{66} +9.92554i q^{67} +(4.11484 - 7.12711i) q^{68} +(-2.47614 + 4.28881i) q^{69} +(-3.77368 - 2.90547i) q^{70} +(-7.84155 - 4.52732i) q^{71} +2.08860i q^{72} +(2.75318 + 1.58955i) q^{73} +(10.8079 + 18.7198i) q^{74} +(-2.17201 + 3.76204i) q^{75} +(10.9757 - 6.33680i) q^{76} +(4.96692 - 6.45114i) q^{77} +(-8.00076 + 0.452072i) q^{78} +(1.13963 + 1.97390i) q^{79} -1.00224i q^{80} +1.00000 q^{81} +21.7811 q^{82} -1.52896i q^{83} +(1.02782 - 7.70958i) q^{84} +(-1.96359 - 1.13368i) q^{85} +(-10.9745 + 6.33610i) q^{86} +(-2.84837 - 4.93353i) q^{87} -6.42719 q^{88} +(2.87613 + 1.66053i) q^{89} +1.80010 q^{90} +(9.51179 + 0.725168i) q^{91} -14.5584 q^{92} +(-2.93282 - 1.69327i) q^{93} +13.6394 q^{94} +(-1.74585 - 3.02390i) q^{95} +(5.99938 - 3.46374i) q^{96} +(11.0330 + 6.36990i) q^{97} +(-4.07581 + 15.0145i) q^{98} +3.07728i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 3 q^{2} + 12 q^{3} + 5 q^{4} + 6 q^{5} - 3 q^{6} + 3 q^{7} + 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q - 3 q^{2} + 12 q^{3} + 5 q^{4} + 6 q^{5} - 3 q^{6} + 3 q^{7} + 12 q^{9} + 14 q^{10} + 5 q^{12} - q^{13} - 16 q^{14} + 6 q^{15} + 3 q^{16} - 3 q^{18} - 27 q^{20} + 3 q^{21} + 7 q^{22} - 16 q^{23} + 10 q^{25} - q^{26} + 12 q^{27} + 24 q^{28} - 5 q^{29} + 14 q^{30} + 15 q^{31} - 6 q^{32} - 2 q^{35} + 5 q^{36} + 6 q^{37} + 24 q^{38} - q^{39} + 21 q^{40} - 15 q^{41} - 16 q^{42} - 13 q^{43} - 30 q^{44} + 6 q^{45} - 9 q^{46} - 9 q^{47} + 3 q^{48} + 9 q^{49} - 63 q^{50} - 55 q^{52} + 18 q^{53} - 3 q^{54} + 13 q^{55} - 21 q^{56} - 33 q^{59} - 27 q^{60} - 52 q^{61} - 13 q^{62} + 3 q^{63} - 4 q^{64} - 41 q^{65} + 7 q^{66} - 16 q^{69} - 42 q^{70} - 15 q^{71} - 18 q^{73} + 38 q^{74} + 10 q^{75} - 30 q^{76} + 20 q^{77} - q^{78} - 4 q^{79} + 12 q^{81} + 28 q^{82} + 24 q^{84} - 12 q^{85} - 15 q^{86} - 5 q^{87} - 32 q^{88} + 12 q^{89} + 14 q^{90} + 49 q^{91} - 40 q^{92} + 15 q^{93} + 6 q^{94} - 28 q^{95} - 6 q^{96} + 45 q^{97} + 48 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/273\mathbb{Z}\right)^\times\).

\(n\) \(92\) \(106\) \(157\)
\(\chi(n)\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.92478 + 1.11128i 1.36103 + 0.785790i 0.989761 0.142736i \(-0.0455899\pi\)
0.371268 + 0.928526i \(0.378923\pi\)
\(3\) 1.00000 0.577350
\(4\) 1.46986 + 2.54588i 0.734932 + 1.27294i
\(5\) 0.701414 0.404962i 0.313682 0.181104i −0.334891 0.942257i \(-0.608699\pi\)
0.648573 + 0.761153i \(0.275366\pi\)
\(6\) 1.92478 + 1.11128i 0.785790 + 0.453676i
\(7\) −2.09638 1.61406i −0.792357 0.610058i
\(8\) 2.08860i 0.738430i
\(9\) 1.00000 0.333333
\(10\) 1.80010 0.569240
\(11\) 3.07728i 0.927834i 0.885879 + 0.463917i \(0.153556\pi\)
−0.885879 + 0.463917i \(0.846444\pi\)
\(12\) 1.46986 + 2.54588i 0.424313 + 0.734932i
\(13\) −3.01583 + 1.97606i −0.836439 + 0.548059i
\(14\) −2.24141 5.43638i −0.599042 1.45293i
\(15\) 0.701414 0.404962i 0.181104 0.104561i
\(16\) 0.618725 1.07166i 0.154681 0.267916i
\(17\) −1.39973 2.42441i −0.339485 0.588006i 0.644851 0.764308i \(-0.276920\pi\)
−0.984336 + 0.176303i \(0.943586\pi\)
\(18\) 1.92478 + 1.11128i 0.453676 + 0.261930i
\(19\) 4.31115i 0.989045i −0.869165 0.494522i \(-0.835343\pi\)
0.869165 0.494522i \(-0.164657\pi\)
\(20\) 2.06197 + 1.19048i 0.461070 + 0.266199i
\(21\) −2.09638 1.61406i −0.457467 0.352217i
\(22\) −3.41970 + 5.92310i −0.729083 + 1.26281i
\(23\) −2.47614 + 4.28881i −0.516312 + 0.894278i 0.483509 + 0.875339i \(0.339362\pi\)
−0.999821 + 0.0189386i \(0.993971\pi\)
\(24\) 2.08860i 0.426333i
\(25\) −2.17201 + 3.76204i −0.434402 + 0.752407i
\(26\) −8.00076 + 0.452072i −1.56908 + 0.0886587i
\(27\) 1.00000 0.192450
\(28\) 1.02782 7.70958i 0.194239 1.45697i
\(29\) −2.84837 4.93353i −0.528930 0.916133i −0.999431 0.0337339i \(-0.989260\pi\)
0.470501 0.882399i \(-0.344073\pi\)
\(30\) 1.80010 0.328651
\(31\) −2.93282 1.69327i −0.526750 0.304119i 0.212942 0.977065i \(-0.431696\pi\)
−0.739692 + 0.672945i \(0.765029\pi\)
\(32\) 5.99938 3.46374i 1.06055 0.612309i
\(33\) 3.07728i 0.535685i
\(34\) 6.22195i 1.06706i
\(35\) −2.12406 0.283173i −0.359032 0.0478650i
\(36\) 1.46986 + 2.54588i 0.244977 + 0.424313i
\(37\) 8.42267 + 4.86283i 1.38468 + 0.799445i 0.992709 0.120533i \(-0.0384605\pi\)
0.391970 + 0.919978i \(0.371794\pi\)
\(38\) 4.79087 8.29803i 0.777182 1.34612i
\(39\) −3.01583 + 1.97606i −0.482919 + 0.316422i
\(40\) 0.845801 + 1.46497i 0.133733 + 0.231632i
\(41\) 8.48708 4.90002i 1.32546 0.765254i 0.340865 0.940112i \(-0.389280\pi\)
0.984594 + 0.174858i \(0.0559468\pi\)
\(42\) −2.24141 5.43638i −0.345857 0.838851i
\(43\) −2.85083 + 4.93777i −0.434747 + 0.753003i −0.997275 0.0737747i \(-0.976495\pi\)
0.562528 + 0.826778i \(0.309829\pi\)
\(44\) −7.83438 + 4.52318i −1.18108 + 0.681895i
\(45\) 0.701414 0.404962i 0.104561 0.0603681i
\(46\) −9.53209 + 5.50335i −1.40543 + 0.811425i
\(47\) 5.31465 3.06841i 0.775221 0.447574i −0.0595130 0.998228i \(-0.518955\pi\)
0.834734 + 0.550654i \(0.185621\pi\)
\(48\) 0.618725 1.07166i 0.0893053 0.154681i
\(49\) 1.78961 + 6.76737i 0.255658 + 0.966767i
\(50\) −8.36131 + 4.82741i −1.18247 + 0.682698i
\(51\) −1.39973 2.42441i −0.196002 0.339485i
\(52\) −9.46366 4.77339i −1.31237 0.661951i
\(53\) 2.83659 4.91312i 0.389636 0.674870i −0.602764 0.797919i \(-0.705934\pi\)
0.992401 + 0.123050i \(0.0392675\pi\)
\(54\) 1.92478 + 1.11128i 0.261930 + 0.151225i
\(55\) 1.24618 + 2.15845i 0.168035 + 0.291045i
\(56\) 3.37112 4.37849i 0.450485 0.585100i
\(57\) 4.31115i 0.571025i
\(58\) 12.6613i 1.66251i
\(59\) −4.27457 + 2.46792i −0.556501 + 0.321296i −0.751740 0.659460i \(-0.770785\pi\)
0.195239 + 0.980756i \(0.437452\pi\)
\(60\) 2.06197 + 1.19048i 0.266199 + 0.153690i
\(61\) −3.03483 −0.388570 −0.194285 0.980945i \(-0.562239\pi\)
−0.194285 + 0.980945i \(0.562239\pi\)
\(62\) −3.76337 6.51834i −0.477948 0.827830i
\(63\) −2.09638 1.61406i −0.264119 0.203353i
\(64\) 12.9218 1.61522
\(65\) −1.31512 + 2.60733i −0.163120 + 0.323399i
\(66\) −3.41970 + 5.92310i −0.420936 + 0.729083i
\(67\) 9.92554i 1.21260i 0.795237 + 0.606299i \(0.207346\pi\)
−0.795237 + 0.606299i \(0.792654\pi\)
\(68\) 4.11484 7.12711i 0.498997 0.864289i
\(69\) −2.47614 + 4.28881i −0.298093 + 0.516312i
\(70\) −3.77368 2.90547i −0.451041 0.347270i
\(71\) −7.84155 4.52732i −0.930621 0.537294i −0.0436133 0.999048i \(-0.513887\pi\)
−0.887008 + 0.461754i \(0.847220\pi\)
\(72\) 2.08860i 0.246143i
\(73\) 2.75318 + 1.58955i 0.322235 + 0.186043i 0.652388 0.757885i \(-0.273767\pi\)
−0.330153 + 0.943927i \(0.607100\pi\)
\(74\) 10.8079 + 18.7198i 1.25639 + 2.17613i
\(75\) −2.17201 + 3.76204i −0.250802 + 0.434402i
\(76\) 10.9757 6.33680i 1.25899 0.726881i
\(77\) 4.96692 6.45114i 0.566033 0.735175i
\(78\) −8.00076 + 0.452072i −0.905907 + 0.0511871i
\(79\) 1.13963 + 1.97390i 0.128219 + 0.222082i 0.922987 0.384832i \(-0.125741\pi\)
−0.794768 + 0.606914i \(0.792407\pi\)
\(80\) 1.00224i 0.112054i
\(81\) 1.00000 0.111111
\(82\) 21.7811 2.40532
\(83\) 1.52896i 0.167825i −0.996473 0.0839126i \(-0.973258\pi\)
0.996473 0.0839126i \(-0.0267417\pi\)
\(84\) 1.02782 7.70958i 0.112144 0.841184i
\(85\) −1.96359 1.13368i −0.212981 0.122965i
\(86\) −10.9745 + 6.33610i −1.18341 + 0.683239i
\(87\) −2.84837 4.93353i −0.305378 0.528930i
\(88\) −6.42719 −0.685140
\(89\) 2.87613 + 1.66053i 0.304869 + 0.176016i 0.644628 0.764496i \(-0.277012\pi\)
−0.339759 + 0.940512i \(0.610346\pi\)
\(90\) 1.80010 0.189747
\(91\) 9.51179 + 0.725168i 0.997106 + 0.0760182i
\(92\) −14.5584 −1.51782
\(93\) −2.93282 1.69327i −0.304119 0.175583i
\(94\) 13.6394 1.40680
\(95\) −1.74585 3.02390i −0.179120 0.310246i
\(96\) 5.99938 3.46374i 0.612309 0.353517i
\(97\) 11.0330 + 6.36990i 1.12023 + 0.646766i 0.941460 0.337125i \(-0.109454\pi\)
0.178771 + 0.983891i \(0.442788\pi\)
\(98\) −4.07581 + 15.0145i −0.411718 + 1.51669i
\(99\) 3.07728i 0.309278i
\(100\) −12.7703 −1.27703
\(101\) −15.1754 −1.51001 −0.755006 0.655717i \(-0.772366\pi\)
−0.755006 + 0.655717i \(0.772366\pi\)
\(102\) 6.22195i 0.616065i
\(103\) −4.00749 6.94118i −0.394870 0.683935i 0.598214 0.801336i \(-0.295877\pi\)
−0.993085 + 0.117401i \(0.962544\pi\)
\(104\) −4.12718 6.29884i −0.404704 0.617652i
\(105\) −2.12406 0.283173i −0.207287 0.0276349i
\(106\) 10.9197 6.30447i 1.06061 0.612344i
\(107\) 4.89324 8.47534i 0.473048 0.819342i −0.526477 0.850190i \(-0.676487\pi\)
0.999524 + 0.0308472i \(0.00982052\pi\)
\(108\) 1.46986 + 2.54588i 0.141438 + 0.244977i
\(109\) −2.60941 1.50655i −0.249937 0.144301i 0.369799 0.929112i \(-0.379427\pi\)
−0.619735 + 0.784811i \(0.712760\pi\)
\(110\) 5.53939i 0.528160i
\(111\) 8.42267 + 4.86283i 0.799445 + 0.461560i
\(112\) −3.02681 + 1.24795i −0.286007 + 0.117920i
\(113\) −1.36880 + 2.37084i −0.128766 + 0.223030i −0.923199 0.384323i \(-0.874435\pi\)
0.794433 + 0.607352i \(0.207768\pi\)
\(114\) 4.79087 8.29803i 0.448706 0.777182i
\(115\) 4.01097i 0.374025i
\(116\) 8.37345 14.5032i 0.777455 1.34659i
\(117\) −3.01583 + 1.97606i −0.278813 + 0.182686i
\(118\) −10.9702 −1.00989
\(119\) −0.978777 + 7.34174i −0.0897243 + 0.673016i
\(120\) 0.845801 + 1.46497i 0.0772107 + 0.133733i
\(121\) 1.53037 0.139124
\(122\) −5.84139 3.37253i −0.528855 0.305334i
\(123\) 8.48708 4.90002i 0.765254 0.441820i
\(124\) 9.95548i 0.894029i
\(125\) 7.56794i 0.676898i
\(126\) −2.24141 5.43638i −0.199681 0.484311i
\(127\) 7.39515 + 12.8088i 0.656214 + 1.13660i 0.981588 + 0.191010i \(0.0611763\pi\)
−0.325374 + 0.945585i \(0.605490\pi\)
\(128\) 12.8729 + 7.43217i 1.13781 + 0.656917i
\(129\) −2.85083 + 4.93777i −0.251001 + 0.434747i
\(130\) −5.42877 + 3.55709i −0.476135 + 0.311977i
\(131\) −1.14893 1.99001i −0.100383 0.173868i 0.811460 0.584408i \(-0.198673\pi\)
−0.911842 + 0.410540i \(0.865340\pi\)
\(132\) −7.83438 + 4.52318i −0.681895 + 0.393692i
\(133\) −6.95846 + 9.03779i −0.603375 + 0.783676i
\(134\) −11.0300 + 19.1045i −0.952847 + 1.65038i
\(135\) 0.701414 0.404962i 0.0603681 0.0348536i
\(136\) 5.06361 2.92348i 0.434201 0.250686i
\(137\) 13.5481 7.82198i 1.15749 0.668276i 0.206788 0.978386i \(-0.433699\pi\)
0.950701 + 0.310109i \(0.100366\pi\)
\(138\) −9.53209 + 5.50335i −0.811425 + 0.468477i
\(139\) −11.2601 + 19.5030i −0.955068 + 1.65423i −0.220855 + 0.975307i \(0.570885\pi\)
−0.734213 + 0.678919i \(0.762449\pi\)
\(140\) −2.40116 5.82384i −0.202935 0.492204i
\(141\) 5.31465 3.06841i 0.447574 0.258407i
\(142\) −10.0622 17.4282i −0.844401 1.46255i
\(143\) −6.08087 9.28053i −0.508508 0.776077i
\(144\) 0.618725 1.07166i 0.0515604 0.0893053i
\(145\) −3.99578 2.30697i −0.331832 0.191583i
\(146\) 3.53285 + 6.11908i 0.292381 + 0.506419i
\(147\) 1.78961 + 6.76737i 0.147604 + 0.558163i
\(148\) 28.5908i 2.35015i
\(149\) 13.5565i 1.11059i 0.831654 + 0.555294i \(0.187394\pi\)
−0.831654 + 0.555294i \(0.812606\pi\)
\(150\) −8.36131 + 4.82741i −0.682698 + 0.394156i
\(151\) −7.26064 4.19193i −0.590863 0.341135i 0.174576 0.984644i \(-0.444145\pi\)
−0.765439 + 0.643509i \(0.777478\pi\)
\(152\) 9.00424 0.730340
\(153\) −1.39973 2.42441i −0.113162 0.196002i
\(154\) 16.7292 6.89744i 1.34808 0.555812i
\(155\) −2.74283 −0.220309
\(156\) −9.46366 4.77339i −0.757699 0.382177i
\(157\) −1.53856 + 2.66486i −0.122790 + 0.212679i −0.920867 0.389877i \(-0.872518\pi\)
0.798077 + 0.602556i \(0.205851\pi\)
\(158\) 5.06579i 0.403012i
\(159\) 2.83659 4.91312i 0.224957 0.389636i
\(160\) 2.80537 4.85904i 0.221784 0.384141i
\(161\) 12.1133 4.99431i 0.954665 0.393607i
\(162\) 1.92478 + 1.11128i 0.151225 + 0.0873100i
\(163\) 6.14897i 0.481624i −0.970572 0.240812i \(-0.922586\pi\)
0.970572 0.240812i \(-0.0774138\pi\)
\(164\) 24.9497 + 14.4047i 1.94824 + 1.12482i
\(165\) 1.24618 + 2.15845i 0.0970149 + 0.168035i
\(166\) 1.69910 2.94292i 0.131875 0.228415i
\(167\) −13.6424 + 7.87645i −1.05568 + 0.609498i −0.924235 0.381825i \(-0.875296\pi\)
−0.131447 + 0.991323i \(0.541962\pi\)
\(168\) 3.37112 4.37849i 0.260088 0.337808i
\(169\) 5.19040 11.9189i 0.399262 0.916837i
\(170\) −2.51965 4.36417i −0.193249 0.334716i
\(171\) 4.31115i 0.329682i
\(172\) −16.7613 −1.27804
\(173\) 16.3092 1.23997 0.619983 0.784615i \(-0.287139\pi\)
0.619983 + 0.784615i \(0.287139\pi\)
\(174\) 12.6613i 0.959851i
\(175\) 10.6255 4.38089i 0.803214 0.331164i
\(176\) 3.29780 + 1.90399i 0.248581 + 0.143519i
\(177\) −4.27457 + 2.46792i −0.321296 + 0.185500i
\(178\) 3.69062 + 6.39234i 0.276624 + 0.479126i
\(179\) −20.3756 −1.52295 −0.761473 0.648196i \(-0.775524\pi\)
−0.761473 + 0.648196i \(0.775524\pi\)
\(180\) 2.06197 + 1.19048i 0.153690 + 0.0887330i
\(181\) −22.1726 −1.64808 −0.824039 0.566533i \(-0.808285\pi\)
−0.824039 + 0.566533i \(0.808285\pi\)
\(182\) 17.5023 + 11.9660i 1.29736 + 0.886979i
\(183\) −3.03483 −0.224341
\(184\) −8.95758 5.17166i −0.660362 0.381260i
\(185\) 7.87704 0.579132
\(186\) −3.76337 6.51834i −0.275943 0.477948i
\(187\) 7.46058 4.30737i 0.545572 0.314986i
\(188\) 15.6236 + 9.02030i 1.13947 + 0.657873i
\(189\) −2.09638 1.61406i −0.152489 0.117406i
\(190\) 7.76047i 0.563004i
\(191\) 21.6850 1.56907 0.784536 0.620083i \(-0.212901\pi\)
0.784536 + 0.620083i \(0.212901\pi\)
\(192\) 12.9218 0.932550
\(193\) 0.0505858i 0.00364124i 0.999998 + 0.00182062i \(0.000579522\pi\)
−0.999998 + 0.00182062i \(0.999420\pi\)
\(194\) 14.1574 + 24.5214i 1.01644 + 1.76053i
\(195\) −1.31512 + 2.60733i −0.0941774 + 0.186715i
\(196\) −14.5984 + 14.5032i −1.04275 + 1.03595i
\(197\) 15.4854 8.94051i 1.10329 0.636985i 0.166207 0.986091i \(-0.446848\pi\)
0.937083 + 0.349106i \(0.113515\pi\)
\(198\) −3.41970 + 5.92310i −0.243028 + 0.420936i
\(199\) −8.08456 14.0029i −0.573099 0.992637i −0.996245 0.0865753i \(-0.972408\pi\)
0.423146 0.906061i \(-0.360926\pi\)
\(200\) −7.85737 4.53645i −0.555600 0.320776i
\(201\) 9.92554i 0.700094i
\(202\) −29.2095 16.8641i −2.05517 1.18655i
\(203\) −1.99175 + 14.9400i −0.139794 + 1.04858i
\(204\) 4.11484 7.12711i 0.288096 0.498997i
\(205\) 3.96864 6.87388i 0.277182 0.480093i
\(206\) 17.8137i 1.24114i
\(207\) −2.47614 + 4.28881i −0.172104 + 0.298093i
\(208\) 0.251700 + 4.45458i 0.0174523 + 0.308870i
\(209\) 13.2666 0.917669
\(210\) −3.77368 2.90547i −0.260409 0.200496i
\(211\) −2.69037 4.65986i −0.185213 0.320798i 0.758435 0.651748i \(-0.225964\pi\)
−0.943648 + 0.330950i \(0.892631\pi\)
\(212\) 16.6776 1.14542
\(213\) −7.84155 4.52732i −0.537294 0.310207i
\(214\) 18.8369 10.8755i 1.28766 0.743432i
\(215\) 4.61790i 0.314938i
\(216\) 2.08860i 0.142111i
\(217\) 3.41527 + 8.28348i 0.231843 + 0.562319i
\(218\) −3.34837 5.79955i −0.226781 0.392795i
\(219\) 2.75318 + 1.58955i 0.186043 + 0.107412i
\(220\) −3.66343 + 6.34525i −0.246988 + 0.427796i
\(221\) 9.01212 + 4.54564i 0.606221 + 0.305773i
\(222\) 10.8079 + 18.7198i 0.725378 + 1.25639i
\(223\) −15.9502 + 9.20887i −1.06811 + 0.616671i −0.927663 0.373418i \(-0.878186\pi\)
−0.140443 + 0.990089i \(0.544853\pi\)
\(224\) −18.1677 2.42206i −1.21388 0.161830i
\(225\) −2.17201 + 3.76204i −0.144801 + 0.250802i
\(226\) −5.26931 + 3.04224i −0.350509 + 0.202367i
\(227\) 20.0696 11.5872i 1.33206 0.769067i 0.346448 0.938069i \(-0.387388\pi\)
0.985616 + 0.169002i \(0.0540545\pi\)
\(228\) 10.9757 6.33680i 0.726881 0.419665i
\(229\) 23.0419 13.3032i 1.52265 0.879103i 0.523009 0.852327i \(-0.324809\pi\)
0.999641 0.0267760i \(-0.00852410\pi\)
\(230\) −4.45730 + 7.72026i −0.293905 + 0.509059i
\(231\) 4.96692 6.45114i 0.326799 0.424454i
\(232\) 10.3041 5.94910i 0.676500 0.390578i
\(233\) −10.9316 18.9341i −0.716155 1.24042i −0.962512 0.271238i \(-0.912567\pi\)
0.246358 0.969179i \(-0.420766\pi\)
\(234\) −8.00076 + 0.452072i −0.523026 + 0.0295529i
\(235\) 2.48518 4.30446i 0.162115 0.280792i
\(236\) −12.5661 7.25502i −0.817981 0.472262i
\(237\) 1.13963 + 1.97390i 0.0740272 + 0.128219i
\(238\) −10.0426 + 13.0436i −0.650967 + 0.845489i
\(239\) 22.4279i 1.45074i −0.688360 0.725370i \(-0.741669\pi\)
0.688360 0.725370i \(-0.258331\pi\)
\(240\) 1.00224i 0.0646943i
\(241\) −1.37512 + 0.793924i −0.0885790 + 0.0511411i −0.543635 0.839322i \(-0.682952\pi\)
0.455056 + 0.890463i \(0.349619\pi\)
\(242\) 2.94563 + 1.70066i 0.189352 + 0.109322i
\(243\) 1.00000 0.0641500
\(244\) −4.46079 7.72631i −0.285573 0.494626i
\(245\) 3.99578 + 4.02201i 0.255281 + 0.256957i
\(246\) 21.7811 1.38871
\(247\) 8.51907 + 13.0017i 0.542055 + 0.827276i
\(248\) 3.53655 6.12548i 0.224571 0.388968i
\(249\) 1.52896i 0.0968939i
\(250\) −8.41007 + 14.5667i −0.531899 + 0.921277i
\(251\) 0.177730 0.307837i 0.0112182 0.0194305i −0.860362 0.509684i \(-0.829762\pi\)
0.871580 + 0.490253i \(0.163096\pi\)
\(252\) 1.02782 7.70958i 0.0647464 0.485658i
\(253\) −13.1978 7.61978i −0.829741 0.479051i
\(254\) 32.8722i 2.06258i
\(255\) −1.96359 1.13368i −0.122965 0.0709936i
\(256\) 3.59659 + 6.22948i 0.224787 + 0.389342i
\(257\) 2.60424 4.51067i 0.162448 0.281368i −0.773298 0.634043i \(-0.781394\pi\)
0.935746 + 0.352674i \(0.114728\pi\)
\(258\) −10.9745 + 6.33610i −0.683239 + 0.394468i
\(259\) −9.80820 23.7891i −0.609452 1.47818i
\(260\) −8.57099 + 0.484292i −0.531550 + 0.0300345i
\(261\) −2.84837 4.93353i −0.176310 0.305378i
\(262\) 5.10712i 0.315519i
\(263\) −21.2763 −1.31195 −0.655975 0.754782i \(-0.727742\pi\)
−0.655975 + 0.754782i \(0.727742\pi\)
\(264\) −6.42719 −0.395566
\(265\) 4.59485i 0.282259i
\(266\) −23.4370 + 9.66305i −1.43702 + 0.592479i
\(267\) 2.87613 + 1.66053i 0.176016 + 0.101623i
\(268\) −25.2692 + 14.5892i −1.54356 + 0.891177i
\(269\) −1.90086 3.29238i −0.115897 0.200740i 0.802241 0.597001i \(-0.203641\pi\)
−0.918138 + 0.396261i \(0.870308\pi\)
\(270\) 1.80010 0.109550
\(271\) −22.5990 13.0475i −1.37279 0.792581i −0.381511 0.924364i \(-0.624596\pi\)
−0.991279 + 0.131784i \(0.957930\pi\)
\(272\) −3.46420 −0.210048
\(273\) 9.51179 + 0.725168i 0.575680 + 0.0438891i
\(274\) 34.7695 2.10050
\(275\) −11.5768 6.68388i −0.698109 0.403053i
\(276\) −14.5584 −0.876312
\(277\) −14.3426 24.8421i −0.861762 1.49262i −0.870227 0.492652i \(-0.836028\pi\)
0.00846431 0.999964i \(-0.497306\pi\)
\(278\) −43.3465 + 25.0261i −2.59975 + 1.50097i
\(279\) −2.93282 1.69327i −0.175583 0.101373i
\(280\) 0.591435 4.43631i 0.0353450 0.265120i
\(281\) 0.959007i 0.0572096i 0.999591 + 0.0286048i \(0.00910643\pi\)
−0.999591 + 0.0286048i \(0.990894\pi\)
\(282\) 13.6394 0.812215
\(283\) −2.25973 −0.134327 −0.0671635 0.997742i \(-0.521395\pi\)
−0.0671635 + 0.997742i \(0.521395\pi\)
\(284\) 26.6182i 1.57950i
\(285\) −1.74585 3.02390i −0.103415 0.179120i
\(286\) −1.39115 24.6205i −0.0822605 1.45584i
\(287\) −25.7011 3.42638i −1.51709 0.202253i
\(288\) 5.99938 3.46374i 0.353517 0.204103i
\(289\) 4.58149 7.93538i 0.269500 0.466787i
\(290\) −5.12735 8.88082i −0.301088 0.521500i
\(291\) 11.0330 + 6.36990i 0.646766 + 0.373410i
\(292\) 9.34569i 0.546915i
\(293\) 4.64615 + 2.68246i 0.271431 + 0.156711i 0.629538 0.776970i \(-0.283244\pi\)
−0.358107 + 0.933681i \(0.616578\pi\)
\(294\) −4.07581 + 15.0145i −0.237706 + 0.875662i
\(295\) −1.99883 + 3.46207i −0.116376 + 0.201570i
\(296\) −10.1565 + 17.5916i −0.590334 + 1.02249i
\(297\) 3.07728i 0.178562i
\(298\) −15.0649 + 26.0933i −0.872689 + 1.51154i
\(299\) −1.00731 17.8273i −0.0582541 1.03098i
\(300\) −12.7703 −0.737291
\(301\) 13.9463 5.75003i 0.803850 0.331426i
\(302\) −9.31678 16.1371i −0.536121 0.928588i
\(303\) −15.1754 −0.871806
\(304\) −4.62010 2.66741i −0.264981 0.152987i
\(305\) −2.12867 + 1.22899i −0.121887 + 0.0703717i
\(306\) 6.22195i 0.355685i
\(307\) 1.80266i 0.102883i −0.998676 0.0514415i \(-0.983618\pi\)
0.998676 0.0514415i \(-0.0163816\pi\)
\(308\) 23.7245 + 3.16288i 1.35183 + 0.180222i
\(309\) −4.00749 6.94118i −0.227978 0.394870i
\(310\) −5.27936 3.04804i −0.299847 0.173117i
\(311\) −9.77057 + 16.9231i −0.554038 + 0.959622i 0.443940 + 0.896057i \(0.353580\pi\)
−0.997978 + 0.0635652i \(0.979753\pi\)
\(312\) −4.12718 6.29884i −0.233656 0.356602i
\(313\) 15.4409 + 26.7444i 0.872770 + 1.51168i 0.859120 + 0.511775i \(0.171012\pi\)
0.0136500 + 0.999907i \(0.495655\pi\)
\(314\) −5.92279 + 3.41952i −0.334242 + 0.192975i
\(315\) −2.12406 0.283173i −0.119677 0.0159550i
\(316\) −3.35021 + 5.80274i −0.188464 + 0.326430i
\(317\) 16.1874 9.34578i 0.909173 0.524911i 0.0290082 0.999579i \(-0.490765\pi\)
0.880165 + 0.474668i \(0.157432\pi\)
\(318\) 10.9197 6.30447i 0.612344 0.353537i
\(319\) 15.1818 8.76524i 0.850020 0.490759i
\(320\) 9.06353 5.23283i 0.506666 0.292524i
\(321\) 4.89324 8.47534i 0.273114 0.473048i
\(322\) 28.8656 + 3.84827i 1.60862 + 0.214456i
\(323\) −10.4520 + 6.03445i −0.581564 + 0.335766i
\(324\) 1.46986 + 2.54588i 0.0816591 + 0.141438i
\(325\) −0.883585 15.6377i −0.0490125 0.867421i
\(326\) 6.83320 11.8354i 0.378456 0.655505i
\(327\) −2.60941 1.50655i −0.144301 0.0833122i
\(328\) 10.2342 + 17.7261i 0.565086 + 0.978758i
\(329\) −16.0941 2.14562i −0.887298 0.118292i
\(330\) 5.53939i 0.304934i
\(331\) 22.9813i 1.26316i 0.775309 + 0.631582i \(0.217594\pi\)
−0.775309 + 0.631582i \(0.782406\pi\)
\(332\) 3.89255 2.24737i 0.213631 0.123340i
\(333\) 8.42267 + 4.86283i 0.461560 + 0.266482i
\(334\) −35.0116 −1.91575
\(335\) 4.01946 + 6.96192i 0.219607 + 0.380370i
\(336\) −3.02681 + 1.24795i −0.165126 + 0.0680813i
\(337\) 30.3389 1.65267 0.826333 0.563182i \(-0.190423\pi\)
0.826333 + 0.563182i \(0.190423\pi\)
\(338\) 23.2356 17.1733i 1.26385 0.934105i
\(339\) −1.36880 + 2.37084i −0.0743433 + 0.128766i
\(340\) 6.66541i 0.361482i
\(341\) 5.21065 9.02510i 0.282172 0.488737i
\(342\) 4.79087 8.29803i 0.259061 0.448706i
\(343\) 7.17127 17.0755i 0.387212 0.921991i
\(344\) −10.3130 5.95422i −0.556040 0.321030i
\(345\) 4.01097i 0.215944i
\(346\) 31.3917 + 18.1240i 1.68763 + 0.974353i
\(347\) 0.359991 + 0.623522i 0.0193253 + 0.0334724i 0.875526 0.483170i \(-0.160515\pi\)
−0.856201 + 0.516643i \(0.827182\pi\)
\(348\) 8.37345 14.5032i 0.448864 0.777455i
\(349\) 15.4556 8.92327i 0.827317 0.477652i −0.0256163 0.999672i \(-0.508155\pi\)
0.852933 + 0.522020i \(0.174821\pi\)
\(350\) 25.3202 + 3.37561i 1.35342 + 0.180434i
\(351\) −3.01583 + 1.97606i −0.160973 + 0.105474i
\(352\) 10.6589 + 18.4618i 0.568121 + 0.984015i
\(353\) 0.252183i 0.0134223i −0.999977 0.00671117i \(-0.997864\pi\)
0.999977 0.00671117i \(-0.00213625\pi\)
\(354\) −10.9702 −0.583057
\(355\) −7.33357 −0.389226
\(356\) 9.76304i 0.517440i
\(357\) −0.978777 + 7.34174i −0.0518024 + 0.388566i
\(358\) −39.2187 22.6429i −2.07277 1.19672i
\(359\) 10.2385 5.91120i 0.540368 0.311981i −0.204860 0.978791i \(-0.565674\pi\)
0.745228 + 0.666810i \(0.232341\pi\)
\(360\) 0.845801 + 1.46497i 0.0445776 + 0.0772107i
\(361\) 0.414022 0.0217906
\(362\) −42.6775 24.6399i −2.24308 1.29504i
\(363\) 1.53037 0.0803234
\(364\) 12.1349 + 25.2818i 0.636039 + 1.32513i
\(365\) 2.57483 0.134773
\(366\) −5.84139 3.37253i −0.305334 0.176285i
\(367\) −14.1834 −0.740367 −0.370183 0.928959i \(-0.620705\pi\)
−0.370183 + 0.928959i \(0.620705\pi\)
\(368\) 3.06410 + 5.30718i 0.159727 + 0.276656i
\(369\) 8.48708 4.90002i 0.441820 0.255085i
\(370\) 15.1616 + 8.75356i 0.788215 + 0.455076i
\(371\) −13.8767 + 5.72133i −0.720440 + 0.297037i
\(372\) 9.95548i 0.516168i
\(373\) −9.94037 −0.514693 −0.257346 0.966319i \(-0.582848\pi\)
−0.257346 + 0.966319i \(0.582848\pi\)
\(374\) 19.1467 0.990051
\(375\) 7.56794i 0.390807i
\(376\) 6.40867 + 11.1001i 0.330502 + 0.572446i
\(377\) 18.3391 + 9.25011i 0.944513 + 0.476405i
\(378\) −2.24141 5.43638i −0.115286 0.279617i
\(379\) 7.91690 4.57083i 0.406664 0.234788i −0.282691 0.959211i \(-0.591227\pi\)
0.689355 + 0.724423i \(0.257894\pi\)
\(380\) 5.13232 8.88945i 0.263283 0.456019i
\(381\) 7.39515 + 12.8088i 0.378865 + 0.656214i
\(382\) 41.7390 + 24.0980i 2.13555 + 1.23296i
\(383\) 23.7089i 1.21147i 0.795668 + 0.605734i \(0.207120\pi\)
−0.795668 + 0.605734i \(0.792880\pi\)
\(384\) 12.8729 + 7.43217i 0.656917 + 0.379271i
\(385\) 0.871403 6.53633i 0.0444108 0.333122i
\(386\) −0.0562147 + 0.0973667i −0.00286125 + 0.00495584i
\(387\) −2.85083 + 4.93777i −0.144916 + 0.251001i
\(388\) 37.4516i 1.90132i
\(389\) −10.2666 + 17.7823i −0.520537 + 0.901596i 0.479178 + 0.877718i \(0.340935\pi\)
−0.999715 + 0.0238784i \(0.992399\pi\)
\(390\) −5.42877 + 3.55709i −0.274897 + 0.180120i
\(391\) 13.8638 0.701121
\(392\) −14.1343 + 3.73776i −0.713890 + 0.188786i
\(393\) −1.14893 1.99001i −0.0579560 0.100383i
\(394\) 39.7415 2.00215
\(395\) 1.59871 + 0.923016i 0.0804399 + 0.0464420i
\(396\) −7.83438 + 4.52318i −0.393692 + 0.227298i
\(397\) 26.5917i 1.33460i −0.744788 0.667301i \(-0.767450\pi\)
0.744788 0.667301i \(-0.232550\pi\)
\(398\) 35.9367i 1.80134i
\(399\) −6.95846 + 9.03779i −0.348359 + 0.452456i
\(400\) 2.68776 + 4.65533i 0.134388 + 0.232767i
\(401\) −21.3708 12.3385i −1.06721 0.616153i −0.139791 0.990181i \(-0.544643\pi\)
−0.927417 + 0.374028i \(0.877976\pi\)
\(402\) −11.0300 + 19.1045i −0.550127 + 0.952847i
\(403\) 12.1909 0.688829i 0.607270 0.0343130i
\(404\) −22.3058 38.6349i −1.10976 1.92216i
\(405\) 0.701414 0.404962i 0.0348536 0.0201227i
\(406\) −20.4361 + 26.5429i −1.01423 + 1.31730i
\(407\) −14.9643 + 25.9189i −0.741752 + 1.28475i
\(408\) 5.06361 2.92348i 0.250686 0.144734i
\(409\) −31.3018 + 18.0721i −1.54777 + 0.893607i −0.549460 + 0.835520i \(0.685167\pi\)
−0.998312 + 0.0580869i \(0.981500\pi\)
\(410\) 15.2775 8.82050i 0.754504 0.435613i
\(411\) 13.5481 7.82198i 0.668276 0.385830i
\(412\) 11.7809 20.4052i 0.580406 1.00529i
\(413\) 12.9445 + 1.72572i 0.636957 + 0.0849170i
\(414\) −9.53209 + 5.50335i −0.468477 + 0.270475i
\(415\) −0.619171 1.07243i −0.0303939 0.0526438i
\(416\) −11.2485 + 22.3012i −0.551504 + 1.09340i
\(417\) −11.2601 + 19.5030i −0.551409 + 0.955068i
\(418\) 25.5353 + 14.7428i 1.24897 + 0.721095i
\(419\) 1.32411 + 2.29343i 0.0646872 + 0.112042i 0.896555 0.442932i \(-0.146062\pi\)
−0.831868 + 0.554974i \(0.812728\pi\)
\(420\) −2.40116 5.82384i −0.117165 0.284174i
\(421\) 4.51819i 0.220203i 0.993920 + 0.110102i \(0.0351176\pi\)
−0.993920 + 0.110102i \(0.964882\pi\)
\(422\) 11.9590i 0.582153i
\(423\) 5.31465 3.06841i 0.258407 0.149191i
\(424\) 10.2615 + 5.92450i 0.498344 + 0.287719i
\(425\) 12.1609 0.589893
\(426\) −10.0622 17.4282i −0.487515 0.844401i
\(427\) 6.36215 + 4.89840i 0.307886 + 0.237050i
\(428\) 28.7696 1.39063
\(429\) −6.08087 9.28053i −0.293587 0.448068i
\(430\) −5.13176 + 8.88846i −0.247475 + 0.428640i
\(431\) 13.6978i 0.659800i −0.944016 0.329900i \(-0.892985\pi\)
0.944016 0.329900i \(-0.107015\pi\)
\(432\) 0.618725 1.07166i 0.0297684 0.0515604i
\(433\) −11.1388 + 19.2929i −0.535296 + 0.927159i 0.463853 + 0.885912i \(0.346466\pi\)
−0.999149 + 0.0412471i \(0.986867\pi\)
\(434\) −2.63157 + 19.7392i −0.126319 + 0.947513i
\(435\) −3.99578 2.30697i −0.191583 0.110611i
\(436\) 8.85768i 0.424206i
\(437\) 18.4897 + 10.6750i 0.884481 + 0.510655i
\(438\) 3.53285 + 6.11908i 0.168806 + 0.292381i
\(439\) −10.7294 + 18.5838i −0.512086 + 0.886958i 0.487816 + 0.872946i \(0.337794\pi\)
−0.999902 + 0.0140120i \(0.995540\pi\)
\(440\) −4.50812 + 2.60276i −0.214916 + 0.124082i
\(441\) 1.78961 + 6.76737i 0.0852193 + 0.322256i
\(442\) 12.2949 + 18.7643i 0.584810 + 0.892528i
\(443\) 3.43706 + 5.95317i 0.163300 + 0.282844i 0.936050 0.351866i \(-0.114453\pi\)
−0.772750 + 0.634710i \(0.781120\pi\)
\(444\) 28.5908i 1.35686i
\(445\) 2.68981 0.127509
\(446\) −40.9343 −1.93830
\(447\) 13.5565i 0.641198i
\(448\) −27.0890 20.8566i −1.27983 0.985380i
\(449\) −25.5631 14.7589i −1.20640 0.696515i −0.244428 0.969667i \(-0.578600\pi\)
−0.961971 + 0.273152i \(0.911934\pi\)
\(450\) −8.36131 + 4.82741i −0.394156 + 0.227566i
\(451\) 15.0787 + 26.1171i 0.710029 + 1.22981i
\(452\) −8.04783 −0.378538
\(453\) −7.26064 4.19193i −0.341135 0.196954i
\(454\) 51.5061 2.41730
\(455\) 6.96537 3.34327i 0.326542 0.156735i
\(456\) 9.00424 0.421662
\(457\) 12.9001 + 7.44788i 0.603441 + 0.348397i 0.770394 0.637568i \(-0.220059\pi\)
−0.166953 + 0.985965i \(0.553393\pi\)
\(458\) 59.1342 2.76316
\(459\) −1.39973 2.42441i −0.0653340 0.113162i
\(460\) −10.2115 + 5.89559i −0.476112 + 0.274883i
\(461\) 21.6772 + 12.5154i 1.00961 + 0.582898i 0.911077 0.412236i \(-0.135252\pi\)
0.0985319 + 0.995134i \(0.468585\pi\)
\(462\) 16.7292 6.89744i 0.778314 0.320898i
\(463\) 34.2885i 1.59352i −0.604295 0.796761i \(-0.706545\pi\)
0.604295 0.796761i \(-0.293455\pi\)
\(464\) −7.04944 −0.327262
\(465\) −2.74283 −0.127196
\(466\) 48.5922i 2.25099i
\(467\) 1.46293 + 2.53387i 0.0676964 + 0.117254i 0.897887 0.440226i \(-0.145102\pi\)
−0.830190 + 0.557480i \(0.811768\pi\)
\(468\) −9.46366 4.77339i −0.437458 0.220650i
\(469\) 16.0204 20.8077i 0.739755 0.960810i
\(470\) 9.56687 5.52344i 0.441287 0.254777i
\(471\) −1.53856 + 2.66486i −0.0708930 + 0.122790i
\(472\) −5.15449 8.92784i −0.237255 0.410937i
\(473\) −15.1949 8.77278i −0.698662 0.403373i
\(474\) 5.06579i 0.232679i
\(475\) 16.2187 + 9.36386i 0.744164 + 0.429643i
\(476\) −20.1298 + 8.29951i −0.922650 + 0.380407i
\(477\) 2.83659 4.91312i 0.129879 0.224957i
\(478\) 24.9236 43.1689i 1.13998 1.97450i
\(479\) 33.3149i 1.52220i −0.648636 0.761099i \(-0.724660\pi\)
0.648636 0.761099i \(-0.275340\pi\)
\(480\) 2.80537 4.85904i 0.128047 0.221784i
\(481\) −35.0105 + 1.97822i −1.59634 + 0.0901993i
\(482\) −3.52907 −0.160745
\(483\) 12.1133 4.99431i 0.551176 0.227249i
\(484\) 2.24943 + 3.89613i 0.102247 + 0.177097i
\(485\) 10.3183 0.468528
\(486\) 1.92478 + 1.11128i 0.0873100 + 0.0504085i
\(487\) −12.9847 + 7.49670i −0.588391 + 0.339708i −0.764461 0.644670i \(-0.776995\pi\)
0.176070 + 0.984378i \(0.443662\pi\)
\(488\) 6.33853i 0.286932i
\(489\) 6.14897i 0.278066i
\(490\) 3.22146 + 12.1819i 0.145531 + 0.550323i
\(491\) 20.3637 + 35.2709i 0.918999 + 1.59175i 0.800939 + 0.598746i \(0.204334\pi\)
0.118060 + 0.993006i \(0.462333\pi\)
\(492\) 24.9497 + 14.4047i 1.12482 + 0.649415i
\(493\) −7.97393 + 13.8112i −0.359128 + 0.622027i
\(494\) 1.94895 + 34.4924i 0.0876874 + 1.55189i
\(495\) 1.24618 + 2.15845i 0.0560116 + 0.0970149i
\(496\) −3.62922 + 2.09533i −0.162957 + 0.0940831i
\(497\) 9.13148 + 22.1477i 0.409603 + 0.993462i
\(498\) 1.69910 2.94292i 0.0761383 0.131875i
\(499\) −0.946024 + 0.546187i −0.0423498 + 0.0244507i −0.521025 0.853541i \(-0.674450\pi\)
0.478676 + 0.877992i \(0.341117\pi\)
\(500\) −19.2671 + 11.1239i −0.861650 + 0.497474i
\(501\) −13.6424 + 7.87645i −0.609498 + 0.351894i
\(502\) 0.684183 0.395013i 0.0305366 0.0176303i
\(503\) 18.2104 31.5413i 0.811961 1.40636i −0.0995283 0.995035i \(-0.531733\pi\)
0.911489 0.411323i \(-0.134933\pi\)
\(504\) 3.37112 4.37849i 0.150162 0.195033i
\(505\) −10.6443 + 6.14547i −0.473664 + 0.273470i
\(506\) −16.9353 29.3329i −0.752868 1.30401i
\(507\) 5.19040 11.9189i 0.230514 0.529336i
\(508\) −21.7397 + 37.6543i −0.964545 + 1.67064i
\(509\) −6.91042 3.98973i −0.306299 0.176842i 0.338970 0.940797i \(-0.389921\pi\)
−0.645269 + 0.763955i \(0.723255\pi\)
\(510\) −2.51965 4.36417i −0.111572 0.193249i
\(511\) −3.20608 7.77610i −0.141828 0.343994i
\(512\) 13.7415i 0.607294i
\(513\) 4.31115i 0.190342i
\(514\) 10.0252 5.78805i 0.442193 0.255300i
\(515\) −5.62183 3.24576i −0.247727 0.143025i
\(516\) −16.7613 −0.737875
\(517\) 9.44236 + 16.3546i 0.415274 + 0.719276i
\(518\) 7.55752 56.6884i 0.332058 2.49075i
\(519\) 16.3092 0.715895
\(520\) −5.44565 2.74674i −0.238808 0.120453i
\(521\) −3.02902 + 5.24643i −0.132704 + 0.229850i −0.924718 0.380653i \(-0.875699\pi\)
0.792014 + 0.610503i \(0.209033\pi\)
\(522\) 12.6613i 0.554171i
\(523\) −5.73446 + 9.93238i −0.250750 + 0.434313i −0.963733 0.266870i \(-0.914011\pi\)
0.712982 + 0.701182i \(0.247344\pi\)
\(524\) 3.37755 5.85009i 0.147549 0.255562i
\(525\) 10.6255 4.38089i 0.463736 0.191198i
\(526\) −40.9522 23.6438i −1.78560 1.03092i
\(527\) 9.48048i 0.412976i
\(528\) 3.29780 + 1.90399i 0.143519 + 0.0828605i
\(529\) −0.762574 1.32082i −0.0331554 0.0574268i
\(530\) 5.10614 8.84409i 0.221797 0.384163i
\(531\) −4.27457 + 2.46792i −0.185500 + 0.107099i
\(532\) −33.2371 4.43107i −1.44101 0.192111i
\(533\) −15.9128 + 31.5485i −0.689261 + 1.36652i
\(534\) 3.69062 + 6.39234i 0.159709 + 0.276624i
\(535\) 7.92630i 0.342684i
\(536\) −20.7304 −0.895419
\(537\) −20.3756 −0.879274
\(538\) 8.44950i 0.364284i
\(539\) −20.8251 + 5.50711i −0.897000 + 0.237208i
\(540\) 2.06197 + 1.19048i 0.0887330 + 0.0512300i
\(541\) −21.2518 + 12.2697i −0.913687 + 0.527517i −0.881616 0.471968i \(-0.843544\pi\)
−0.0320714 + 0.999486i \(0.510210\pi\)
\(542\) −28.9988 50.2274i −1.24560 2.15745i
\(543\) −22.1726 −0.951519
\(544\) −16.7951 9.69663i −0.720082 0.415740i
\(545\) −2.44037 −0.104534
\(546\) 17.5023 + 11.9660i 0.749029 + 0.512098i
\(547\) −20.6787 −0.884155 −0.442078 0.896977i \(-0.645758\pi\)
−0.442078 + 0.896977i \(0.645758\pi\)
\(548\) 39.8276 + 22.9945i 1.70135 + 0.982276i
\(549\) −3.03483 −0.129523
\(550\) −14.8553 25.7301i −0.633431 1.09713i
\(551\) −21.2692 + 12.2798i −0.906097 + 0.523135i
\(552\) −8.95758 5.17166i −0.381260 0.220121i
\(553\) 0.796900 5.97749i 0.0338876 0.254189i
\(554\) 63.7542i 2.70866i
\(555\) 7.87704 0.334362
\(556\) −66.2032 −2.80764
\(557\) 19.2157i 0.814196i 0.913384 + 0.407098i \(0.133459\pi\)
−0.913384 + 0.407098i \(0.866541\pi\)
\(558\) −3.76337 6.51834i −0.159316 0.275943i
\(559\) −1.15973 20.5249i −0.0490513 0.868109i
\(560\) −1.61768 + 2.10107i −0.0683594 + 0.0887866i
\(561\) 7.46058 4.30737i 0.314986 0.181857i
\(562\) −1.06572 + 1.84588i −0.0449547 + 0.0778639i
\(563\) 2.96132 + 5.12915i 0.124805 + 0.216168i 0.921657 0.388007i \(-0.126836\pi\)
−0.796852 + 0.604175i \(0.793503\pi\)
\(564\) 15.6236 + 9.02030i 0.657873 + 0.379823i
\(565\) 2.21725i 0.0932806i
\(566\) −4.34949 2.51118i −0.182823 0.105553i
\(567\) −2.09638 1.61406i −0.0880396 0.0677842i
\(568\) 9.45575 16.3778i 0.396754 0.687199i
\(569\) −17.8849 + 30.9775i −0.749773 + 1.29865i 0.198158 + 0.980170i \(0.436504\pi\)
−0.947931 + 0.318475i \(0.896829\pi\)
\(570\) 7.76047i 0.325051i
\(571\) 1.69895 2.94266i 0.0710987 0.123147i −0.828284 0.560308i \(-0.810683\pi\)
0.899383 + 0.437161i \(0.144016\pi\)
\(572\) 14.6891 29.1223i 0.614180 1.21766i
\(573\) 21.6850 0.905904
\(574\) −45.6613 35.1560i −1.90587 1.46738i
\(575\) −10.7564 18.6307i −0.448574 0.776953i
\(576\) 12.9218 0.538408
\(577\) 7.14796 + 4.12687i 0.297573 + 0.171804i 0.641352 0.767247i \(-0.278374\pi\)
−0.343779 + 0.939051i \(0.611707\pi\)
\(578\) 17.6368 10.1826i 0.733593 0.423540i
\(579\) 0.0505858i 0.00210227i
\(580\) 13.5637i 0.563202i
\(581\) −2.46784 + 3.20528i −0.102383 + 0.132977i
\(582\) 14.1574 + 24.5214i 0.586844 + 1.01644i
\(583\) 15.1190 + 8.72898i 0.626167 + 0.361518i
\(584\) −3.31992 + 5.75028i −0.137379 + 0.237948i
\(585\) −1.31512 + 2.60733i −0.0543733 + 0.107800i
\(586\) 5.96189 + 10.3263i 0.246283 + 0.426576i
\(587\) −20.9087 + 12.0716i −0.862994 + 0.498250i −0.865014 0.501748i \(-0.832690\pi\)
0.00201975 + 0.999998i \(0.499357\pi\)
\(588\) −14.5984 + 14.5032i −0.602029 + 0.598104i
\(589\) −7.29991 + 12.6438i −0.300788 + 0.520980i
\(590\) −7.69463 + 4.44249i −0.316783 + 0.182895i
\(591\) 15.4854 8.94051i 0.636985 0.367764i
\(592\) 10.4226 6.01751i 0.428368 0.247318i
\(593\) 7.24219 4.18128i 0.297401 0.171705i −0.343874 0.939016i \(-0.611739\pi\)
0.641275 + 0.767311i \(0.278406\pi\)
\(594\) −3.41970 + 5.92310i −0.140312 + 0.243028i
\(595\) 2.28659 + 5.54597i 0.0937412 + 0.227362i
\(596\) −34.5131 + 19.9262i −1.41371 + 0.816207i
\(597\) −8.08456 14.0029i −0.330879 0.573099i
\(598\) 17.8722 35.4331i 0.730847 1.44897i
\(599\) −4.25916 + 7.37709i −0.174025 + 0.301420i −0.939823 0.341661i \(-0.889011\pi\)
0.765799 + 0.643080i \(0.222344\pi\)
\(600\) −7.85737 4.53645i −0.320776 0.185200i
\(601\) 0.714622 + 1.23776i 0.0291500 + 0.0504894i 0.880232 0.474543i \(-0.157387\pi\)
−0.851082 + 0.525032i \(0.824053\pi\)
\(602\) 33.2335 + 4.43058i 1.35449 + 0.180577i
\(603\) 9.92554i 0.404199i
\(604\) 24.6463i 1.00284i
\(605\) 1.07342 0.619740i 0.0436408 0.0251960i
\(606\) −29.2095 16.8641i −1.18655 0.685057i
\(607\) 15.0311 0.610094 0.305047 0.952337i \(-0.401328\pi\)
0.305047 + 0.952337i \(0.401328\pi\)
\(608\) −14.9327 25.8642i −0.605601 1.04893i
\(609\) −1.99175 + 14.9400i −0.0807099 + 0.605399i
\(610\) −5.46298 −0.221190
\(611\) −9.96469 + 19.7558i −0.403128 + 0.799236i
\(612\) 4.11484 7.12711i 0.166332 0.288096i
\(613\) 17.9059i 0.723213i 0.932331 + 0.361606i \(0.117772\pi\)
−0.932331 + 0.361606i \(0.882228\pi\)
\(614\) 2.00325 3.46973i 0.0808445 0.140027i
\(615\) 3.96864 6.87388i 0.160031 0.277182i
\(616\) 13.4738 + 10.3739i 0.542876 + 0.417976i
\(617\) 34.2385 + 19.7676i 1.37839 + 0.795813i 0.991966 0.126509i \(-0.0403771\pi\)
0.386423 + 0.922322i \(0.373710\pi\)
\(618\) 17.8137i 0.716573i
\(619\) 23.1290 + 13.3535i 0.929634 + 0.536724i 0.886696 0.462354i \(-0.152995\pi\)
0.0429379 + 0.999078i \(0.486328\pi\)
\(620\) −4.03159 6.98292i −0.161913 0.280441i
\(621\) −2.47614 + 4.28881i −0.0993642 + 0.172104i
\(622\) −37.6125 + 21.7156i −1.50812 + 0.870715i
\(623\) −3.34925 8.12335i −0.134185 0.325455i
\(624\) 0.251700 + 4.45458i 0.0100761 + 0.178326i
\(625\) −7.79533 13.5019i −0.311813 0.540076i
\(626\) 68.6362i 2.74326i
\(627\) 13.2666 0.529817
\(628\) −9.04589 −0.360970
\(629\) 27.2267i 1.08560i
\(630\) −3.77368 2.90547i −0.150347 0.115757i
\(631\) 15.8415 + 9.14610i 0.630640 + 0.364100i 0.781000 0.624531i \(-0.214710\pi\)
−0.150360 + 0.988631i \(0.548043\pi\)
\(632\) −4.12269 + 2.38023i −0.163992 + 0.0946806i
\(633\) −2.69037 4.65986i −0.106933 0.185213i
\(634\) 41.5429 1.64988
\(635\) 10.3741 + 5.98951i 0.411685 + 0.237686i
\(636\) 16.6776 0.661311
\(637\) −18.7698 16.8728i −0.743688 0.668527i
\(638\) 38.9624 1.54253
\(639\) −7.84155 4.52732i −0.310207 0.179098i
\(640\) 12.0390 0.475883
\(641\) −19.2412 33.3267i −0.759981 1.31633i −0.942860 0.333190i \(-0.891875\pi\)
0.182879 0.983135i \(-0.441458\pi\)
\(642\) 18.8369 10.8755i 0.743432 0.429221i
\(643\) 9.32291 + 5.38258i 0.367660 + 0.212268i 0.672436 0.740156i \(-0.265248\pi\)
−0.304776 + 0.952424i \(0.598582\pi\)
\(644\) 30.5199 + 23.4981i 1.20265 + 0.925956i
\(645\) 4.61790i 0.181830i
\(646\) −26.8238 −1.05537
\(647\) −6.12507 −0.240801 −0.120401 0.992725i \(-0.538418\pi\)
−0.120401 + 0.992725i \(0.538418\pi\)
\(648\) 2.08860i 0.0820478i
\(649\) −7.59448 13.1540i −0.298109 0.516341i
\(650\) 15.6770 31.0810i 0.614904 1.21910i
\(651\) 3.41527 + 8.28348i 0.133855 + 0.324655i
\(652\) 15.6545 9.03815i 0.613079 0.353961i
\(653\) −11.7103 + 20.2828i −0.458258 + 0.793726i −0.998869 0.0475467i \(-0.984860\pi\)
0.540611 + 0.841273i \(0.318193\pi\)
\(654\) −3.34837 5.79955i −0.130932 0.226781i
\(655\) −1.61176 0.930547i −0.0629765 0.0363595i
\(656\) 12.1270i 0.473482i
\(657\) 2.75318 + 1.58955i 0.107412 + 0.0620142i
\(658\) −28.5933 22.0148i −1.11468 0.858228i
\(659\) −8.15148 + 14.1188i −0.317537 + 0.549989i −0.979973 0.199128i \(-0.936189\pi\)
0.662437 + 0.749118i \(0.269522\pi\)
\(660\) −3.66343 + 6.34525i −0.142599 + 0.246988i
\(661\) 48.0978i 1.87079i 0.353608 + 0.935394i \(0.384955\pi\)
−0.353608 + 0.935394i \(0.615045\pi\)
\(662\) −25.5385 + 44.2340i −0.992582 + 1.71920i
\(663\) 9.01212 + 4.54564i 0.350002 + 0.176538i
\(664\) 3.19338 0.123927
\(665\) −1.22080 + 9.15715i −0.0473407 + 0.355099i
\(666\) 10.8079 + 18.7198i 0.418797 + 0.725378i
\(667\) 28.2119 1.09237
\(668\) −40.1050 23.1546i −1.55171 0.895880i
\(669\) −15.9502 + 9.20887i −0.616671 + 0.356035i
\(670\) 17.8669i 0.690259i
\(671\) 9.33901i 0.360528i
\(672\) −18.1677 2.42206i −0.700833 0.0934328i
\(673\) −22.0349 38.1655i −0.849382 1.47117i −0.881760 0.471698i \(-0.843641\pi\)
0.0323778 0.999476i \(-0.489692\pi\)
\(674\) 58.3959 + 33.7149i 2.24932 + 1.29865i
\(675\) −2.17201 + 3.76204i −0.0836008 + 0.144801i
\(676\) 37.9732 4.30500i 1.46051 0.165577i
\(677\) −3.08805 5.34866i −0.118684 0.205566i 0.800563 0.599249i \(-0.204534\pi\)
−0.919246 + 0.393683i \(0.871201\pi\)
\(678\) −5.26931 + 3.04224i −0.202367 + 0.116836i
\(679\) −12.8479 31.1617i −0.493058 1.19588i
\(680\) 2.36779 4.10114i 0.0908007 0.157271i
\(681\) 20.0696 11.5872i 0.769067 0.444021i
\(682\) 20.0587 11.5809i 0.768089 0.443456i
\(683\) −12.2977 + 7.10008i −0.470558 + 0.271677i −0.716473 0.697614i \(-0.754245\pi\)
0.245915 + 0.969291i \(0.420912\pi\)
\(684\) 10.9757 6.33680i 0.419665 0.242294i
\(685\) 6.33520 10.9729i 0.242056 0.419253i
\(686\) 32.7787 24.8974i 1.25150 0.950588i
\(687\) 23.0419 13.3032i 0.879103 0.507550i
\(688\) 3.52775 + 6.11025i 0.134494 + 0.232951i
\(689\) 1.15394 + 20.4224i 0.0439616 + 0.778031i
\(690\) −4.45730 + 7.72026i −0.169686 + 0.293905i
\(691\) −0.336981 0.194556i −0.0128193 0.00740126i 0.493577 0.869702i \(-0.335689\pi\)
−0.506396 + 0.862301i \(0.669023\pi\)
\(692\) 23.9723 + 41.5213i 0.911291 + 1.57840i
\(693\) 4.96692 6.45114i 0.188678 0.245058i
\(694\) 1.60020i 0.0607426i
\(695\) 18.2396i 0.691868i
\(696\) 10.3041 5.94910i 0.390578 0.225500i
\(697\) −23.7593 13.7174i −0.899947 0.519585i
\(698\) 39.6648 1.50134
\(699\) −10.9316 18.9341i −0.413472 0.716155i
\(700\) 26.7713 + 20.6120i 1.01186 + 0.779060i
\(701\) −3.60438 −0.136135 −0.0680677 0.997681i \(-0.521683\pi\)
−0.0680677 + 0.997681i \(0.521683\pi\)
\(702\) −8.00076 + 0.452072i −0.301969 + 0.0170624i
\(703\) 20.9644 36.3114i 0.790687 1.36951i
\(704\) 39.7639i 1.49866i
\(705\) 2.48518 4.30446i 0.0935973 0.162115i
\(706\) 0.280244 0.485397i 0.0105471 0.0182682i
\(707\) 31.8135 + 24.4941i 1.19647 + 0.921196i
\(708\) −12.5661 7.25502i −0.472262 0.272660i
\(709\) 41.5509i 1.56048i 0.625483 + 0.780238i \(0.284902\pi\)
−0.625483 + 0.780238i \(0.715098\pi\)
\(710\) −14.1155 8.14962i −0.529747 0.305850i
\(711\) 1.13963 + 1.97390i 0.0427396 + 0.0740272i
\(712\) −3.46818 + 6.00707i −0.129976 + 0.225124i
\(713\) 14.5242 8.38554i 0.543935 0.314041i
\(714\) −10.0426 + 13.0436i −0.375836 + 0.488143i
\(715\) −8.02347 4.04698i −0.300061 0.151348i
\(716\) −29.9494 51.8739i −1.11926 1.93862i
\(717\) 22.4279i 0.837585i
\(718\) 26.2759 0.980607
\(719\) 40.2967 1.50281 0.751407 0.659839i \(-0.229376\pi\)
0.751407 + 0.659839i \(0.229376\pi\)
\(720\) 1.00224i 0.0373513i
\(721\) −2.80228 + 21.0197i −0.104362 + 0.782814i
\(722\) 0.796903 + 0.460092i 0.0296577 + 0.0171229i
\(723\) −1.37512 + 0.793924i −0.0511411 + 0.0295263i
\(724\) −32.5908 56.4489i −1.21123 2.09791i
\(725\) 24.7468 0.919074
\(726\) 2.94563 + 1.70066i 0.109322 + 0.0631173i
\(727\) −31.8052 −1.17959 −0.589796 0.807553i \(-0.700792\pi\)
−0.589796 + 0.807553i \(0.700792\pi\)
\(728\) −1.51458 + 19.8663i −0.0561341 + 0.736293i
\(729\) 1.00000 0.0370370
\(730\) 4.95599 + 2.86134i 0.183429 + 0.105903i
\(731\) 15.9616 0.590360
\(732\) −4.46079 7.72631i −0.164875 0.285573i
\(733\) −13.1128 + 7.57067i −0.484332 + 0.279629i −0.722220 0.691664i \(-0.756878\pi\)
0.237888 + 0.971293i \(0.423545\pi\)
\(734\) −27.3000 15.7616i −1.00766 0.581773i
\(735\) 3.99578 + 4.02201i 0.147387 + 0.148354i
\(736\) 34.3069i 1.26457i
\(737\) −30.5436 −1.12509
\(738\) 21.7811 0.801772
\(739\) 23.6795i 0.871066i 0.900173 + 0.435533i \(0.143440\pi\)
−0.900173 + 0.435533i \(0.856560\pi\)
\(740\) 11.5782 + 20.0540i 0.425623 + 0.737200i
\(741\) 8.51907 + 13.0017i 0.312956 + 0.477628i
\(742\) −33.0676 4.40846i −1.21395 0.161840i
\(743\) 37.9709 21.9225i 1.39302 0.804260i 0.399370 0.916790i \(-0.369229\pi\)
0.993648 + 0.112530i \(0.0358954\pi\)
\(744\) 3.53655 6.12548i 0.129656 0.224571i
\(745\) 5.48984 + 9.50869i 0.201132 + 0.348371i
\(746\) −19.1331 11.0465i −0.700512 0.404441i
\(747\) 1.52896i 0.0559417i
\(748\) 21.9321 + 12.6625i 0.801916 + 0.462987i
\(749\) −23.9378 + 9.86953i −0.874669 + 0.360625i
\(750\) −8.41007 + 14.5667i −0.307092 + 0.531899i
\(751\) −7.54542 + 13.0690i −0.275336 + 0.476896i −0.970220 0.242226i \(-0.922123\pi\)
0.694884 + 0.719122i \(0.255456\pi\)
\(752\) 7.59401i 0.276925i
\(753\) 0.177730 0.307837i 0.00647683 0.0112182i
\(754\) 25.0195 + 38.1843i 0.911155 + 1.39059i
\(755\) −6.79029 −0.247124
\(756\) 1.02782 7.70958i 0.0373813 0.280395i
\(757\) −8.25531 14.2986i −0.300044 0.519692i 0.676101 0.736809i \(-0.263668\pi\)
−0.976146 + 0.217117i \(0.930335\pi\)
\(758\) 20.3178 0.737975
\(759\) −13.1978 7.61978i −0.479051 0.276580i
\(760\) 6.31570 3.64637i 0.229095 0.132268i
\(761\) 20.3189i 0.736560i −0.929715 0.368280i \(-0.879947\pi\)
0.929715 0.368280i \(-0.120053\pi\)
\(762\) 32.8722i 1.19083i
\(763\) 3.03866 + 7.37005i 0.110007 + 0.266814i
\(764\) 31.8740 + 55.2074i 1.15316 + 1.99733i
\(765\) −1.96359 1.13368i −0.0709936 0.0409882i
\(766\) −26.3471 + 45.6345i −0.951959 + 1.64884i
\(767\) 8.01459 15.8896i 0.289390 0.573740i
\(768\) 3.59659 + 6.22948i 0.129781 + 0.224787i
\(769\) −29.3351 + 16.9366i −1.05785 + 0.610750i −0.924837 0.380364i \(-0.875799\pi\)
−0.133013 + 0.991114i \(0.542465\pi\)
\(770\) 8.94093 11.6127i 0.322209 0.418491i
\(771\) 2.60424 4.51067i 0.0937894 0.162448i
\(772\) −0.128785 + 0.0743542i −0.00463508 + 0.00267607i
\(773\) 11.7224 6.76796i 0.421627 0.243426i −0.274146 0.961688i \(-0.588395\pi\)
0.695773 + 0.718262i \(0.255062\pi\)
\(774\) −10.9745 + 6.33610i −0.394468 + 0.227746i
\(775\) 12.7402 7.35558i 0.457643 0.264220i
\(776\) −13.3042 + 23.0435i −0.477591 + 0.827212i
\(777\) −9.80820 23.7891i −0.351867 0.853428i
\(778\) −39.5220 + 22.8180i −1.41693 + 0.818065i
\(779\) −21.1247 36.5890i −0.756870 1.31094i
\(780\) −8.57099 + 0.484292i −0.306891 + 0.0173404i
\(781\) 13.9318 24.1306i 0.498520 0.863462i
\(782\) 26.6848 + 15.4065i 0.954245 + 0.550934i
\(783\) −2.84837 4.93353i −0.101793 0.176310i
\(784\) 8.35962 + 2.26929i 0.298558 + 0.0810460i
\(785\) 2.49223i 0.0889515i
\(786\) 5.10712i 0.182165i
\(787\) 39.6850 22.9121i 1.41462 0.816729i 0.418797 0.908080i \(-0.362452\pi\)
0.995819 + 0.0913511i \(0.0291186\pi\)
\(788\) 45.5230 + 26.2827i 1.62169 + 0.936282i
\(789\) −21.2763 −0.757455
\(790\) 2.05145 + 3.55322i 0.0729873 + 0.126418i
\(791\) 6.69622 2.76084i 0.238090 0.0981642i
\(792\) −6.42719 −0.228380
\(793\) 9.15251 5.99699i 0.325015 0.212959i
\(794\) 29.5507 51.1834i 1.04872 1.81643i
\(795\) 4.59485i 0.162962i
\(796\) 23.7664 41.1646i 0.842378 1.45904i
\(797\) −4.79076 + 8.29783i −0.169697 + 0.293924i −0.938313 0.345786i \(-0.887612\pi\)
0.768616 + 0.639710i \(0.220946\pi\)
\(798\) −23.4370 + 9.66305i −0.829661 + 0.342068i
\(799\) −14.8782 8.58992i −0.526352 0.303889i
\(800\) 30.0932i 1.06395i
\(801\) 2.87613 + 1.66053i 0.101623 + 0.0586720i
\(802\) −27.4228 47.4977i −0.968334 1.67720i
\(803\) −4.89148 + 8.47230i −0.172617 + 0.298981i
\(804\) −25.2692 + 14.5892i −0.891177 + 0.514521i
\(805\) 6.47396 8.40852i 0.228177 0.296361i
\(806\) 24.2303 + 12.2216i 0.853475 + 0.430486i
\(807\) −1.90086 3.29238i −0.0669133 0.115897i
\(808\) 31.6954i 1.11504i
\(809\) 49.9290 1.75541 0.877705 0.479202i \(-0.159074\pi\)
0.877705 + 0.479202i \(0.159074\pi\)
\(810\) 1.80010 0.0632489
\(811\) 12.4298i 0.436470i −0.975896 0.218235i \(-0.929970\pi\)
0.975896 0.218235i \(-0.0700299\pi\)
\(812\) −40.9631 + 16.8890i −1.43752 + 0.592688i
\(813\) −22.5990 13.0475i −0.792581 0.457597i
\(814\) −57.6061 + 33.2589i −2.01909 + 1.16572i
\(815\) −2.49010 4.31297i −0.0872243 0.151077i
\(816\) −3.46420 −0.121271
\(817\) 21.2875 + 12.2903i 0.744754 + 0.429984i
\(818\) −80.3322 −2.80875
\(819\) 9.51179 + 0.725168i 0.332369 + 0.0253394i
\(820\) 23.3334 0.814839
\(821\) −21.3546 12.3291i −0.745280 0.430288i 0.0787058 0.996898i \(-0.474921\pi\)
−0.823986 + 0.566610i \(0.808255\pi\)
\(822\) 34.7695 1.21272
\(823\) −1.24407 2.15479i −0.0433655 0.0751113i 0.843528 0.537085i \(-0.180475\pi\)
−0.886893 + 0.461974i \(0.847141\pi\)
\(824\) 14.4973 8.37003i 0.505038 0.291584i
\(825\) −11.5768 6.68388i −0.403053 0.232703i
\(826\) 22.9976 + 17.7065i 0.800189 + 0.616089i
\(827\) 5.29835i 0.184242i 0.995748 + 0.0921208i \(0.0293646\pi\)
−0.995748 + 0.0921208i \(0.970635\pi\)
\(828\) −14.5584 −0.505939
\(829\) −15.1316 −0.525542 −0.262771 0.964858i \(-0.584636\pi\)
−0.262771 + 0.964858i \(0.584636\pi\)
\(830\) 2.75228i 0.0955329i
\(831\) −14.3426 24.8421i −0.497539 0.861762i
\(832\) −38.9698 + 25.5342i −1.35104 + 0.885238i
\(833\) 13.9019 13.8112i 0.481672 0.478531i
\(834\) −43.3465 + 25.0261i −1.50097 + 0.866583i
\(835\) −6.37933 + 11.0493i −0.220766 + 0.382377i
\(836\) 19.5001 + 33.7751i 0.674425 + 1.16814i
\(837\) −2.93282 1.69327i −0.101373 0.0585278i
\(838\) 5.88582i 0.203322i
\(839\) −31.1992 18.0129i −1.07712 0.621874i −0.147000 0.989136i \(-0.546962\pi\)
−0.930117 + 0.367262i \(0.880295\pi\)
\(840\) 0.591435 4.43631i 0.0204064 0.153067i
\(841\) −1.72648 + 2.99034i −0.0595336 + 0.103115i
\(842\) −5.02096 + 8.69655i −0.173034 + 0.299703i
\(843\) 0.959007i 0.0330300i
\(844\) 7.90896 13.6987i 0.272238 0.471529i
\(845\) −1.18607 10.4620i −0.0408020 0.359903i
\(846\) 13.6394 0.468932
\(847\) −3.20823 2.47011i −0.110236 0.0848739i
\(848\) −3.51014 6.07975i −0.120539 0.208779i
\(849\) −2.25973 −0.0775537
\(850\) 23.4072 + 13.5142i 0.802861 + 0.463532i
\(851\) −41.7115 + 24.0821i −1.42985 + 0.825525i
\(852\) 26.6182i 0.911925i
\(853\) 32.0255i 1.09653i 0.836304 + 0.548266i \(0.184712\pi\)
−0.836304 + 0.548266i \(0.815288\pi\)
\(854\) 6.80229 + 16.4985i 0.232770 + 0.564566i
\(855\) −1.74585 3.02390i −0.0597068 0.103415i
\(856\) 17.7016 + 10.2200i 0.605027 + 0.349313i
\(857\) 4.19647 7.26850i 0.143349 0.248287i −0.785407 0.618980i \(-0.787546\pi\)
0.928756 + 0.370693i \(0.120880\pi\)
\(858\) −1.39115 24.6205i −0.0474931 0.840532i
\(859\) 8.88475 + 15.3888i 0.303144 + 0.525060i 0.976846 0.213942i \(-0.0686304\pi\)
−0.673703 + 0.739003i \(0.735297\pi\)
\(860\) −11.7566 + 6.78769i −0.400897 + 0.231458i
\(861\) −25.7011 3.42638i −0.875890 0.116771i
\(862\) 15.2220 26.3653i 0.518464 0.898007i
\(863\) −1.15148 + 0.664805i −0.0391967 + 0.0226302i −0.519470 0.854489i \(-0.673871\pi\)
0.480274 + 0.877119i \(0.340537\pi\)
\(864\) 5.99938 3.46374i 0.204103 0.117839i
\(865\) 11.4395 6.60461i 0.388955 0.224563i
\(866\) −42.8795 + 24.7565i −1.45710 + 0.841260i
\(867\) 4.58149 7.93538i 0.155596 0.269500i
\(868\) −16.0688 + 20.8705i −0.545410 + 0.708390i
\(869\) −6.07425 + 3.50697i −0.206055 + 0.118966i
\(870\) −5.12735 8.88082i −0.173833 0.301088i
\(871\) −19.6134 29.9337i −0.664576 1.01426i
\(872\) 3.14657 5.45001i 0.106556 0.184561i
\(873\) 11.0330 + 6.36990i 0.373410 + 0.215589i
\(874\) 23.7258 + 41.0942i 0.802536 + 1.39003i
\(875\) 12.2151 15.8653i 0.412947 0.536344i
\(876\) 9.34569i 0.315762i
\(877\) 52.9883i 1.78929i −0.446778 0.894645i \(-0.647429\pi\)
0.446778 0.894645i \(-0.352571\pi\)
\(878\) −41.3035 + 23.8466i −1.39393 + 0.804784i
\(879\) 4.64615 + 2.68246i 0.156711 + 0.0904770i
\(880\) 3.08417 0.103967
\(881\) −18.3266 31.7426i −0.617439 1.06944i −0.989951 0.141408i \(-0.954837\pi\)
0.372512 0.928027i \(-0.378496\pi\)
\(882\) −4.07581 + 15.0145i −0.137239 + 0.505564i
\(883\) 45.3649 1.52665 0.763324 0.646015i \(-0.223566\pi\)
0.763324 + 0.646015i \(0.223566\pi\)
\(884\) 1.67394 + 29.6253i 0.0563006 + 0.996405i
\(885\) −1.99883 + 3.46207i −0.0671899 + 0.116376i
\(886\) 15.2781i 0.513278i
\(887\) −14.9103 + 25.8254i −0.500639 + 0.867132i 0.499361 + 0.866394i \(0.333568\pi\)
−1.00000 0.000738181i \(0.999765\pi\)
\(888\) −10.1565 + 17.5916i −0.340830 + 0.590334i
\(889\) 5.17113 38.7883i 0.173434 1.30092i
\(890\) 5.17730 + 2.98912i 0.173544 + 0.100195i
\(891\) 3.07728i 0.103093i
\(892\) −46.8893 27.0716i −1.56997 0.906423i
\(893\) −13.2284 22.9122i −0.442671 0.766728i
\(894\) −15.0649 + 26.0933i −0.503847 + 0.872689i
\(895\) −14.2918 + 8.25136i −0.477721 + 0.275812i
\(896\) −14.9905 36.3583i −0.500797 1.21465i
\(897\) −1.00731 17.8273i −0.0336330 0.595236i
\(898\) −32.8024 56.8154i −1.09463 1.89595i
\(899\) 19.2922i 0.643431i
\(900\) −12.7703 −0.425675
\(901\) −15.8819 −0.529103
\(902\) 67.0264i 2.23173i
\(903\) 13.9463 5.75003i 0.464103 0.191349i
\(904\) −4.95173 2.85888i −0.164692 0.0950849i
\(905\) −15.5522 + 8.97907i −0.516973 + 0.298474i
\(906\) −9.31678 16.1371i −0.309529 0.536121i
\(907\) 49.4066 1.64052 0.820259 0.571993i \(-0.193829\pi\)
0.820259 + 0.571993i \(0.193829\pi\)
\(908\) 58.9991 + 34.0631i 1.95795 + 1.13042i
\(909\) −15.1754 −0.503338
\(910\) 17.1221 + 1.30537i 0.567593 + 0.0432726i
\(911\) −22.3495 −0.740471 −0.370235 0.928938i \(-0.620723\pi\)
−0.370235 + 0.928938i \(0.620723\pi\)
\(912\) −4.62010 2.66741i −0.152987 0.0883269i
\(913\) 4.70504 0.155714
\(914\) 16.5533 + 28.6711i 0.547534 + 0.948357i
\(915\) −2.12867 + 1.22899i −0.0703717 + 0.0406291i
\(916\) 67.7369 + 39.1079i 2.23809 + 1.29216i
\(917\) −0.803402 + 6.02626i −0.0265307 + 0.199005i
\(918\) 6.22195i 0.205355i
\(919\) 35.0529 1.15629 0.578144 0.815935i \(-0.303777\pi\)
0.578144 + 0.815935i \(0.303777\pi\)
\(920\) −8.37730 −0.276191
\(921\) 1.80266i 0.0593996i
\(922\) 27.8160 + 48.1787i 0.916071 + 1.58668i
\(923\) 32.5950 1.84174i 1.07288 0.0606215i
\(924\) 23.7245 + 3.16288i 0.780479 + 0.104051i
\(925\) −36.5883 + 21.1243i −1.20302 + 0.694561i
\(926\) 38.1039 65.9980i 1.25217 2.16883i
\(927\) −4.00749 6.94118i −0.131623 0.227978i
\(928\) −34.1770 19.7321i −1.12191 0.647737i
\(929\) 54.5442i 1.78954i −0.446530 0.894768i \(-0.647341\pi\)
0.446530 0.894768i \(-0.352659\pi\)
\(930\) −5.27936 3.04804i −0.173117 0.0999491i
\(931\) 29.1751 7.71525i 0.956176 0.252857i
\(932\) 32.1360 55.6612i 1.05265 1.82324i
\(933\) −9.77057 + 16.9231i −0.319874 + 0.554038i
\(934\) 6.50288i 0.212781i
\(935\) 3.48864 6.04250i 0.114091 0.197611i
\(936\) −4.12718 6.29884i −0.134901 0.205884i
\(937\) −4.92743 −0.160972 −0.0804861 0.996756i \(-0.525647\pi\)
−0.0804861 + 0.996756i \(0.525647\pi\)
\(938\) 53.9590 22.2472i 1.76182 0.726397i
\(939\) 15.4409 + 26.7444i 0.503894 + 0.872770i
\(940\) 14.6115 0.476575
\(941\) 21.0883 + 12.1753i 0.687459 + 0.396905i 0.802659 0.596438i \(-0.203418\pi\)
−0.115201 + 0.993342i \(0.536751\pi\)
\(942\) −5.92279 + 3.41952i −0.192975 + 0.111414i
\(943\) 48.5326i 1.58044i
\(944\) 6.10786i 0.198794i
\(945\) −2.12406 0.283173i −0.0690958 0.00921163i
\(946\) −19.4979 33.7714i −0.633933 1.09800i
\(947\) 21.3651 + 12.3351i 0.694271 + 0.400838i 0.805210 0.592990i \(-0.202053\pi\)
−0.110939 + 0.993827i \(0.535386\pi\)
\(948\) −3.35021 + 5.80274i −0.108810 + 0.188464i
\(949\) −11.4441 + 0.646636i −0.371493 + 0.0209907i
\(950\) 20.8116 + 36.0468i 0.675219 + 1.16951i
\(951\) 16.1874 9.34578i 0.524911 0.303058i
\(952\) −15.3339 2.04427i −0.496975 0.0662551i
\(953\) 3.31494 5.74164i 0.107381 0.185990i −0.807327 0.590104i \(-0.799087\pi\)
0.914709 + 0.404114i \(0.132420\pi\)
\(954\) 10.9197 6.30447i 0.353537 0.204115i
\(955\) 15.2102 8.78160i 0.492190 0.284166i
\(956\) 57.0987 32.9660i 1.84670 1.06620i
\(957\) 15.1818 8.76524i 0.490759 0.283340i
\(958\) 37.0220 64.1241i 1.19613 2.07175i
\(959\) −41.0270 5.46959i −1.32483 0.176622i
\(960\) 9.06353 5.23283i 0.292524 0.168889i
\(961\) −9.76571 16.9147i −0.315023 0.545635i
\(962\) −69.5861 35.0987i −2.24355 1.13163i
\(963\) 4.89324 8.47534i 0.157683 0.273114i
\(964\) −4.04247 2.33392i −0.130199 0.0751705i
\(965\) 0.0204853 + 0.0354816i 0.000659445 + 0.00114219i
\(966\) 28.8656 + 3.84827i 0.928736 + 0.123816i
\(967\) 47.9993i 1.54355i 0.635893 + 0.771777i \(0.280632\pi\)
−0.635893 + 0.771777i \(0.719368\pi\)
\(968\) 3.19632i 0.102733i
\(969\) −10.4520 + 6.03445i −0.335766 + 0.193855i
\(970\) 19.8604 + 11.4664i 0.637681 + 0.368165i
\(971\) 37.8183 1.21365 0.606824 0.794836i \(-0.292443\pi\)
0.606824 + 0.794836i \(0.292443\pi\)
\(972\) 1.46986 + 2.54588i 0.0471459 + 0.0816591i
\(973\) 55.0845 22.7113i 1.76593 0.728090i
\(974\) −33.3236 −1.06776
\(975\) −0.883585 15.6377i −0.0282974 0.500806i
\(976\) −1.87772 + 3.25231i −0.0601045 + 0.104104i
\(977\) 28.5939i 0.914801i −0.889261 0.457400i \(-0.848781\pi\)
0.889261 0.457400i \(-0.151219\pi\)
\(978\) 6.83320 11.8354i 0.218502 0.378456i
\(979\) −5.10992 + 8.85064i −0.163314 + 0.282868i
\(980\) −4.36630 + 16.0846i −0.139476 + 0.513803i
\(981\) −2.60941 1.50655i −0.0833122 0.0481003i
\(982\) 90.5185i 2.88856i
\(983\) −2.49292 1.43929i −0.0795118 0.0459061i 0.459717 0.888065i \(-0.347951\pi\)
−0.539229 + 0.842159i \(0.681284\pi\)
\(984\) 10.2342 + 17.7261i 0.326253 + 0.565086i
\(985\) 7.24113 12.5420i 0.230722 0.399622i
\(986\) −30.6962 + 17.7225i −0.977566 + 0.564398i
\(987\) −16.0941 2.14562i −0.512281 0.0682957i
\(988\) −20.5788 + 40.7992i −0.654699 + 1.29800i
\(989\) −14.1181 24.4533i −0.448930 0.777569i
\(990\) 5.53939i 0.176053i
\(991\) 20.7810 0.660130 0.330065 0.943958i \(-0.392929\pi\)
0.330065 + 0.943958i \(0.392929\pi\)
\(992\) −23.4601 −0.744860
\(993\) 22.9813i 0.729289i
\(994\) −7.03609 + 52.7772i −0.223171 + 1.67399i
\(995\) −11.3412 6.54787i −0.359542 0.207582i
\(996\) 3.89255 2.24737i 0.123340 0.0712105i
\(997\) 20.5619 + 35.6143i 0.651202 + 1.12792i 0.982831 + 0.184506i \(0.0590685\pi\)
−0.331629 + 0.943410i \(0.607598\pi\)
\(998\) −2.42786 −0.0768525
\(999\) 8.42267 + 4.86283i 0.266482 + 0.153853i
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 273.2.bl.c.88.6 yes 12
3.2 odd 2 819.2.do.f.361.1 12
7.2 even 3 273.2.t.c.205.1 yes 12
13.4 even 6 273.2.t.c.4.6 12
21.2 odd 6 819.2.bm.e.478.6 12
39.17 odd 6 819.2.bm.e.550.1 12
91.30 even 6 inner 273.2.bl.c.121.6 yes 12
273.212 odd 6 819.2.do.f.667.1 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
273.2.t.c.4.6 12 13.4 even 6
273.2.t.c.205.1 yes 12 7.2 even 3
273.2.bl.c.88.6 yes 12 1.1 even 1 trivial
273.2.bl.c.121.6 yes 12 91.30 even 6 inner
819.2.bm.e.478.6 12 21.2 odd 6
819.2.bm.e.550.1 12 39.17 odd 6
819.2.do.f.361.1 12 3.2 odd 2
819.2.do.f.667.1 12 273.212 odd 6