Properties

Label 276.2.c.b.47.14
Level $276$
Weight $2$
Character 276.47
Analytic conductor $2.204$
Analytic rank $0$
Dimension $22$
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] = [276,2,Mod(47,276)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(276, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("276.47");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 276 = 2^{2} \cdot 3 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 276.c (of order \(2\), degree \(1\), 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: \(2.20387109579\)
Analytic rank: \(0\)
Dimension: \(22\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 47.14
Character \(\chi\) \(=\) 276.47
Dual form 276.2.c.b.47.13

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.469504 + 1.33400i) q^{2} +(-1.64481 - 0.542779i) q^{3} +(-1.55913 + 1.25264i) q^{4} +2.34886i q^{5} +(-0.0481753 - 2.44902i) q^{6} -0.796368i q^{7} +(-2.40305 - 1.49177i) q^{8} +(2.41078 + 1.78553i) q^{9} +O(q^{10})\) \(q+(0.469504 + 1.33400i) q^{2} +(-1.64481 - 0.542779i) q^{3} +(-1.55913 + 1.25264i) q^{4} +2.34886i q^{5} +(-0.0481753 - 2.44902i) q^{6} -0.796368i q^{7} +(-2.40305 - 1.49177i) q^{8} +(2.41078 + 1.78553i) q^{9} +(-3.13338 + 1.10280i) q^{10} -3.21461 q^{11} +(3.24438 - 1.21409i) q^{12} -6.69212 q^{13} +(1.06236 - 0.373898i) q^{14} +(1.27491 - 3.86342i) q^{15} +(0.861782 - 3.90606i) q^{16} +0.675569i q^{17} +(-1.25003 + 4.05431i) q^{18} +0.720048i q^{19} +(-2.94227 - 3.66218i) q^{20} +(-0.432251 + 1.30987i) q^{21} +(-1.50927 - 4.28831i) q^{22} -1.00000 q^{23} +(3.14285 + 3.75799i) q^{24} -0.517128 q^{25} +(-3.14198 - 8.92731i) q^{26} +(-2.99612 - 4.24538i) q^{27} +(0.997563 + 1.24164i) q^{28} +1.92582i q^{29} +(5.75239 - 0.113157i) q^{30} +7.61577i q^{31} +(5.61531 - 0.684292i) q^{32} +(5.28742 + 1.74482i) q^{33} +(-0.901212 + 0.317183i) q^{34} +1.87055 q^{35} +(-5.99536 + 0.235964i) q^{36} +1.89808 q^{37} +(-0.960546 + 0.338065i) q^{38} +(11.0072 + 3.63234i) q^{39} +(3.50395 - 5.64441i) q^{40} +7.63841i q^{41} +(-1.95032 + 0.0383653i) q^{42} +11.0728i q^{43} +(5.01201 - 4.02676i) q^{44} +(-4.19396 + 5.66258i) q^{45} +(-0.469504 - 1.33400i) q^{46} -1.22603 q^{47} +(-3.53759 + 5.95696i) q^{48} +6.36580 q^{49} +(-0.242794 - 0.689851i) q^{50} +(0.366685 - 1.11118i) q^{51} +(10.4339 - 8.38282i) q^{52} -11.3409i q^{53} +(4.25666 - 5.99006i) q^{54} -7.55067i q^{55} +(-1.18800 + 1.91371i) q^{56} +(0.390826 - 1.18434i) q^{57} +(-2.56905 + 0.904180i) q^{58} +0.176969 q^{59} +(2.85172 + 7.62058i) q^{60} +6.71562 q^{61} +(-10.1595 + 3.57564i) q^{62} +(1.42194 - 1.91987i) q^{63} +(3.54926 + 7.16957i) q^{64} -15.7188i q^{65} +(0.154865 + 7.87264i) q^{66} +9.36728i q^{67} +(-0.846246 - 1.05330i) q^{68} +(1.64481 + 0.542779i) q^{69} +(0.878233 + 2.49533i) q^{70} -9.44253 q^{71} +(-3.12962 - 7.88704i) q^{72} +0.422106 q^{73} +(0.891158 + 2.53205i) q^{74} +(0.850576 + 0.280686i) q^{75} +(-0.901961 - 1.12265i) q^{76} +2.56002i q^{77} +(0.322395 + 16.3891i) q^{78} -10.1253i q^{79} +(9.17478 + 2.02420i) q^{80} +(2.62375 + 8.60906i) q^{81} +(-10.1897 + 3.58627i) q^{82} -8.44270 q^{83} +(-0.966862 - 2.58372i) q^{84} -1.58682 q^{85} +(-14.7712 + 5.19874i) q^{86} +(1.04529 - 3.16760i) q^{87} +(7.72487 + 4.79546i) q^{88} +11.2794i q^{89} +(-9.52299 - 2.93615i) q^{90} +5.32939i q^{91} +(1.55913 - 1.25264i) q^{92} +(4.13368 - 12.5265i) q^{93} +(-0.575627 - 1.63553i) q^{94} -1.69129 q^{95} +(-9.60753 - 1.92234i) q^{96} -7.27066 q^{97} +(2.98877 + 8.49200i) q^{98} +(-7.74974 - 5.73980i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 22 q + 9 q^{8} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 22 q + 9 q^{8} - 2 q^{9} + 4 q^{10} - 7 q^{12} - 4 q^{13} - 12 q^{14} + 4 q^{16} + 13 q^{18} + 14 q^{20} + 2 q^{22} - 22 q^{23} - 30 q^{24} - 18 q^{25} - 27 q^{26} - 12 q^{27} + 6 q^{28} + 34 q^{30} + 20 q^{32} - 8 q^{33} - 6 q^{34} + 8 q^{35} - 36 q^{36} - 4 q^{37} - 22 q^{38} + 24 q^{39} - 4 q^{40} + 26 q^{42} + 56 q^{44} - 8 q^{47} - 22 q^{48} - 14 q^{49} - 20 q^{50} - 16 q^{51} - 19 q^{52} + 22 q^{54} + 18 q^{56} + 12 q^{57} + 3 q^{58} + 72 q^{59} - 28 q^{60} + 12 q^{61} - 63 q^{62} + 20 q^{63} + 3 q^{64} + 60 q^{66} + 20 q^{68} - 40 q^{71} - 36 q^{72} - 4 q^{73} - 28 q^{74} - 48 q^{75} + 26 q^{76} + 11 q^{78} + 84 q^{80} + 10 q^{81} - 29 q^{82} + 8 q^{83} - 38 q^{84} + 8 q^{85} - 28 q^{86} + 48 q^{87} - 30 q^{88} + 84 q^{90} + 12 q^{93} - 13 q^{94} - 32 q^{95} - 45 q^{96} - 4 q^{97} - 64 q^{98} - 20 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/276\mathbb{Z}\right)^\times\).

\(n\) \(97\) \(139\) \(185\)
\(\chi(n)\) \(1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.469504 + 1.33400i 0.331990 + 0.943283i
\(3\) −1.64481 0.542779i −0.949630 0.313373i
\(4\) −1.55913 + 1.25264i −0.779566 + 0.626320i
\(5\) 2.34886i 1.05044i 0.850966 + 0.525220i \(0.176017\pi\)
−0.850966 + 0.525220i \(0.823983\pi\)
\(6\) −0.0481753 2.44902i −0.0196675 0.999807i
\(7\) 0.796368i 0.300999i −0.988610 0.150499i \(-0.951912\pi\)
0.988610 0.150499i \(-0.0480882\pi\)
\(8\) −2.40305 1.49177i −0.849605 0.527419i
\(9\) 2.41078 + 1.78553i 0.803594 + 0.595178i
\(10\) −3.13338 + 1.10280i −0.990863 + 0.348735i
\(11\) −3.21461 −0.969243 −0.484621 0.874724i \(-0.661043\pi\)
−0.484621 + 0.874724i \(0.661043\pi\)
\(12\) 3.24438 1.21409i 0.936571 0.350477i
\(13\) −6.69212 −1.85606 −0.928030 0.372505i \(-0.878499\pi\)
−0.928030 + 0.372505i \(0.878499\pi\)
\(14\) 1.06236 0.373898i 0.283927 0.0999285i
\(15\) 1.27491 3.86342i 0.329180 0.997530i
\(16\) 0.861782 3.90606i 0.215446 0.976516i
\(17\) 0.675569i 0.163850i 0.996639 + 0.0819248i \(0.0261067\pi\)
−0.996639 + 0.0819248i \(0.973893\pi\)
\(18\) −1.25003 + 4.05431i −0.294636 + 0.955610i
\(19\) 0.720048i 0.165190i 0.996583 + 0.0825951i \(0.0263208\pi\)
−0.996583 + 0.0825951i \(0.973679\pi\)
\(20\) −2.94227 3.66218i −0.657912 0.818888i
\(21\) −0.432251 + 1.30987i −0.0943250 + 0.285837i
\(22\) −1.50927 4.28831i −0.321778 0.914270i
\(23\) −1.00000 −0.208514
\(24\) 3.14285 + 3.75799i 0.641531 + 0.767097i
\(25\) −0.517128 −0.103426
\(26\) −3.14198 8.92731i −0.616193 1.75079i
\(27\) −2.99612 4.24538i −0.576604 0.817023i
\(28\) 0.997563 + 1.24164i 0.188522 + 0.234648i
\(29\) 1.92582i 0.357616i 0.983884 + 0.178808i \(0.0572240\pi\)
−0.983884 + 0.178808i \(0.942776\pi\)
\(30\) 5.75239 0.113157i 1.05024 0.0206595i
\(31\) 7.61577i 1.36783i 0.729560 + 0.683917i \(0.239725\pi\)
−0.729560 + 0.683917i \(0.760275\pi\)
\(32\) 5.61531 0.684292i 0.992657 0.120967i
\(33\) 5.28742 + 1.74482i 0.920422 + 0.303735i
\(34\) −0.901212 + 0.317183i −0.154557 + 0.0543964i
\(35\) 1.87055 0.316181
\(36\) −5.99536 + 0.235964i −0.999226 + 0.0393274i
\(37\) 1.89808 0.312043 0.156021 0.987754i \(-0.450133\pi\)
0.156021 + 0.987754i \(0.450133\pi\)
\(38\) −0.960546 + 0.338065i −0.155821 + 0.0548414i
\(39\) 11.0072 + 3.63234i 1.76257 + 0.581640i
\(40\) 3.50395 5.64441i 0.554023 0.892460i
\(41\) 7.63841i 1.19292i 0.802643 + 0.596460i \(0.203426\pi\)
−0.802643 + 0.596460i \(0.796574\pi\)
\(42\) −1.95032 + 0.0383653i −0.300941 + 0.00591989i
\(43\) 11.0728i 1.68859i 0.535879 + 0.844295i \(0.319980\pi\)
−0.535879 + 0.844295i \(0.680020\pi\)
\(44\) 5.01201 4.02676i 0.755588 0.607056i
\(45\) −4.19396 + 5.66258i −0.625199 + 0.844128i
\(46\) −0.469504 1.33400i −0.0692246 0.196688i
\(47\) −1.22603 −0.178835 −0.0894175 0.995994i \(-0.528501\pi\)
−0.0894175 + 0.995994i \(0.528501\pi\)
\(48\) −3.53759 + 5.95696i −0.510608 + 0.859814i
\(49\) 6.36580 0.909400
\(50\) −0.242794 0.689851i −0.0343362 0.0975596i
\(51\) 0.366685 1.11118i 0.0513461 0.155597i
\(52\) 10.4339 8.38282i 1.44692 1.16249i
\(53\) 11.3409i 1.55780i −0.627151 0.778898i \(-0.715779\pi\)
0.627151 0.778898i \(-0.284221\pi\)
\(54\) 4.25666 5.99006i 0.579258 0.815144i
\(55\) 7.55067i 1.01813i
\(56\) −1.18800 + 1.91371i −0.158753 + 0.255730i
\(57\) 0.390826 1.18434i 0.0517662 0.156870i
\(58\) −2.56905 + 0.904180i −0.337333 + 0.118725i
\(59\) 0.176969 0.0230394 0.0115197 0.999934i \(-0.496333\pi\)
0.0115197 + 0.999934i \(0.496333\pi\)
\(60\) 2.85172 + 7.62058i 0.368156 + 0.983812i
\(61\) 6.71562 0.859847 0.429923 0.902865i \(-0.358541\pi\)
0.429923 + 0.902865i \(0.358541\pi\)
\(62\) −10.1595 + 3.57564i −1.29025 + 0.454106i
\(63\) 1.42194 1.91987i 0.179148 0.241881i
\(64\) 3.54926 + 7.16957i 0.443658 + 0.896196i
\(65\) 15.7188i 1.94968i
\(66\) 0.154865 + 7.87264i 0.0190626 + 0.969055i
\(67\) 9.36728i 1.14440i 0.820116 + 0.572198i \(0.193909\pi\)
−0.820116 + 0.572198i \(0.806091\pi\)
\(68\) −0.846246 1.05330i −0.102622 0.127732i
\(69\) 1.64481 + 0.542779i 0.198012 + 0.0653429i
\(70\) 0.878233 + 2.49533i 0.104969 + 0.298249i
\(71\) −9.44253 −1.12062 −0.560311 0.828282i \(-0.689319\pi\)
−0.560311 + 0.828282i \(0.689319\pi\)
\(72\) −3.12962 7.88704i −0.368830 0.929497i
\(73\) 0.422106 0.0494037 0.0247019 0.999695i \(-0.492136\pi\)
0.0247019 + 0.999695i \(0.492136\pi\)
\(74\) 0.891158 + 2.53205i 0.103595 + 0.294345i
\(75\) 0.850576 + 0.280686i 0.0982161 + 0.0324108i
\(76\) −0.901961 1.12265i −0.103462 0.128777i
\(77\) 2.56002i 0.291741i
\(78\) 0.322395 + 16.3891i 0.0365041 + 1.85570i
\(79\) 10.1253i 1.13918i −0.821928 0.569591i \(-0.807101\pi\)
0.821928 0.569591i \(-0.192899\pi\)
\(80\) 9.17478 + 2.02420i 1.02577 + 0.226313i
\(81\) 2.62375 + 8.60906i 0.291527 + 0.956562i
\(82\) −10.1897 + 3.58627i −1.12526 + 0.396037i
\(83\) −8.44270 −0.926706 −0.463353 0.886174i \(-0.653354\pi\)
−0.463353 + 0.886174i \(0.653354\pi\)
\(84\) −0.966862 2.58372i −0.105493 0.281907i
\(85\) −1.58682 −0.172114
\(86\) −14.7712 + 5.19874i −1.59282 + 0.560594i
\(87\) 1.04529 3.16760i 0.112067 0.339602i
\(88\) 7.72487 + 4.79546i 0.823473 + 0.511197i
\(89\) 11.2794i 1.19562i 0.801640 + 0.597808i \(0.203961\pi\)
−0.801640 + 0.597808i \(0.796039\pi\)
\(90\) −9.52299 2.93615i −1.00381 0.309498i
\(91\) 5.32939i 0.558672i
\(92\) 1.55913 1.25264i 0.162551 0.130597i
\(93\) 4.13368 12.5265i 0.428643 1.29894i
\(94\) −0.575627 1.63553i −0.0593714 0.168692i
\(95\) −1.69129 −0.173523
\(96\) −9.60753 1.92234i −0.980564 0.196198i
\(97\) −7.27066 −0.738224 −0.369112 0.929385i \(-0.620338\pi\)
−0.369112 + 0.929385i \(0.620338\pi\)
\(98\) 2.98877 + 8.49200i 0.301911 + 0.857821i
\(99\) −7.74974 5.73980i −0.778878 0.576871i
\(100\) 0.806271 0.647776i 0.0806271 0.0647776i
\(101\) 7.25596i 0.721995i −0.932567 0.360997i \(-0.882436\pi\)
0.932567 0.360997i \(-0.117564\pi\)
\(102\) 1.65448 0.0325458i 0.163818 0.00322251i
\(103\) 11.6113i 1.14410i 0.820219 + 0.572050i \(0.193852\pi\)
−0.820219 + 0.572050i \(0.806148\pi\)
\(104\) 16.0815 + 9.98308i 1.57692 + 0.978922i
\(105\) −3.07670 1.01530i −0.300255 0.0990828i
\(106\) 15.1288 5.32461i 1.46944 0.517172i
\(107\) 19.9682 1.93040 0.965198 0.261521i \(-0.0842240\pi\)
0.965198 + 0.261521i \(0.0842240\pi\)
\(108\) 9.98929 + 2.86604i 0.961219 + 0.275784i
\(109\) −14.8640 −1.42371 −0.711855 0.702327i \(-0.752145\pi\)
−0.711855 + 0.702327i \(0.752145\pi\)
\(110\) 10.0726 3.54507i 0.960386 0.338009i
\(111\) −3.12198 1.03024i −0.296325 0.0977859i
\(112\) −3.11066 0.686296i −0.293930 0.0648489i
\(113\) 11.7321i 1.10367i −0.833954 0.551834i \(-0.813928\pi\)
0.833954 0.551834i \(-0.186072\pi\)
\(114\) 1.76341 0.0346885i 0.165158 0.00324888i
\(115\) 2.34886i 0.219032i
\(116\) −2.41236 3.00261i −0.223982 0.278785i
\(117\) −16.1332 11.9490i −1.49152 1.10469i
\(118\) 0.0830878 + 0.236077i 0.00764885 + 0.0217327i
\(119\) 0.538002 0.0493185
\(120\) −8.82698 + 7.38210i −0.805790 + 0.673891i
\(121\) −0.666258 −0.0605689
\(122\) 3.15301 + 8.95866i 0.285460 + 0.811079i
\(123\) 4.14597 12.5637i 0.373829 1.13283i
\(124\) −9.53983 11.8740i −0.856702 1.06632i
\(125\) 10.5296i 0.941798i
\(126\) 3.22872 + 0.995487i 0.287637 + 0.0886851i
\(127\) 10.7727i 0.955926i −0.878380 0.477963i \(-0.841375\pi\)
0.878380 0.477963i \(-0.158625\pi\)
\(128\) −7.89784 + 8.10087i −0.698077 + 0.716023i
\(129\) 6.01009 18.2127i 0.529159 1.60354i
\(130\) 20.9690 7.38006i 1.83910 0.647274i
\(131\) 5.76563 0.503745 0.251873 0.967760i \(-0.418954\pi\)
0.251873 + 0.967760i \(0.418954\pi\)
\(132\) −10.4294 + 3.90283i −0.907765 + 0.339698i
\(133\) 0.573423 0.0497221
\(134\) −12.4960 + 4.39798i −1.07949 + 0.379927i
\(135\) 9.97179 7.03747i 0.858235 0.605689i
\(136\) 1.00779 1.62342i 0.0864175 0.139208i
\(137\) 14.4134i 1.23142i −0.787971 0.615712i \(-0.788868\pi\)
0.787971 0.615712i \(-0.211132\pi\)
\(138\) 0.0481753 + 2.44902i 0.00410096 + 0.208474i
\(139\) 11.6755i 0.990301i −0.868807 0.495150i \(-0.835113\pi\)
0.868807 0.495150i \(-0.164887\pi\)
\(140\) −2.91644 + 2.34313i −0.246484 + 0.198031i
\(141\) 2.01659 + 0.665464i 0.169827 + 0.0560421i
\(142\) −4.43331 12.5964i −0.372035 1.05706i
\(143\) 21.5126 1.79897
\(144\) 9.05197 7.87793i 0.754331 0.656494i
\(145\) −4.52347 −0.375654
\(146\) 0.198180 + 0.563091i 0.0164015 + 0.0466017i
\(147\) −10.4705 3.45522i −0.863593 0.284982i
\(148\) −2.95936 + 2.37762i −0.243258 + 0.195439i
\(149\) 15.0305i 1.23135i 0.788000 + 0.615675i \(0.211117\pi\)
−0.788000 + 0.615675i \(0.788883\pi\)
\(150\) 0.0249128 + 1.26645i 0.00203412 + 0.103406i
\(151\) 0.656832i 0.0534523i 0.999643 + 0.0267261i \(0.00850821\pi\)
−0.999643 + 0.0267261i \(0.991492\pi\)
\(152\) 1.07414 1.73031i 0.0871245 0.140346i
\(153\) −1.20625 + 1.62865i −0.0975196 + 0.131669i
\(154\) −3.41507 + 1.20194i −0.275194 + 0.0968549i
\(155\) −17.8884 −1.43683
\(156\) −21.7118 + 8.12483i −1.73833 + 0.650507i
\(157\) −13.6112 −1.08629 −0.543146 0.839638i \(-0.682767\pi\)
−0.543146 + 0.839638i \(0.682767\pi\)
\(158\) 13.5072 4.75386i 1.07457 0.378197i
\(159\) −6.15561 + 18.6536i −0.488172 + 1.47933i
\(160\) 1.60730 + 13.1896i 0.127069 + 1.04273i
\(161\) 0.796368i 0.0627626i
\(162\) −10.2527 + 7.54208i −0.805525 + 0.592562i
\(163\) 3.07465i 0.240825i 0.992724 + 0.120413i \(0.0384218\pi\)
−0.992724 + 0.120413i \(0.961578\pi\)
\(164\) −9.56818 11.9093i −0.747150 0.929959i
\(165\) −4.09834 + 12.4194i −0.319055 + 0.966848i
\(166\) −3.96388 11.2626i −0.307657 0.874146i
\(167\) 4.30533 0.333157 0.166578 0.986028i \(-0.446728\pi\)
0.166578 + 0.986028i \(0.446728\pi\)
\(168\) 2.99274 2.50286i 0.230895 0.193100i
\(169\) 31.7845 2.44496
\(170\) −0.745017 2.11682i −0.0571402 0.162353i
\(171\) −1.28567 + 1.73588i −0.0983175 + 0.132746i
\(172\) −13.8703 17.2640i −1.05760 1.31637i
\(173\) 5.68962i 0.432574i 0.976330 + 0.216287i \(0.0693947\pi\)
−0.976330 + 0.216287i \(0.930605\pi\)
\(174\) 4.71636 0.0927770i 0.357546 0.00703341i
\(175\) 0.411824i 0.0311310i
\(176\) −2.77030 + 12.5565i −0.208819 + 0.946481i
\(177\) −0.291080 0.0960551i −0.0218789 0.00721994i
\(178\) −15.0468 + 5.29573i −1.12780 + 0.396932i
\(179\) 21.1309 1.57939 0.789697 0.613497i \(-0.210238\pi\)
0.789697 + 0.613497i \(0.210238\pi\)
\(180\) −0.554247 14.0822i −0.0413111 1.04963i
\(181\) −12.7953 −0.951067 −0.475533 0.879698i \(-0.657745\pi\)
−0.475533 + 0.879698i \(0.657745\pi\)
\(182\) −7.10942 + 2.50217i −0.526986 + 0.185473i
\(183\) −11.0459 3.64509i −0.816536 0.269453i
\(184\) 2.40305 + 1.49177i 0.177155 + 0.109975i
\(185\) 4.45832i 0.327782i
\(186\) 18.6512 0.366893i 1.36757 0.0269019i
\(187\) 2.17169i 0.158810i
\(188\) 1.91154 1.53578i 0.139414 0.112008i
\(189\) −3.38088 + 2.38602i −0.245923 + 0.173557i
\(190\) −0.794067 2.25619i −0.0576077 0.163681i
\(191\) 8.07378 0.584198 0.292099 0.956388i \(-0.405646\pi\)
0.292099 + 0.956388i \(0.405646\pi\)
\(192\) −1.94636 13.7190i −0.140467 0.990085i
\(193\) 5.34117 0.384466 0.192233 0.981349i \(-0.438427\pi\)
0.192233 + 0.981349i \(0.438427\pi\)
\(194\) −3.41361 9.69909i −0.245083 0.696354i
\(195\) −8.53185 + 25.8544i −0.610978 + 1.85148i
\(196\) −9.92512 + 7.97406i −0.708937 + 0.569576i
\(197\) 1.19189i 0.0849186i −0.999098 0.0424593i \(-0.986481\pi\)
0.999098 0.0424593i \(-0.0135193\pi\)
\(198\) 4.01838 13.0330i 0.285574 0.926217i
\(199\) 24.2553i 1.71941i 0.510788 + 0.859707i \(0.329354\pi\)
−0.510788 + 0.859707i \(0.670646\pi\)
\(200\) 1.24268 + 0.771435i 0.0878709 + 0.0545487i
\(201\) 5.08436 15.4074i 0.358623 1.08675i
\(202\) 9.67948 3.40670i 0.681046 0.239695i
\(203\) 1.53366 0.107642
\(204\) 0.820202 + 2.19180i 0.0574256 + 0.153457i
\(205\) −17.9415 −1.25309
\(206\) −15.4896 + 5.45158i −1.07921 + 0.379829i
\(207\) −2.41078 1.78553i −0.167561 0.124103i
\(208\) −5.76715 + 26.1398i −0.399880 + 1.81247i
\(209\) 2.31467i 0.160109i
\(210\) −0.0901146 4.58102i −0.00621850 0.316120i
\(211\) 18.3549i 1.26361i 0.775129 + 0.631803i \(0.217685\pi\)
−0.775129 + 0.631803i \(0.782315\pi\)
\(212\) 14.2061 + 17.6820i 0.975679 + 1.21440i
\(213\) 15.5312 + 5.12521i 1.06418 + 0.351173i
\(214\) 9.37514 + 26.6376i 0.640871 + 1.82091i
\(215\) −26.0085 −1.77376
\(216\) 0.866709 + 14.6714i 0.0589721 + 0.998260i
\(217\) 6.06496 0.411716
\(218\) −6.97869 19.8286i −0.472657 1.34296i
\(219\) −0.694283 0.229110i −0.0469153 0.0154818i
\(220\) 9.45827 + 11.7725i 0.637677 + 0.793701i
\(221\) 4.52099i 0.304115i
\(222\) −0.0914408 4.64843i −0.00613710 0.311982i
\(223\) 26.3795i 1.76650i −0.468899 0.883252i \(-0.655349\pi\)
0.468899 0.883252i \(-0.344651\pi\)
\(224\) −0.544948 4.47186i −0.0364109 0.298788i
\(225\) −1.24668 0.923349i −0.0831122 0.0615566i
\(226\) 15.6507 5.50829i 1.04107 0.366406i
\(227\) −6.18899 −0.410778 −0.205389 0.978680i \(-0.565846\pi\)
−0.205389 + 0.978680i \(0.565846\pi\)
\(228\) 0.874202 + 2.33611i 0.0578955 + 0.154712i
\(229\) 5.28251 0.349078 0.174539 0.984650i \(-0.444156\pi\)
0.174539 + 0.984650i \(0.444156\pi\)
\(230\) 3.13338 1.10280i 0.206609 0.0727164i
\(231\) 1.38952 4.21073i 0.0914238 0.277046i
\(232\) 2.87287 4.62783i 0.188613 0.303832i
\(233\) 10.0481i 0.658272i −0.944283 0.329136i \(-0.893243\pi\)
0.944283 0.329136i \(-0.106757\pi\)
\(234\) 8.36538 27.1319i 0.546862 1.77367i
\(235\) 2.87977i 0.187856i
\(236\) −0.275918 + 0.221679i −0.0179607 + 0.0144301i
\(237\) −5.49579 + 16.6541i −0.356990 + 1.08180i
\(238\) 0.252594 + 0.717696i 0.0163732 + 0.0465214i
\(239\) 13.7376 0.888613 0.444307 0.895875i \(-0.353450\pi\)
0.444307 + 0.895875i \(0.353450\pi\)
\(240\) −13.9921 8.30930i −0.903183 0.536363i
\(241\) −14.6530 −0.943881 −0.471940 0.881631i \(-0.656446\pi\)
−0.471940 + 0.881631i \(0.656446\pi\)
\(242\) −0.312811 0.888791i −0.0201082 0.0571336i
\(243\) 0.357257 15.5844i 0.0229180 0.999737i
\(244\) −10.4705 + 8.41226i −0.670307 + 0.538540i
\(245\) 14.9523i 0.955270i
\(246\) 18.7066 0.367983i 1.19269 0.0234617i
\(247\) 4.81864i 0.306603i
\(248\) 11.3610 18.3011i 0.721422 1.16212i
\(249\) 13.8866 + 4.58252i 0.880028 + 0.290405i
\(250\) −14.0466 + 4.94370i −0.888382 + 0.312667i
\(251\) 0.497047 0.0313734 0.0156867 0.999877i \(-0.495007\pi\)
0.0156867 + 0.999877i \(0.495007\pi\)
\(252\) 0.187914 + 4.77451i 0.0118375 + 0.300766i
\(253\) 3.21461 0.202101
\(254\) 14.3709 5.05785i 0.901709 0.317358i
\(255\) 2.61001 + 0.861290i 0.163445 + 0.0539361i
\(256\) −14.5147 6.73235i −0.907166 0.420772i
\(257\) 15.6813i 0.978170i 0.872236 + 0.489085i \(0.162669\pi\)
−0.872236 + 0.489085i \(0.837331\pi\)
\(258\) 27.1175 0.533437i 1.68826 0.0332103i
\(259\) 1.51157i 0.0939245i
\(260\) 19.6900 + 24.5077i 1.22112 + 1.51990i
\(261\) −3.43861 + 4.64273i −0.212845 + 0.287378i
\(262\) 2.70699 + 7.69137i 0.167238 + 0.475174i
\(263\) −27.6024 −1.70204 −0.851018 0.525136i \(-0.824015\pi\)
−0.851018 + 0.525136i \(0.824015\pi\)
\(264\) −10.1030 12.0805i −0.621799 0.743503i
\(265\) 26.6382 1.63637
\(266\) 0.269224 + 0.764948i 0.0165072 + 0.0469020i
\(267\) 6.12222 18.5525i 0.374674 1.13539i
\(268\) −11.7338 14.6048i −0.716758 0.892131i
\(269\) 26.6429i 1.62444i 0.583348 + 0.812222i \(0.301742\pi\)
−0.583348 + 0.812222i \(0.698258\pi\)
\(270\) 14.0698 + 9.99828i 0.856261 + 0.608476i
\(271\) 3.04363i 0.184888i 0.995718 + 0.0924438i \(0.0294678\pi\)
−0.995718 + 0.0924438i \(0.970532\pi\)
\(272\) 2.63882 + 0.582194i 0.160002 + 0.0353007i
\(273\) 2.89268 8.76582i 0.175073 0.530531i
\(274\) 19.2276 6.76717i 1.16158 0.408820i
\(275\) 1.66237 0.100244
\(276\) −3.24438 + 1.21409i −0.195289 + 0.0730796i
\(277\) 0.169013 0.0101550 0.00507749 0.999987i \(-0.498384\pi\)
0.00507749 + 0.999987i \(0.498384\pi\)
\(278\) 15.5751 5.48168i 0.934134 0.328770i
\(279\) −13.5982 + 18.3600i −0.814104 + 1.09918i
\(280\) −4.49503 2.79043i −0.268629 0.166760i
\(281\) 4.21550i 0.251476i −0.992064 0.125738i \(-0.959870\pi\)
0.992064 0.125738i \(-0.0401298\pi\)
\(282\) 0.0590645 + 3.00257i 0.00351724 + 0.178800i
\(283\) 3.01367i 0.179144i 0.995980 + 0.0895719i \(0.0285499\pi\)
−0.995980 + 0.0895719i \(0.971450\pi\)
\(284\) 14.7222 11.8281i 0.873599 0.701869i
\(285\) 2.78184 + 0.917995i 0.164782 + 0.0543773i
\(286\) 10.1002 + 28.6979i 0.597240 + 1.69694i
\(287\) 6.08298 0.359067
\(288\) 14.7591 + 8.37665i 0.869690 + 0.493599i
\(289\) 16.5436 0.973153
\(290\) −2.12379 6.03433i −0.124713 0.354348i
\(291\) 11.9588 + 3.94636i 0.701039 + 0.231340i
\(292\) −0.658118 + 0.528747i −0.0385135 + 0.0309426i
\(293\) 9.32392i 0.544709i −0.962197 0.272355i \(-0.912198\pi\)
0.962197 0.272355i \(-0.0878023\pi\)
\(294\) −0.306675 15.5899i −0.0178856 0.909224i
\(295\) 0.415675i 0.0242015i
\(296\) −4.56118 2.83150i −0.265113 0.164577i
\(297\) 9.63138 + 13.6473i 0.558870 + 0.791894i
\(298\) −20.0508 + 7.05690i −1.16151 + 0.408795i
\(299\) 6.69212 0.387015
\(300\) −1.67776 + 0.627840i −0.0968654 + 0.0362483i
\(301\) 8.81804 0.508263
\(302\) −0.876217 + 0.308386i −0.0504206 + 0.0177456i
\(303\) −3.93838 + 11.9347i −0.226254 + 0.685628i
\(304\) 2.81255 + 0.620524i 0.161311 + 0.0355895i
\(305\) 15.7740i 0.903218i
\(306\) −2.73897 0.844485i −0.156576 0.0482760i
\(307\) 4.19690i 0.239529i −0.992802 0.119765i \(-0.961786\pi\)
0.992802 0.119765i \(-0.0382140\pi\)
\(308\) −3.20678 3.99140i −0.182723 0.227431i
\(309\) 6.30239 19.0984i 0.358530 1.08647i
\(310\) −8.39866 23.8631i −0.477012 1.35534i
\(311\) 1.57780 0.0894688 0.0447344 0.998999i \(-0.485756\pi\)
0.0447344 + 0.998999i \(0.485756\pi\)
\(312\) −21.0323 25.1489i −1.19072 1.42378i
\(313\) 7.02504 0.397079 0.198539 0.980093i \(-0.436380\pi\)
0.198539 + 0.980093i \(0.436380\pi\)
\(314\) −6.39052 18.1574i −0.360638 1.02468i
\(315\) 4.50950 + 3.33994i 0.254082 + 0.188184i
\(316\) 12.6833 + 15.7866i 0.713493 + 0.888068i
\(317\) 0.0798294i 0.00448367i −0.999997 0.00224183i \(-0.999286\pi\)
0.999997 0.00224183i \(-0.000713598\pi\)
\(318\) −27.7741 + 0.546353i −1.55749 + 0.0306380i
\(319\) 6.19076i 0.346616i
\(320\) −16.8403 + 8.33671i −0.941401 + 0.466036i
\(321\) −32.8438 10.8383i −1.83316 0.604935i
\(322\) −1.06236 + 0.373898i −0.0592029 + 0.0208365i
\(323\) −0.486442 −0.0270664
\(324\) −14.8748 10.1360i −0.826379 0.563114i
\(325\) 3.46068 0.191964
\(326\) −4.10160 + 1.44356i −0.227166 + 0.0799515i
\(327\) 24.4484 + 8.06784i 1.35200 + 0.446153i
\(328\) 11.3947 18.3555i 0.629169 1.01351i
\(329\) 0.976372i 0.0538291i
\(330\) −18.4917 + 0.363756i −1.01793 + 0.0200241i
\(331\) 29.4692i 1.61977i −0.586588 0.809886i \(-0.699529\pi\)
0.586588 0.809886i \(-0.300471\pi\)
\(332\) 13.1633 10.5757i 0.722429 0.580415i
\(333\) 4.57586 + 3.38909i 0.250756 + 0.185721i
\(334\) 2.02137 + 5.74333i 0.110605 + 0.314261i
\(335\) −22.0024 −1.20212
\(336\) 4.74394 + 2.81723i 0.258803 + 0.153692i
\(337\) −12.3468 −0.672575 −0.336287 0.941759i \(-0.609171\pi\)
−0.336287 + 0.941759i \(0.609171\pi\)
\(338\) 14.9229 + 42.4006i 0.811701 + 2.30629i
\(339\) −6.36796 + 19.2971i −0.345860 + 1.04808i
\(340\) 2.47405 1.98771i 0.134174 0.107799i
\(341\) 24.4818i 1.32576i
\(342\) −2.91929 0.900084i −0.157857 0.0486710i
\(343\) 10.6441i 0.574727i
\(344\) 16.5181 26.6085i 0.890595 1.43463i
\(345\) −1.27491 + 3.86342i −0.0686388 + 0.207999i
\(346\) −7.58998 + 2.67130i −0.408040 + 0.143610i
\(347\) 17.0322 0.914339 0.457169 0.889380i \(-0.348863\pi\)
0.457169 + 0.889380i \(0.348863\pi\)
\(348\) 2.33812 + 6.24808i 0.125336 + 0.334932i
\(349\) 18.1974 0.974082 0.487041 0.873379i \(-0.338076\pi\)
0.487041 + 0.873379i \(0.338076\pi\)
\(350\) −0.549375 + 0.193353i −0.0293653 + 0.0103352i
\(351\) 20.0504 + 28.4106i 1.07021 + 1.51644i
\(352\) −18.0511 + 2.19974i −0.962125 + 0.117246i
\(353\) 9.37154i 0.498797i 0.968401 + 0.249398i \(0.0802329\pi\)
−0.968401 + 0.249398i \(0.919767\pi\)
\(354\) −0.00852555 0.433400i −0.000453128 0.0230350i
\(355\) 22.1792i 1.17715i
\(356\) −14.1290 17.5861i −0.748838 0.932061i
\(357\) −0.884909 0.292016i −0.0468344 0.0154551i
\(358\) 9.92103 + 28.1886i 0.524343 + 1.48982i
\(359\) −34.0837 −1.79887 −0.899434 0.437057i \(-0.856021\pi\)
−0.899434 + 0.437057i \(0.856021\pi\)
\(360\) 18.5255 7.35104i 0.976381 0.387434i
\(361\) 18.4815 0.972712
\(362\) −6.00745 17.0690i −0.315744 0.897125i
\(363\) 1.09587 + 0.361631i 0.0575180 + 0.0189807i
\(364\) −6.67581 8.30922i −0.349908 0.435521i
\(365\) 0.991466i 0.0518957i
\(366\) −0.323527 16.4467i −0.0169110 0.859680i
\(367\) 31.6260i 1.65086i 0.564502 + 0.825432i \(0.309068\pi\)
−0.564502 + 0.825432i \(0.690932\pi\)
\(368\) −0.861782 + 3.90606i −0.0449235 + 0.203618i
\(369\) −13.6386 + 18.4145i −0.709999 + 0.958623i
\(370\) −5.94742 + 2.09320i −0.309192 + 0.108820i
\(371\) −9.03155 −0.468895
\(372\) 9.24623 + 24.7084i 0.479395 + 1.28107i
\(373\) −10.5471 −0.546110 −0.273055 0.961998i \(-0.588034\pi\)
−0.273055 + 0.961998i \(0.588034\pi\)
\(374\) 2.89705 1.01962i 0.149803 0.0527233i
\(375\) 5.71525 17.3192i 0.295134 0.894360i
\(376\) 2.94621 + 1.82895i 0.151939 + 0.0943211i
\(377\) 12.8878i 0.663756i
\(378\) −4.77029 3.38987i −0.245357 0.174356i
\(379\) 11.3796i 0.584531i 0.956337 + 0.292265i \(0.0944091\pi\)
−0.956337 + 0.292265i \(0.905591\pi\)
\(380\) 2.63694 2.11858i 0.135272 0.108681i
\(381\) −5.84721 + 17.7191i −0.299562 + 0.907776i
\(382\) 3.79068 + 10.7705i 0.193948 + 0.551065i
\(383\) −15.0762 −0.770360 −0.385180 0.922842i \(-0.625861\pi\)
−0.385180 + 0.922842i \(0.625861\pi\)
\(384\) 17.3874 9.03760i 0.887297 0.461198i
\(385\) −6.01311 −0.306456
\(386\) 2.50770 + 7.12514i 0.127639 + 0.362660i
\(387\) −19.7709 + 26.6942i −1.00501 + 1.35694i
\(388\) 11.3359 9.10753i 0.575494 0.462365i
\(389\) 9.20298i 0.466610i 0.972404 + 0.233305i \(0.0749540\pi\)
−0.972404 + 0.233305i \(0.925046\pi\)
\(390\) −38.4957 + 0.757260i −1.94930 + 0.0383454i
\(391\) 0.675569i 0.0341650i
\(392\) −15.2973 9.49629i −0.772631 0.479635i
\(393\) −9.48335 3.12946i −0.478372 0.157860i
\(394\) 1.58998 0.559597i 0.0801023 0.0281921i
\(395\) 23.7828 1.19664
\(396\) 19.2728 0.758534i 0.968493 0.0381178i
\(397\) −28.5280 −1.43178 −0.715890 0.698214i \(-0.753979\pi\)
−0.715890 + 0.698214i \(0.753979\pi\)
\(398\) −32.3567 + 11.3880i −1.62189 + 0.570827i
\(399\) −0.943170 0.311242i −0.0472176 0.0155816i
\(400\) −0.445652 + 2.01993i −0.0222826 + 0.100997i
\(401\) 5.92896i 0.296078i −0.988982 0.148039i \(-0.952704\pi\)
0.988982 0.148039i \(-0.0472961\pi\)
\(402\) 22.9406 0.451272i 1.14417 0.0225074i
\(403\) 50.9657i 2.53878i
\(404\) 9.08911 + 11.3130i 0.452200 + 0.562843i
\(405\) −20.2215 + 6.16281i −1.00481 + 0.306232i
\(406\) 0.720060 + 2.04591i 0.0357360 + 0.101537i
\(407\) −6.10160 −0.302445
\(408\) −2.53878 + 2.12321i −0.125689 + 0.105115i
\(409\) 1.37988 0.0682306 0.0341153 0.999418i \(-0.489139\pi\)
0.0341153 + 0.999418i \(0.489139\pi\)
\(410\) −8.42362 23.9341i −0.416013 1.18202i
\(411\) −7.82331 + 23.7073i −0.385895 + 1.16940i
\(412\) −14.5448 18.1036i −0.716573 0.891901i
\(413\) 0.140933i 0.00693484i
\(414\) 1.25003 4.05431i 0.0614358 0.199258i
\(415\) 19.8307i 0.973450i
\(416\) −37.5783 + 4.57937i −1.84243 + 0.224522i
\(417\) −6.33720 + 19.2039i −0.310334 + 0.940419i
\(418\) 3.08778 1.08675i 0.151028 0.0531547i
\(419\) −15.3755 −0.751144 −0.375572 0.926793i \(-0.622554\pi\)
−0.375572 + 0.926793i \(0.622554\pi\)
\(420\) 6.06878 2.27102i 0.296126 0.110814i
\(421\) 25.5241 1.24397 0.621984 0.783030i \(-0.286327\pi\)
0.621984 + 0.783030i \(0.286327\pi\)
\(422\) −24.4855 + 8.61772i −1.19194 + 0.419504i
\(423\) −2.95569 2.18912i −0.143711 0.106439i
\(424\) −16.9180 + 27.2528i −0.821612 + 1.32351i
\(425\) 0.349356i 0.0169463i
\(426\) 0.454897 + 23.1249i 0.0220398 + 1.12041i
\(427\) 5.34810i 0.258813i
\(428\) −31.1330 + 25.0129i −1.50487 + 1.20905i
\(429\) −35.3841 11.6766i −1.70836 0.563750i
\(430\) −12.2111 34.6954i −0.588871 1.67316i
\(431\) −17.1182 −0.824556 −0.412278 0.911058i \(-0.635267\pi\)
−0.412278 + 0.911058i \(0.635267\pi\)
\(432\) −19.1647 + 8.04446i −0.922063 + 0.387039i
\(433\) −31.8725 −1.53169 −0.765846 0.643024i \(-0.777680\pi\)
−0.765846 + 0.643024i \(0.777680\pi\)
\(434\) 2.84752 + 8.09068i 0.136685 + 0.388365i
\(435\) 7.44024 + 2.45524i 0.356732 + 0.117720i
\(436\) 23.1749 18.6192i 1.10988 0.891698i
\(437\) 0.720048i 0.0344445i
\(438\) −0.0203351 1.03374i −0.000971648 0.0493942i
\(439\) 9.98392i 0.476507i 0.971203 + 0.238253i \(0.0765748\pi\)
−0.971203 + 0.238253i \(0.923425\pi\)
\(440\) −11.2638 + 18.1446i −0.536982 + 0.865010i
\(441\) 15.3466 + 11.3663i 0.730788 + 0.541254i
\(442\) 6.03102 2.12262i 0.286866 0.100963i
\(443\) 39.5217 1.87773 0.938866 0.344284i \(-0.111878\pi\)
0.938866 + 0.344284i \(0.111878\pi\)
\(444\) 6.15810 2.30444i 0.292250 0.109364i
\(445\) −26.4937 −1.25592
\(446\) 35.1904 12.3853i 1.66631 0.586461i
\(447\) 8.15826 24.7223i 0.385872 1.16933i
\(448\) 5.70962 2.82652i 0.269754 0.133540i
\(449\) 22.2438i 1.04975i 0.851180 + 0.524875i \(0.175888\pi\)
−0.851180 + 0.524875i \(0.824112\pi\)
\(450\) 0.646428 2.09660i 0.0304729 0.0988345i
\(451\) 24.5545i 1.15623i
\(452\) 14.6962 + 18.2920i 0.691249 + 0.860381i
\(453\) 0.356515 1.08036i 0.0167505 0.0507599i
\(454\) −2.90576 8.25614i −0.136374 0.387480i
\(455\) −12.5180 −0.586852
\(456\) −2.70593 + 2.26300i −0.126717 + 0.105975i
\(457\) 12.2420 0.572657 0.286329 0.958131i \(-0.407565\pi\)
0.286329 + 0.958131i \(0.407565\pi\)
\(458\) 2.48016 + 7.04689i 0.115890 + 0.329280i
\(459\) 2.86805 2.02409i 0.133869 0.0944764i
\(460\) 2.94227 + 3.66218i 0.137184 + 0.170750i
\(461\) 25.1325i 1.17054i −0.810840 0.585268i \(-0.800989\pi\)
0.810840 0.585268i \(-0.199011\pi\)
\(462\) 6.26952 0.123330i 0.291684 0.00573781i
\(463\) 22.2615i 1.03458i 0.855810 + 0.517290i \(0.173059\pi\)
−0.855810 + 0.517290i \(0.826941\pi\)
\(464\) 7.52237 + 1.65964i 0.349217 + 0.0770467i
\(465\) 29.4229 + 9.70942i 1.36445 + 0.450264i
\(466\) 13.4042 4.71762i 0.620937 0.218539i
\(467\) 10.3712 0.479921 0.239960 0.970783i \(-0.422866\pi\)
0.239960 + 0.970783i \(0.422866\pi\)
\(468\) 40.1217 1.57910i 1.85462 0.0729940i
\(469\) 7.45980 0.344462
\(470\) 3.84163 1.35206i 0.177201 0.0623661i
\(471\) 22.3878 + 7.38787i 1.03158 + 0.340415i
\(472\) −0.425265 0.263997i −0.0195744 0.0121514i
\(473\) 35.5949i 1.63665i
\(474\) −24.7970 + 0.487789i −1.13896 + 0.0224049i
\(475\) 0.372357i 0.0170849i
\(476\) −0.838816 + 0.673923i −0.0384471 + 0.0308892i
\(477\) 20.2496 27.3405i 0.927165 1.25184i
\(478\) 6.44988 + 18.3260i 0.295010 + 0.838214i
\(479\) 14.8914 0.680407 0.340203 0.940352i \(-0.389504\pi\)
0.340203 + 0.940352i \(0.389504\pi\)
\(480\) 4.51531 22.5667i 0.206095 1.03002i
\(481\) −12.7022 −0.579170
\(482\) −6.87963 19.5471i −0.313359 0.890347i
\(483\) 0.432251 1.30987i 0.0196681 0.0596012i
\(484\) 1.03878 0.834582i 0.0472174 0.0379355i
\(485\) 17.0777i 0.775460i
\(486\) 20.9573 6.84034i 0.950644 0.310284i
\(487\) 13.0830i 0.592848i −0.955056 0.296424i \(-0.904206\pi\)
0.955056 0.296424i \(-0.0957942\pi\)
\(488\) −16.1379 10.0181i −0.730530 0.453500i
\(489\) 1.66885 5.05721i 0.0754682 0.228695i
\(490\) −19.9465 + 7.02019i −0.901090 + 0.317140i
\(491\) 33.1384 1.49552 0.747758 0.663972i \(-0.231130\pi\)
0.747758 + 0.663972i \(0.231130\pi\)
\(492\) 9.27371 + 24.7819i 0.418091 + 1.11725i
\(493\) −1.30102 −0.0585952
\(494\) 6.42809 2.26237i 0.289213 0.101789i
\(495\) 13.4820 18.2030i 0.605969 0.818165i
\(496\) 29.7477 + 6.56314i 1.33571 + 0.294694i
\(497\) 7.51973i 0.337306i
\(498\) 0.406730 + 20.6763i 0.0182260 + 0.926527i
\(499\) 41.0462i 1.83748i 0.394865 + 0.918739i \(0.370791\pi\)
−0.394865 + 0.918739i \(0.629209\pi\)
\(500\) −13.1898 16.4171i −0.589867 0.734194i
\(501\) −7.08144 2.33684i −0.316376 0.104402i
\(502\) 0.233366 + 0.663063i 0.0104156 + 0.0295940i
\(503\) 15.3234 0.683239 0.341619 0.939838i \(-0.389025\pi\)
0.341619 + 0.939838i \(0.389025\pi\)
\(504\) −6.28099 + 2.49233i −0.279777 + 0.111017i
\(505\) 17.0432 0.758413
\(506\) 1.50927 + 4.28831i 0.0670954 + 0.190638i
\(507\) −52.2793 17.2519i −2.32181 0.766185i
\(508\) 13.4944 + 16.7961i 0.598716 + 0.745207i
\(509\) 15.9280i 0.705996i −0.935624 0.352998i \(-0.885162\pi\)
0.935624 0.352998i \(-0.114838\pi\)
\(510\) 0.0764454 + 3.88614i 0.00338506 + 0.172081i
\(511\) 0.336151i 0.0148705i
\(512\) 2.16629 22.5235i 0.0957374 0.995407i
\(513\) 3.05687 2.15735i 0.134964 0.0952494i
\(514\) −20.9188 + 7.36241i −0.922691 + 0.324742i
\(515\) −27.2734 −1.20181
\(516\) 13.4434 + 35.9244i 0.591813 + 1.58148i
\(517\) 3.94122 0.173335
\(518\) 2.01644 0.709689i 0.0885974 0.0311820i
\(519\) 3.08821 9.35834i 0.135557 0.410785i
\(520\) −23.4488 + 37.7731i −1.02830 + 1.65646i
\(521\) 8.57243i 0.375565i 0.982211 + 0.187783i \(0.0601300\pi\)
−0.982211 + 0.187783i \(0.939870\pi\)
\(522\) −7.80786 2.40734i −0.341741 0.105366i
\(523\) 18.2693i 0.798860i −0.916764 0.399430i \(-0.869208\pi\)
0.916764 0.399430i \(-0.130792\pi\)
\(524\) −8.98937 + 7.22226i −0.392703 + 0.315506i
\(525\) 0.223529 0.677371i 0.00975562 0.0295629i
\(526\) −12.9594 36.8217i −0.565059 1.60550i
\(527\) −5.14498 −0.224119
\(528\) 11.3720 19.1493i 0.494903 0.833368i
\(529\) 1.00000 0.0434783
\(530\) 12.5068 + 35.5355i 0.543259 + 1.54356i
\(531\) 0.426634 + 0.315984i 0.0185143 + 0.0137125i
\(532\) −0.894042 + 0.718293i −0.0387616 + 0.0311419i
\(533\) 51.1172i 2.21413i
\(534\) 27.6235 0.543389i 1.19538 0.0235148i
\(535\) 46.9024i 2.02777i
\(536\) 13.9738 22.5100i 0.603576 0.972284i
\(537\) −34.7562 11.4694i −1.49984 0.494940i
\(538\) −35.5417 + 12.5089i −1.53231 + 0.539299i
\(539\) −20.4636 −0.881429
\(540\) −6.73191 + 23.4634i −0.289695 + 1.00970i
\(541\) −7.80032 −0.335362 −0.167681 0.985841i \(-0.553628\pi\)
−0.167681 + 0.985841i \(0.553628\pi\)
\(542\) −4.06022 + 1.42900i −0.174401 + 0.0613807i
\(543\) 21.0458 + 6.94501i 0.903162 + 0.298039i
\(544\) 0.462287 + 3.79353i 0.0198204 + 0.162646i
\(545\) 34.9133i 1.49552i
\(546\) 13.0518 0.256745i 0.558564 0.0109877i
\(547\) 8.69373i 0.371717i 0.982577 + 0.185859i \(0.0595066\pi\)
−0.982577 + 0.185859i \(0.940493\pi\)
\(548\) 18.0549 + 22.4725i 0.771266 + 0.959976i
\(549\) 16.1899 + 11.9910i 0.690968 + 0.511761i
\(550\) 0.780488 + 2.21760i 0.0332801 + 0.0945589i
\(551\) −1.38668 −0.0590746
\(552\) −3.14285 3.75799i −0.133769 0.159951i
\(553\) −8.06345 −0.342893
\(554\) 0.0793521 + 0.225463i 0.00337135 + 0.00957902i
\(555\) 2.41988 7.33308i 0.102718 0.311272i
\(556\) 14.6252 + 18.2036i 0.620246 + 0.772005i
\(557\) 15.8975i 0.673598i 0.941577 + 0.336799i \(0.109344\pi\)
−0.941577 + 0.336799i \(0.890656\pi\)
\(558\) −30.8767 9.51998i −1.30711 0.403013i
\(559\) 74.1007i 3.13412i
\(560\) 1.61201 7.30650i 0.0681199 0.308756i
\(561\) −1.17875 + 3.57202i −0.0497668 + 0.150811i
\(562\) 5.62349 1.97919i 0.237213 0.0834873i
\(563\) 22.2168 0.936325 0.468162 0.883642i \(-0.344916\pi\)
0.468162 + 0.883642i \(0.344916\pi\)
\(564\) −3.97771 + 1.48851i −0.167492 + 0.0626776i
\(565\) 27.5571 1.15934
\(566\) −4.02024 + 1.41493i −0.168983 + 0.0594739i
\(567\) 6.85598 2.08947i 0.287924 0.0877494i
\(568\) 22.6908 + 14.0861i 0.952087 + 0.591038i
\(569\) 2.61033i 0.109431i 0.998502 + 0.0547155i \(0.0174252\pi\)
−0.998502 + 0.0547155i \(0.982575\pi\)
\(570\) 0.0814784 + 4.14199i 0.00341276 + 0.173489i
\(571\) 17.4391i 0.729802i 0.931046 + 0.364901i \(0.118897\pi\)
−0.931046 + 0.364901i \(0.881103\pi\)
\(572\) −33.5409 + 26.9475i −1.40242 + 1.12673i
\(573\) −13.2798 4.38228i −0.554772 0.183072i
\(574\) 2.85599 + 8.11472i 0.119207 + 0.338702i
\(575\) 0.517128 0.0215657
\(576\) −4.24500 + 23.6216i −0.176875 + 0.984233i
\(577\) 31.5241 1.31237 0.656184 0.754601i \(-0.272170\pi\)
0.656184 + 0.754601i \(0.272170\pi\)
\(578\) 7.76729 + 22.0692i 0.323077 + 0.917959i
\(579\) −8.78520 2.89907i −0.365100 0.120481i
\(580\) 7.05269 5.66629i 0.292847 0.235280i
\(581\) 6.72349i 0.278937i
\(582\) 0.350267 + 17.8060i 0.0145190 + 0.738081i
\(583\) 36.4567i 1.50988i
\(584\) −1.01434 0.629684i −0.0419737 0.0260565i
\(585\) 28.0665 37.8947i 1.16041 1.56675i
\(586\) 12.4381 4.37762i 0.513815 0.180838i
\(587\) −1.18762 −0.0490183 −0.0245092 0.999700i \(-0.507802\pi\)
−0.0245092 + 0.999700i \(0.507802\pi\)
\(588\) 20.6531 7.72865i 0.851718 0.318724i
\(589\) −5.48372 −0.225953
\(590\) −0.554512 + 0.195161i −0.0228289 + 0.00803466i
\(591\) −0.646932 + 1.96043i −0.0266112 + 0.0806412i
\(592\) 1.63573 7.41403i 0.0672283 0.304715i
\(593\) 1.62727i 0.0668238i −0.999442 0.0334119i \(-0.989363\pi\)
0.999442 0.0334119i \(-0.0106373\pi\)
\(594\) −13.6835 + 19.2557i −0.561441 + 0.790073i
\(595\) 1.26369i 0.0518062i
\(596\) −18.8279 23.4346i −0.771220 0.959918i
\(597\) 13.1653 39.8953i 0.538818 1.63281i
\(598\) 3.14198 + 8.92731i 0.128485 + 0.365065i
\(599\) −6.10795 −0.249564 −0.124782 0.992184i \(-0.539823\pi\)
−0.124782 + 0.992184i \(0.539823\pi\)
\(600\) −1.62526 1.94336i −0.0663508 0.0793375i
\(601\) −31.6552 −1.29124 −0.645621 0.763658i \(-0.723401\pi\)
−0.645621 + 0.763658i \(0.723401\pi\)
\(602\) 4.14011 + 11.7633i 0.168738 + 0.479436i
\(603\) −16.7256 + 22.5825i −0.681118 + 0.919629i
\(604\) −0.822775 1.02409i −0.0334782 0.0416696i
\(605\) 1.56494i 0.0636240i
\(606\) −17.7700 + 0.349558i −0.721855 + 0.0141998i
\(607\) 16.3567i 0.663898i −0.943297 0.331949i \(-0.892294\pi\)
0.943297 0.331949i \(-0.107706\pi\)
\(608\) 0.492723 + 4.04329i 0.0199826 + 0.163977i
\(609\) −2.52258 0.832438i −0.102220 0.0337321i
\(610\) −21.0426 + 7.40597i −0.851990 + 0.299859i
\(611\) 8.20475 0.331929
\(612\) −0.159410 4.05028i −0.00644378 0.163723i
\(613\) 35.0612 1.41611 0.708054 0.706158i \(-0.249573\pi\)
0.708054 + 0.706158i \(0.249573\pi\)
\(614\) 5.59867 1.97046i 0.225944 0.0795213i
\(615\) 29.5104 + 9.73828i 1.18997 + 0.392685i
\(616\) 3.81895 6.15183i 0.153870 0.247864i
\(617\) 30.9142i 1.24456i 0.782795 + 0.622279i \(0.213793\pi\)
−0.782795 + 0.622279i \(0.786207\pi\)
\(618\) 28.4364 0.559381i 1.14388 0.0225016i
\(619\) 31.1753i 1.25304i 0.779405 + 0.626520i \(0.215521\pi\)
−0.779405 + 0.626520i \(0.784479\pi\)
\(620\) 27.8903 22.4077i 1.12010 0.899915i
\(621\) 2.99612 + 4.24538i 0.120230 + 0.170361i
\(622\) 0.740784 + 2.10479i 0.0297027 + 0.0843944i
\(623\) 8.98256 0.359879
\(624\) 23.6740 39.8647i 0.947719 1.59587i
\(625\) −27.3182 −1.09273
\(626\) 3.29829 + 9.37143i 0.131826 + 0.374558i
\(627\) −1.25636 + 3.80719i −0.0501740 + 0.152045i
\(628\) 21.2216 17.0499i 0.846836 0.680367i
\(629\) 1.28229i 0.0511281i
\(630\) −2.33826 + 7.58380i −0.0931584 + 0.302146i
\(631\) 29.0712i 1.15731i −0.815574 0.578653i \(-0.803578\pi\)
0.815574 0.578653i \(-0.196422\pi\)
\(632\) −15.1046 + 24.3315i −0.600827 + 0.967856i
\(633\) 9.96266 30.1903i 0.395980 1.19996i
\(634\) 0.106493 0.0374802i 0.00422937 0.00148853i
\(635\) 25.3036 1.00414
\(636\) −13.7689 36.7942i −0.545972 1.45899i
\(637\) −42.6007 −1.68790
\(638\) 8.25850 2.90659i 0.326957 0.115073i
\(639\) −22.7639 16.8600i −0.900526 0.666969i
\(640\) −19.0278 18.5509i −0.752139 0.733289i
\(641\) 1.69974i 0.0671358i −0.999436 0.0335679i \(-0.989313\pi\)
0.999436 0.0335679i \(-0.0106870\pi\)
\(642\) −0.961973 48.9024i −0.0379661 1.93002i
\(643\) 8.93016i 0.352171i 0.984375 + 0.176086i \(0.0563436\pi\)
−0.984375 + 0.176086i \(0.943656\pi\)
\(644\) −0.997563 1.24164i −0.0393095 0.0489276i
\(645\) 42.7789 + 14.1168i 1.68442 + 0.555850i
\(646\) −0.228387 0.648916i −0.00898575 0.0255312i
\(647\) −23.1977 −0.911997 −0.455999 0.889981i \(-0.650718\pi\)
−0.455999 + 0.889981i \(0.650718\pi\)
\(648\) 6.53773 24.6020i 0.256826 0.966458i
\(649\) −0.568887 −0.0223308
\(650\) 1.62481 + 4.61656i 0.0637301 + 0.181077i
\(651\) −9.97569 3.29193i −0.390978 0.129021i
\(652\) −3.85143 4.79379i −0.150834 0.187739i
\(653\) 18.6140i 0.728422i 0.931317 + 0.364211i \(0.118661\pi\)
−0.931317 + 0.364211i \(0.881339\pi\)
\(654\) 0.716076 + 36.4021i 0.0280008 + 1.42343i
\(655\) 13.5426i 0.529154i
\(656\) 29.8361 + 6.58265i 1.16490 + 0.257009i
\(657\) 1.01761 + 0.753684i 0.0397006 + 0.0294040i
\(658\) −1.30248 + 0.458411i −0.0507761 + 0.0178707i
\(659\) −9.00688 −0.350858 −0.175429 0.984492i \(-0.556131\pi\)
−0.175429 + 0.984492i \(0.556131\pi\)
\(660\) −9.16719 24.4972i −0.356832 0.953553i
\(661\) 7.53200 0.292961 0.146480 0.989214i \(-0.453205\pi\)
0.146480 + 0.989214i \(0.453205\pi\)
\(662\) 39.3120 13.8359i 1.52790 0.537747i
\(663\) −2.45390 + 7.43616i −0.0953015 + 0.288797i
\(664\) 20.2882 + 12.5945i 0.787334 + 0.488763i
\(665\) 1.34689i 0.0522301i
\(666\) −2.37267 + 7.69541i −0.0919390 + 0.298191i
\(667\) 1.92582i 0.0745680i
\(668\) −6.71258 + 5.39304i −0.259718 + 0.208663i
\(669\) −14.3182 + 43.3892i −0.553575 + 1.67752i
\(670\) −10.3302 29.3513i −0.399091 1.13394i
\(671\) −21.5881 −0.833400
\(672\) −1.53089 + 7.65113i −0.0590555 + 0.295149i
\(673\) −18.3835 −0.708633 −0.354316 0.935126i \(-0.615286\pi\)
−0.354316 + 0.935126i \(0.615286\pi\)
\(674\) −5.79689 16.4707i −0.223288 0.634428i
\(675\) 1.54938 + 2.19540i 0.0596357 + 0.0845011i
\(676\) −49.5562 + 39.8145i −1.90601 + 1.53133i
\(677\) 39.7266i 1.52682i 0.645915 + 0.763409i \(0.276476\pi\)
−0.645915 + 0.763409i \(0.723524\pi\)
\(678\) −28.7322 + 0.565200i −1.10345 + 0.0217064i
\(679\) 5.79012i 0.222204i
\(680\) 3.81319 + 2.36716i 0.146229 + 0.0907764i
\(681\) 10.1797 + 3.35925i 0.390087 + 0.128727i
\(682\) 32.6588 11.4943i 1.25057 0.440139i
\(683\) 1.64291 0.0628641 0.0314320 0.999506i \(-0.489993\pi\)
0.0314320 + 0.999506i \(0.489993\pi\)
\(684\) −0.169906 4.31694i −0.00649650 0.165062i
\(685\) 33.8551 1.29354
\(686\) 14.1993 4.99745i 0.542130 0.190803i
\(687\) −8.68871 2.86723i −0.331495 0.109392i
\(688\) 43.2512 + 9.54237i 1.64893 + 0.363799i
\(689\) 75.8948i 2.89136i
\(690\) −5.75239 + 0.113157i −0.218990 + 0.00430781i
\(691\) 43.5396i 1.65632i −0.560489 0.828162i \(-0.689387\pi\)
0.560489 0.828162i \(-0.310613\pi\)
\(692\) −7.12706 8.87087i −0.270930 0.337220i
\(693\) −4.57099 + 6.17164i −0.173638 + 0.234441i
\(694\) 7.99671 + 22.7211i 0.303551 + 0.862480i
\(695\) 27.4240 1.04025
\(696\) −7.23721 + 6.05256i −0.274326 + 0.229422i
\(697\) −5.16028 −0.195459
\(698\) 8.54373 + 24.2753i 0.323385 + 0.918835i
\(699\) −5.45388 + 16.5272i −0.206285 + 0.625115i
\(700\) −0.515868 0.642088i −0.0194980 0.0242686i
\(701\) 40.8332i 1.54225i −0.636684 0.771125i \(-0.719695\pi\)
0.636684 0.771125i \(-0.280305\pi\)
\(702\) −28.4861 + 40.0862i −1.07514 + 1.51296i
\(703\) 1.36671i 0.0515464i
\(704\) −11.4095 23.0474i −0.430012 0.868632i
\(705\) −1.56308 + 4.73667i −0.0588689 + 0.178393i
\(706\) −12.5017 + 4.39998i −0.470507 + 0.165595i
\(707\) −5.77841 −0.217320
\(708\) 0.574155 0.214856i 0.0215781 0.00807480i
\(709\) 6.73893 0.253086 0.126543 0.991961i \(-0.459612\pi\)
0.126543 + 0.991961i \(0.459612\pi\)
\(710\) 29.5871 10.4132i 1.11038 0.390801i
\(711\) 18.0790 24.4098i 0.678016 0.915441i
\(712\) 16.8263 27.1049i 0.630591 1.01580i
\(713\) 7.61577i 0.285213i
\(714\) −0.0259184 1.31758i −0.000969973 0.0493090i
\(715\) 50.5300i 1.88971i
\(716\) −32.9458 + 26.4694i −1.23124 + 0.989207i
\(717\) −22.5958 7.45649i −0.843854 0.278468i
\(718\) −16.0024 45.4678i −0.597205 1.69684i
\(719\) 16.1780 0.603339 0.301670 0.953413i \(-0.402456\pi\)
0.301670 + 0.953413i \(0.402456\pi\)
\(720\) 18.5041 + 21.2618i 0.689608 + 0.792380i
\(721\) 9.24690 0.344373
\(722\) 8.67716 + 24.6544i 0.322930 + 0.917543i
\(723\) 24.1013 + 7.95332i 0.896337 + 0.295787i
\(724\) 19.9495 16.0279i 0.741419 0.595673i
\(725\) 0.995895i 0.0369866i
\(726\) 0.0320972 + 1.63168i 0.00119124 + 0.0605572i
\(727\) 17.7372i 0.657836i 0.944358 + 0.328918i \(0.106684\pi\)
−0.944358 + 0.328918i \(0.893316\pi\)
\(728\) 7.95021 12.8068i 0.294654 0.474650i
\(729\) −9.04648 + 25.4394i −0.335055 + 0.942199i
\(730\) −1.32262 + 0.465497i −0.0489523 + 0.0172288i
\(731\) −7.48046 −0.276675
\(732\) 21.7880 8.15336i 0.805308 0.301357i
\(733\) −21.9273 −0.809903 −0.404951 0.914338i \(-0.632712\pi\)
−0.404951 + 0.914338i \(0.632712\pi\)
\(734\) −42.1892 + 14.8485i −1.55723 + 0.548070i
\(735\) 8.11581 24.5937i 0.299356 0.907153i
\(736\) −5.61531 + 0.684292i −0.206983 + 0.0252233i
\(737\) 30.1122i 1.10920i
\(738\) −30.9685 9.54827i −1.13997 0.351477i
\(739\) 21.5215i 0.791682i 0.918319 + 0.395841i \(0.129547\pi\)
−0.918319 + 0.395841i \(0.870453\pi\)
\(740\) −5.58468 6.95111i −0.205297 0.255528i
\(741\) −2.61546 + 7.92574i −0.0960812 + 0.291159i
\(742\) −4.24035 12.0481i −0.155668 0.442300i
\(743\) 6.40397 0.234939 0.117469 0.993076i \(-0.462522\pi\)
0.117469 + 0.993076i \(0.462522\pi\)
\(744\) −28.6200 + 23.9352i −1.04926 + 0.877508i
\(745\) −35.3046 −1.29346
\(746\) −4.95192 14.0699i −0.181303 0.515136i
\(747\) −20.3535 15.0747i −0.744696 0.551555i
\(748\) 2.72035 + 3.38596i 0.0994660 + 0.123803i
\(749\) 15.9020i 0.581047i
\(750\) 25.7872 0.507268i 0.941616 0.0185228i
\(751\) 49.9030i 1.82099i 0.413525 + 0.910493i \(0.364297\pi\)
−0.413525 + 0.910493i \(0.635703\pi\)
\(752\) −1.05657 + 4.78896i −0.0385292 + 0.174635i
\(753\) −0.817547 0.269787i −0.0297931 0.00983158i
\(754\) 17.1924 6.05088i 0.626110 0.220360i
\(755\) −1.54281 −0.0561484
\(756\) 2.28242 7.95515i 0.0830108 0.289326i
\(757\) 29.0398 1.05547 0.527735 0.849409i \(-0.323041\pi\)
0.527735 + 0.849409i \(0.323041\pi\)
\(758\) −15.1804 + 5.34277i −0.551378 + 0.194058i
\(759\) −5.28742 1.74482i −0.191921 0.0633331i
\(760\) 4.06424 + 2.52301i 0.147426 + 0.0915191i
\(761\) 26.7922i 0.971216i 0.874177 + 0.485608i \(0.161402\pi\)
−0.874177 + 0.485608i \(0.838598\pi\)
\(762\) −26.3826 + 0.518981i −0.955741 + 0.0188007i
\(763\) 11.8372i 0.428535i
\(764\) −12.5881 + 10.1136i −0.455421 + 0.365895i
\(765\) −3.82547 2.83331i −0.138310 0.102439i
\(766\) −7.07836 20.1118i −0.255751 0.726667i
\(767\) −1.18430 −0.0427625
\(768\) 20.2196 + 18.9517i 0.729614 + 0.683860i
\(769\) −35.3787 −1.27579 −0.637894 0.770124i \(-0.720194\pi\)
−0.637894 + 0.770124i \(0.720194\pi\)
\(770\) −2.82318 8.02151i −0.101740 0.289075i
\(771\) 8.51145 25.7926i 0.306532 0.928899i
\(772\) −8.32759 + 6.69057i −0.299717 + 0.240799i
\(773\) 42.2942i 1.52122i 0.649211 + 0.760608i \(0.275099\pi\)
−0.649211 + 0.760608i \(0.724901\pi\)
\(774\) −44.8926 13.8414i −1.61363 0.497519i
\(775\) 3.93833i 0.141469i
\(776\) 17.4717 + 10.8461i 0.627199 + 0.389354i
\(777\) −0.820449 + 2.48624i −0.0294334 + 0.0891935i
\(778\) −12.2768 + 4.32084i −0.440145 + 0.154910i
\(779\) −5.50002 −0.197059
\(780\) −19.0841 50.9978i −0.683319 1.82601i
\(781\) 30.3541 1.08616
\(782\) 0.901212 0.317183i 0.0322273 0.0113424i
\(783\) 8.17583 5.76999i 0.292180 0.206203i
\(784\) 5.48593 24.8652i 0.195926 0.888043i
\(785\) 31.9708i 1.14109i
\(786\) −0.277761 14.1201i −0.00990741 0.503648i
\(787\) 1.09045i 0.0388705i 0.999811 + 0.0194352i \(0.00618682\pi\)
−0.999811 + 0.0194352i \(0.993813\pi\)
\(788\) 1.49301 + 1.85831i 0.0531862 + 0.0661996i
\(789\) 45.4006 + 14.9820i 1.61631 + 0.533373i
\(790\) 11.1661 + 31.7264i 0.397273 + 1.12877i
\(791\) −9.34310 −0.332202
\(792\) 10.0605 + 25.3538i 0.357485 + 0.900908i
\(793\) −44.9417 −1.59593
\(794\) −13.3940 38.0565i −0.475336 1.35057i
\(795\) −43.8147 14.4587i −1.55395 0.512796i
\(796\) −30.3832 37.8172i −1.07690 1.34040i
\(797\) 17.1558i 0.607688i 0.952722 + 0.303844i \(0.0982702\pi\)
−0.952722 + 0.303844i \(0.901730\pi\)
\(798\) −0.0276248 1.40432i −0.000977909 0.0497124i
\(799\) 0.828269i 0.0293021i
\(800\) −2.90384 + 0.353867i −0.102666 + 0.0125111i
\(801\) −20.1398 + 27.1922i −0.711603 + 0.960789i
\(802\) 7.90926 2.78367i 0.279286 0.0982949i
\(803\) −1.35691 −0.0478842
\(804\) 11.3727 + 30.3910i 0.401085 + 1.07181i
\(805\) −1.87055 −0.0659284
\(806\) 67.9884 23.9286i 2.39479 0.842849i
\(807\) 14.4612 43.8224i 0.509058 1.54262i
\(808\) −10.8242 + 17.4364i −0.380794 + 0.613411i
\(809\) 41.0217i 1.44225i −0.692806 0.721124i \(-0.743626\pi\)
0.692806 0.721124i \(-0.256374\pi\)
\(810\) −17.7153 24.0820i −0.622451 0.846156i
\(811\) 0.995583i 0.0349596i 0.999847 + 0.0174798i \(0.00556428\pi\)
−0.999847 + 0.0174798i \(0.994436\pi\)
\(812\) −2.39118 + 1.92113i −0.0839139 + 0.0674183i
\(813\) 1.65202 5.00619i 0.0579388 0.175575i
\(814\) −2.86473 8.13956i −0.100409 0.285291i
\(815\) −7.22192 −0.252973
\(816\) −4.02434 2.38989i −0.140880 0.0836629i
\(817\) −7.97296 −0.278939
\(818\) 0.647859 + 1.84076i 0.0226519 + 0.0643608i
\(819\) −9.51580 + 12.8480i −0.332509 + 0.448945i
\(820\) 27.9732 22.4743i 0.976867 0.784836i
\(821\) 1.60669i 0.0560738i −0.999607 0.0280369i \(-0.991074\pi\)
0.999607 0.0280369i \(-0.00892559\pi\)
\(822\) −35.2988 + 0.694373i −1.23119 + 0.0242190i
\(823\) 19.6188i 0.683869i 0.939724 + 0.341934i \(0.111082\pi\)
−0.939724 + 0.341934i \(0.888918\pi\)
\(824\) 17.3214 27.9026i 0.603420 0.972033i
\(825\) −2.73427 0.902297i −0.0951952 0.0314140i
\(826\) 0.188005 0.0661684i 0.00654151 0.00230229i
\(827\) −22.2783 −0.774694 −0.387347 0.921934i \(-0.626608\pi\)
−0.387347 + 0.921934i \(0.626608\pi\)
\(828\) 5.99536 0.235964i 0.208353 0.00820033i
\(829\) 37.8163 1.31341 0.656707 0.754146i \(-0.271949\pi\)
0.656707 + 0.754146i \(0.271949\pi\)
\(830\) 26.4542 9.31059i 0.918239 0.323175i
\(831\) −0.277993 0.0917364i −0.00964347 0.00318230i
\(832\) −23.7521 47.9796i −0.823455 1.66339i
\(833\) 4.30054i 0.149005i
\(834\) −28.5934 + 0.562470i −0.990109 + 0.0194767i
\(835\) 10.1126i 0.349961i
\(836\) 2.89946 + 3.60888i 0.100280 + 0.124816i
\(837\) 32.3318 22.8178i 1.11755 0.788699i
\(838\) −7.21888 20.5110i −0.249372 0.708541i
\(839\) 9.88894 0.341404 0.170702 0.985323i \(-0.445396\pi\)
0.170702 + 0.985323i \(0.445396\pi\)
\(840\) 5.87887 + 7.02953i 0.202840 + 0.242542i
\(841\) 25.2912 0.872111
\(842\) 11.9837 + 34.0492i 0.412985 + 1.17341i
\(843\) −2.28808 + 6.93368i −0.0788057 + 0.238809i
\(844\) −22.9921 28.6178i −0.791422 0.985064i
\(845\) 74.6572i 2.56828i
\(846\) 1.53258 4.97071i 0.0526912 0.170896i
\(847\) 0.530586i 0.0182312i
\(848\) −44.2984 9.77341i −1.52121 0.335620i
\(849\) 1.63575 4.95690i 0.0561389 0.170120i
\(850\) 0.466042 0.164024i 0.0159851 0.00562598i
\(851\) −1.89808 −0.0650654
\(852\) −30.6351 + 11.4641i −1.04954 + 0.392753i
\(853\) 18.9941 0.650345 0.325173 0.945655i \(-0.394578\pi\)
0.325173 + 0.945655i \(0.394578\pi\)
\(854\) 7.13439 2.51096i 0.244134 0.0859232i
\(855\) −4.07733 3.01985i −0.139442 0.103277i
\(856\) −47.9844 29.7879i −1.64007 1.01813i
\(857\) 31.1980i 1.06570i 0.846208 + 0.532852i \(0.178880\pi\)
−0.846208 + 0.532852i \(0.821120\pi\)
\(858\) −1.03638 52.6847i −0.0353813 1.79862i
\(859\) 30.5041i 1.04079i −0.853927 0.520393i \(-0.825786\pi\)
0.853927 0.520393i \(-0.174214\pi\)
\(860\) 40.5506 32.5793i 1.38277 1.11094i
\(861\) −10.0053 3.30171i −0.340981 0.112522i
\(862\) −8.03708 22.8358i −0.273744 0.777789i
\(863\) −36.1335 −1.23000 −0.614999 0.788528i \(-0.710843\pi\)
−0.614999 + 0.788528i \(0.710843\pi\)
\(864\) −19.7293 21.7889i −0.671203 0.741274i
\(865\) −13.3641 −0.454393
\(866\) −14.9643 42.5180i −0.508506 1.44482i
\(867\) −27.2110 8.97952i −0.924136 0.304960i
\(868\) −9.45607 + 7.59721i −0.320960 + 0.257866i
\(869\) 32.5489i 1.10414i
\(870\) 0.217920 + 11.0781i 0.00738818 + 0.375581i
\(871\) 62.6869i 2.12407i
\(872\) 35.7188 + 22.1736i 1.20959 + 0.750892i
\(873\) −17.5280 12.9820i −0.593232 0.439374i
\(874\) 0.960546 0.338065i 0.0324910 0.0114352i
\(875\) 8.38545 0.283480
\(876\) 1.36947 0.512474i 0.0462701 0.0173149i
\(877\) −29.8694 −1.00862 −0.504308 0.863524i \(-0.668252\pi\)
−0.504308 + 0.863524i \(0.668252\pi\)
\(878\) −13.3186 + 4.68749i −0.449481 + 0.158195i
\(879\) −5.06082 + 15.3360i −0.170697 + 0.517272i
\(880\) −29.4934 6.50703i −0.994222 0.219352i
\(881\) 18.4324i 0.621003i −0.950573 0.310501i \(-0.899503\pi\)
0.950573 0.310501i \(-0.100497\pi\)
\(882\) −7.95747 + 25.8089i −0.267942 + 0.869031i
\(883\) 30.3693i 1.02201i −0.859579 0.511003i \(-0.829274\pi\)
0.859579 0.511003i \(-0.170726\pi\)
\(884\) 5.66318 + 7.04882i 0.190473 + 0.237078i
\(885\) 0.225620 0.683706i 0.00758412 0.0229825i
\(886\) 18.5556 + 52.7221i 0.623387 + 1.77123i
\(887\) 26.0710 0.875377 0.437688 0.899127i \(-0.355797\pi\)
0.437688 + 0.899127i \(0.355797\pi\)
\(888\) 5.96539 + 7.13298i 0.200185 + 0.239367i
\(889\) −8.57907 −0.287733
\(890\) −12.4389 35.3427i −0.416953 1.18469i
\(891\) −8.43433 27.6748i −0.282561 0.927141i
\(892\) 33.0441 + 41.1291i 1.10640 + 1.37711i
\(893\) 0.882801i 0.0295418i
\(894\) 36.8100 0.724102i 1.23111 0.0242176i
\(895\) 49.6334i 1.65906i
\(896\) 6.45127 + 6.28959i 0.215522 + 0.210120i
\(897\) −11.0072 3.63234i −0.367521 0.121280i
\(898\) −29.6733 + 10.4436i −0.990211 + 0.348506i
\(899\) −14.6666 −0.489159
\(900\) 3.10037 0.122024i 0.103346 0.00406746i
\(901\) 7.66158 0.255244
\(902\) 32.7558 11.5285i 1.09065 0.383856i
\(903\) −14.5040 4.78624i −0.482662 0.159276i
\(904\) −17.5016 + 28.1929i −0.582095 + 0.937681i
\(905\) 30.0543i 0.999039i
\(906\) 1.60859 0.0316431i 0.0534419 0.00105127i
\(907\) 1.21466i 0.0403321i 0.999797 + 0.0201661i \(0.00641949\pi\)
−0.999797 + 0.0201661i \(0.993581\pi\)
\(908\) 9.64946 7.75259i 0.320228 0.257279i
\(909\) 12.9558 17.4925i 0.429715 0.580191i
\(910\) −5.87724 16.6990i −0.194829 0.553567i
\(911\) 27.8311 0.922085 0.461042 0.887378i \(-0.347476\pi\)
0.461042 + 0.887378i \(0.347476\pi\)
\(912\) −4.28930 2.54724i −0.142033 0.0843474i
\(913\) 27.1400 0.898203
\(914\) 5.74768 + 16.3309i 0.190116 + 0.540178i
\(915\) 8.56180 25.9452i 0.283044 0.857723i
\(916\) −8.23613 + 6.61709i −0.272129 + 0.218635i
\(917\) 4.59156i 0.151627i
\(918\) 4.04670 + 2.87567i 0.133561 + 0.0949112i
\(919\) 33.8802i 1.11760i −0.829301 0.558802i \(-0.811261\pi\)
0.829301 0.558802i \(-0.188739\pi\)
\(920\) −3.50395 + 5.64441i −0.115522 + 0.186091i
\(921\) −2.27799 + 6.90308i −0.0750622 + 0.227464i
\(922\) 33.5268 11.7998i 1.10415 0.388606i
\(923\) 63.1906 2.07994
\(924\) 3.10809 + 8.30566i 0.102249 + 0.273236i
\(925\) −0.981552 −0.0322732
\(926\) −29.6970 + 10.4519i −0.975902 + 0.343470i
\(927\) −20.7324 + 27.9924i −0.680942 + 0.919392i
\(928\) 1.31782 + 10.8141i 0.0432597 + 0.354989i
\(929\) 38.5389i 1.26442i 0.774798 + 0.632209i \(0.217852\pi\)
−0.774798 + 0.632209i \(0.782148\pi\)
\(930\) 0.861778 + 43.8089i 0.0282588 + 1.43655i
\(931\) 4.58368i 0.150224i
\(932\) 12.5866 + 15.6663i 0.412289 + 0.513166i
\(933\) −2.59518 0.856396i −0.0849623 0.0280372i
\(934\) 4.86931 + 13.8352i 0.159329 + 0.452701i
\(935\) 5.10100 0.166821
\(936\) 20.9438 + 52.7810i 0.684570 + 1.72520i
\(937\) 31.1633 1.01806 0.509031 0.860748i \(-0.330004\pi\)
0.509031 + 0.860748i \(0.330004\pi\)
\(938\) 3.50241 + 9.95140i 0.114358 + 0.324925i
\(939\) −11.5548 3.81304i −0.377078 0.124434i
\(940\) 3.60732 + 4.48994i 0.117658 + 0.146446i
\(941\) 39.0601i 1.27332i −0.771143 0.636662i \(-0.780315\pi\)
0.771143 0.636662i \(-0.219685\pi\)
\(942\) 0.655724 + 33.3340i 0.0213646 + 1.08608i
\(943\) 7.63841i 0.248741i
\(944\) 0.152509 0.691253i 0.00496374 0.0224984i
\(945\) −5.60441 7.94121i −0.182312 0.258328i
\(946\) 47.4837 16.7119i 1.54383 0.543352i
\(947\) 51.7977 1.68320 0.841599 0.540103i \(-0.181615\pi\)
0.841599 + 0.540103i \(0.181615\pi\)
\(948\) −12.2930 32.8502i −0.399258 1.06693i
\(949\) −2.82478 −0.0916963
\(950\) 0.496725 0.174823i 0.0161159 0.00567201i
\(951\) −0.0433297 + 0.131304i −0.00140506 + 0.00425782i
\(952\) −1.29284 0.802573i −0.0419013 0.0260116i
\(953\) 33.0339i 1.07007i 0.844829 + 0.535036i \(0.179702\pi\)
−0.844829 + 0.535036i \(0.820298\pi\)
\(954\) 45.9796 + 14.1765i 1.48864 + 0.458983i
\(955\) 18.9642i 0.613666i
\(956\) −21.4188 + 17.2083i −0.692733 + 0.556557i
\(957\) −3.36021 + 10.1826i −0.108620 + 0.329157i
\(958\) 6.99159 + 19.8652i 0.225888 + 0.641816i
\(959\) −11.4784 −0.370657
\(960\) 32.2240 4.57173i 1.04003 0.147552i
\(961\) −27.0000 −0.870968
\(962\) −5.96373 16.9448i −0.192278 0.546321i
\(963\) 48.1389 + 35.6538i 1.55125 + 1.14893i
\(964\) 22.8459 18.3549i 0.735817 0.591172i
\(965\) 12.5456i 0.403859i
\(966\) 1.95032 0.0383653i 0.0627504 0.00123438i
\(967\) 1.66263i 0.0534665i 0.999643 + 0.0267332i \(0.00851047\pi\)
−0.999643 + 0.0267332i \(0.991490\pi\)
\(968\) 1.60105 + 0.993902i 0.0514597 + 0.0319452i
\(969\) 0.800104 + 0.264030i 0.0257030 + 0.00848188i
\(970\) 22.7818 8.01807i 0.731479 0.257445i
\(971\) −48.4858 −1.55598 −0.777991 0.628275i \(-0.783761\pi\)
−0.777991 + 0.628275i \(0.783761\pi\)
\(972\) 18.9646 + 24.7456i 0.608290 + 0.793715i
\(973\) −9.29797 −0.298079
\(974\) 17.4528 6.14254i 0.559224 0.196820i
\(975\) −5.69216 1.87838i −0.182295 0.0601564i
\(976\) 5.78740 26.2316i 0.185250 0.839654i
\(977\) 39.7689i 1.27232i 0.771557 + 0.636160i \(0.219478\pi\)
−0.771557 + 0.636160i \(0.780522\pi\)
\(978\) 7.52987 0.148122i 0.240779 0.00473643i
\(979\) 36.2589i 1.15884i
\(980\) −18.7299 23.3127i −0.598305 0.744696i
\(981\) −35.8338 26.5401i −1.14408 0.847360i
\(982\) 15.5586 + 44.2068i 0.496496 + 1.41069i
\(983\) 11.2968 0.360313 0.180156 0.983638i \(-0.442340\pi\)
0.180156 + 0.983638i \(0.442340\pi\)
\(984\) −28.7051 + 24.0064i −0.915085 + 0.765295i
\(985\) 2.79958 0.0892019
\(986\) −0.610836 1.73557i −0.0194530 0.0552719i
\(987\) 0.529954 1.60594i 0.0168686 0.0511178i
\(988\) 6.03603 + 7.51290i 0.192032 + 0.239017i
\(989\) 11.0728i 0.352095i
\(990\) 30.6127 + 9.43859i 0.972936 + 0.299978i
\(991\) 9.26312i 0.294253i 0.989118 + 0.147126i \(0.0470024\pi\)
−0.989118 + 0.147126i \(0.952998\pi\)
\(992\) 5.21141 + 42.7650i 0.165463 + 1.35779i
\(993\) −15.9952 + 48.4711i −0.507593 + 1.53818i
\(994\) −10.0313 + 3.53055i −0.318175 + 0.111982i
\(995\) −56.9722 −1.80614
\(996\) −27.3913 + 10.2502i −0.867926 + 0.324790i
\(997\) −6.05016 −0.191610 −0.0958052 0.995400i \(-0.530543\pi\)
−0.0958052 + 0.995400i \(0.530543\pi\)
\(998\) −54.7557 + 19.2713i −1.73326 + 0.610024i
\(999\) −5.68689 8.05808i −0.179925 0.254946i
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 276.2.c.b.47.14 yes 22
3.2 odd 2 276.2.c.a.47.9 22
4.3 odd 2 276.2.c.a.47.10 yes 22
12.11 even 2 inner 276.2.c.b.47.13 yes 22
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
276.2.c.a.47.9 22 3.2 odd 2
276.2.c.a.47.10 yes 22 4.3 odd 2
276.2.c.b.47.13 yes 22 12.11 even 2 inner
276.2.c.b.47.14 yes 22 1.1 even 1 trivial