Properties

Label 280.2.h.b.251.3
Level $280$
Weight $2$
Character 280.251
Analytic conductor $2.236$
Analytic rank $0$
Dimension $16$
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] = [280,2,Mod(251,280)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(280, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1, 0, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("280.251");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 280.h (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: \(2.23581125660\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - x^{15} - 2x^{12} + 6x^{11} - 12x^{9} + 8x^{8} - 24x^{7} + 48x^{5} - 32x^{4} - 128x + 256 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{4} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 251.3
Root \(-1.24098 + 0.678208i\) of defining polynomial
Character \(\chi\) \(=\) 280.251
Dual form 280.2.h.b.251.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.24098 - 0.678208i) q^{2} +1.61069i q^{3} +(1.08007 + 1.68329i) q^{4} +1.00000 q^{5} +(1.09238 - 1.99883i) q^{6} +(2.13463 + 1.56312i) q^{7} +(-0.198727 - 2.82144i) q^{8} +0.405694 q^{9} +O(q^{10})\) \(q+(-1.24098 - 0.678208i) q^{2} +1.61069i q^{3} +(1.08007 + 1.68329i) q^{4} +1.00000 q^{5} +(1.09238 - 1.99883i) q^{6} +(2.13463 + 1.56312i) q^{7} +(-0.198727 - 2.82144i) q^{8} +0.405694 q^{9} +(-1.24098 - 0.678208i) q^{10} -6.01679 q^{11} +(-2.71124 + 1.73965i) q^{12} +4.25411 q^{13} +(-1.58892 - 3.38753i) q^{14} +1.61069i q^{15} +(-1.66690 + 3.63613i) q^{16} +5.42124i q^{17} +(-0.503458 - 0.275145i) q^{18} -4.53588i q^{19} +(1.08007 + 1.68329i) q^{20} +(-2.51769 + 3.43822i) q^{21} +(7.46673 + 4.08064i) q^{22} +5.19890i q^{23} +(4.54445 - 0.320086i) q^{24} +1.00000 q^{25} +(-5.27927 - 2.88517i) q^{26} +5.48550i q^{27} +(-0.325625 + 5.28147i) q^{28} +0.376818i q^{29} +(1.09238 - 1.99883i) q^{30} +2.93636 q^{31} +(4.53465 - 3.38186i) q^{32} -9.69116i q^{33} +(3.67672 - 6.72765i) q^{34} +(2.13463 + 1.56312i) q^{35} +(0.438177 + 0.682898i) q^{36} -0.372265i q^{37} +(-3.07627 + 5.62894i) q^{38} +6.85203i q^{39} +(-0.198727 - 2.82144i) q^{40} -5.75560i q^{41} +(5.45624 - 2.55925i) q^{42} -4.96515 q^{43} +(-6.49855 - 10.1280i) q^{44} +0.405694 q^{45} +(3.52593 - 6.45173i) q^{46} +3.86303 q^{47} +(-5.85666 - 2.68486i) q^{48} +(2.11332 + 6.67337i) q^{49} +(-1.24098 - 0.678208i) q^{50} -8.73190 q^{51} +(4.59473 + 7.16089i) q^{52} -10.2224i q^{53} +(3.72031 - 6.80740i) q^{54} -6.01679 q^{55} +(3.98603 - 6.33337i) q^{56} +7.30587 q^{57} +(0.255561 - 0.467624i) q^{58} +10.5835i q^{59} +(-2.71124 + 1.73965i) q^{60} -5.58001 q^{61} +(-3.64396 - 1.99146i) q^{62} +(0.866007 + 0.634147i) q^{63} +(-7.92102 + 1.12139i) q^{64} +4.25411 q^{65} +(-6.57262 + 12.0265i) q^{66} -0.782596 q^{67} +(-9.12549 + 5.85531i) q^{68} -8.37378 q^{69} +(-1.58892 - 3.38753i) q^{70} -15.3803i q^{71} +(-0.0806221 - 1.14464i) q^{72} -8.77164i q^{73} +(-0.252473 + 0.461974i) q^{74} +1.61069i q^{75} +(7.63518 - 4.89906i) q^{76} +(-12.8437 - 9.40496i) q^{77} +(4.64710 - 8.50324i) q^{78} -8.74609i q^{79} +(-1.66690 + 3.63613i) q^{80} -7.61833 q^{81} +(-3.90349 + 7.14259i) q^{82} -8.42742i q^{83} +(-8.50679 - 0.524480i) q^{84} +5.42124i q^{85} +(6.16165 + 3.36740i) q^{86} -0.606935 q^{87} +(1.19570 + 16.9760i) q^{88} -1.94765i q^{89} +(-0.503458 - 0.275145i) q^{90} +(9.08097 + 6.64968i) q^{91} +(-8.75123 + 5.61516i) q^{92} +4.72954i q^{93} +(-4.79395 - 2.61994i) q^{94} -4.53588i q^{95} +(5.44711 + 7.30389i) q^{96} -3.14377i q^{97} +(1.90334 - 9.71480i) q^{98} -2.44098 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + q^{2} + q^{4} + 16 q^{5} + q^{8} - 16 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + q^{2} + q^{4} + 16 q^{5} + q^{8} - 16 q^{9} + q^{10} - 4 q^{11} + 14 q^{12} - q^{14} + 9 q^{16} - 15 q^{18} + q^{20} - 4 q^{21} + 6 q^{22} + 22 q^{24} + 16 q^{25} - 20 q^{26} + q^{28} - 16 q^{31} - 19 q^{32} - 14 q^{34} + 15 q^{36} - 30 q^{38} + q^{40} + 44 q^{42} - 4 q^{43} - 20 q^{44} - 16 q^{45} + 6 q^{46} - 34 q^{48} - 8 q^{49} + q^{50} - 40 q^{51} - 38 q^{52} + 26 q^{54} - 4 q^{55} + 33 q^{56} - 16 q^{57} + 18 q^{58} + 14 q^{60} - 8 q^{61} + 28 q^{62} + 28 q^{63} - 23 q^{64} + 46 q^{66} + 20 q^{67} + 12 q^{68} - 40 q^{69} - q^{70} - 13 q^{72} - 28 q^{74} + 34 q^{76} - 4 q^{77} - 6 q^{78} + 9 q^{80} + 24 q^{81} - 16 q^{82} - 42 q^{84} - 24 q^{86} + 72 q^{87} - 44 q^{88} - 15 q^{90} - 32 q^{91} - 30 q^{92} - 58 q^{94} - 30 q^{96} + 5 q^{98} + 20 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/280\mathbb{Z}\right)^\times\).

\(n\) \(57\) \(71\) \(141\) \(241\)
\(\chi(n)\) \(1\) \(-1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.24098 0.678208i −0.877506 0.479565i
\(3\) 1.61069i 0.929929i 0.885329 + 0.464965i \(0.153933\pi\)
−0.885329 + 0.464965i \(0.846067\pi\)
\(4\) 1.08007 + 1.68329i 0.540034 + 0.841643i
\(5\) 1.00000 0.447214
\(6\) 1.09238 1.99883i 0.445962 0.816019i
\(7\) 2.13463 + 1.56312i 0.806816 + 0.590803i
\(8\) −0.198727 2.82144i −0.0702605 0.997529i
\(9\) 0.405694 0.135231
\(10\) −1.24098 0.678208i −0.392433 0.214468i
\(11\) −6.01679 −1.81413 −0.907066 0.420989i \(-0.861683\pi\)
−0.907066 + 0.420989i \(0.861683\pi\)
\(12\) −2.71124 + 1.73965i −0.782669 + 0.502194i
\(13\) 4.25411 1.17988 0.589939 0.807448i \(-0.299152\pi\)
0.589939 + 0.807448i \(0.299152\pi\)
\(14\) −1.58892 3.38753i −0.424657 0.905354i
\(15\) 1.61069i 0.415877i
\(16\) −1.66690 + 3.63613i −0.416726 + 0.909032i
\(17\) 5.42124i 1.31484i 0.753523 + 0.657421i \(0.228353\pi\)
−0.753523 + 0.657421i \(0.771647\pi\)
\(18\) −0.503458 0.275145i −0.118666 0.0648522i
\(19\) 4.53588i 1.04060i −0.853983 0.520301i \(-0.825820\pi\)
0.853983 0.520301i \(-0.174180\pi\)
\(20\) 1.08007 + 1.68329i 0.241511 + 0.376394i
\(21\) −2.51769 + 3.43822i −0.549405 + 0.750282i
\(22\) 7.46673 + 4.08064i 1.59191 + 0.869995i
\(23\) 5.19890i 1.08404i 0.840364 + 0.542022i \(0.182341\pi\)
−0.840364 + 0.542022i \(0.817659\pi\)
\(24\) 4.54445 0.320086i 0.927631 0.0653373i
\(25\) 1.00000 0.200000
\(26\) −5.27927 2.88517i −1.03535 0.565829i
\(27\) 5.48550i 1.05568i
\(28\) −0.325625 + 5.28147i −0.0615374 + 0.998105i
\(29\) 0.376818i 0.0699733i 0.999388 + 0.0349866i \(0.0111389\pi\)
−0.999388 + 0.0349866i \(0.988861\pi\)
\(30\) 1.09238 1.99883i 0.199440 0.364935i
\(31\) 2.93636 0.527385 0.263693 0.964607i \(-0.415060\pi\)
0.263693 + 0.964607i \(0.415060\pi\)
\(32\) 4.53465 3.38186i 0.801620 0.597834i
\(33\) 9.69116i 1.68701i
\(34\) 3.67672 6.72765i 0.630553 1.15378i
\(35\) 2.13463 + 1.56312i 0.360819 + 0.264215i
\(36\) 0.438177 + 0.682898i 0.0730295 + 0.113816i
\(37\) 0.372265i 0.0612000i −0.999532 0.0306000i \(-0.990258\pi\)
0.999532 0.0306000i \(-0.00974181\pi\)
\(38\) −3.07627 + 5.62894i −0.499037 + 0.913135i
\(39\) 6.85203i 1.09720i
\(40\) −0.198727 2.82144i −0.0314214 0.446108i
\(41\) 5.75560i 0.898874i −0.893312 0.449437i \(-0.851625\pi\)
0.893312 0.449437i \(-0.148375\pi\)
\(42\) 5.45624 2.55925i 0.841916 0.394901i
\(43\) −4.96515 −0.757178 −0.378589 0.925565i \(-0.623591\pi\)
−0.378589 + 0.925565i \(0.623591\pi\)
\(44\) −6.49855 10.1280i −0.979693 1.52685i
\(45\) 0.405694 0.0604772
\(46\) 3.52593 6.45173i 0.519870 0.951256i
\(47\) 3.86303 0.563481 0.281741 0.959491i \(-0.409088\pi\)
0.281741 + 0.959491i \(0.409088\pi\)
\(48\) −5.85666 2.68486i −0.845336 0.387526i
\(49\) 2.11332 + 6.67337i 0.301903 + 0.953339i
\(50\) −1.24098 0.678208i −0.175501 0.0959131i
\(51\) −8.73190 −1.22271
\(52\) 4.59473 + 7.16089i 0.637174 + 0.993036i
\(53\) 10.2224i 1.40416i −0.712099 0.702079i \(-0.752255\pi\)
0.712099 0.702079i \(-0.247745\pi\)
\(54\) 3.72031 6.80740i 0.506270 0.926370i
\(55\) −6.01679 −0.811304
\(56\) 3.98603 6.33337i 0.532656 0.846332i
\(57\) 7.30587 0.967686
\(58\) 0.255561 0.467624i 0.0335568 0.0614020i
\(59\) 10.5835i 1.37786i 0.724828 + 0.688930i \(0.241919\pi\)
−0.724828 + 0.688930i \(0.758081\pi\)
\(60\) −2.71124 + 1.73965i −0.350020 + 0.224588i
\(61\) −5.58001 −0.714447 −0.357223 0.934019i \(-0.616277\pi\)
−0.357223 + 0.934019i \(0.616277\pi\)
\(62\) −3.64396 1.99146i −0.462784 0.252916i
\(63\) 0.866007 + 0.634147i 0.109107 + 0.0798950i
\(64\) −7.92102 + 1.12139i −0.990127 + 0.140174i
\(65\) 4.25411 0.527657
\(66\) −6.57262 + 12.0265i −0.809034 + 1.48037i
\(67\) −0.782596 −0.0956093 −0.0478047 0.998857i \(-0.515223\pi\)
−0.0478047 + 0.998857i \(0.515223\pi\)
\(68\) −9.12549 + 5.85531i −1.10663 + 0.710060i
\(69\) −8.37378 −1.00809
\(70\) −1.58892 3.38753i −0.189912 0.404887i
\(71\) 15.3803i 1.82531i −0.408735 0.912653i \(-0.634030\pi\)
0.408735 0.912653i \(-0.365970\pi\)
\(72\) −0.0806221 1.14464i −0.00950141 0.134897i
\(73\) 8.77164i 1.02664i −0.858196 0.513321i \(-0.828415\pi\)
0.858196 0.513321i \(-0.171585\pi\)
\(74\) −0.252473 + 0.461974i −0.0293494 + 0.0537034i
\(75\) 1.61069i 0.185986i
\(76\) 7.63518 4.89906i 0.875816 0.561961i
\(77\) −12.8437 9.40496i −1.46367 1.07179i
\(78\) 4.64710 8.50324i 0.526181 0.962803i
\(79\) 8.74609i 0.984012i −0.870592 0.492006i \(-0.836264\pi\)
0.870592 0.492006i \(-0.163736\pi\)
\(80\) −1.66690 + 3.63613i −0.186366 + 0.406531i
\(81\) −7.61833 −0.846481
\(82\) −3.90349 + 7.14259i −0.431069 + 0.788767i
\(83\) 8.42742i 0.925029i −0.886612 0.462515i \(-0.846947\pi\)
0.886612 0.462515i \(-0.153053\pi\)
\(84\) −8.50679 0.524480i −0.928167 0.0572254i
\(85\) 5.42124i 0.588016i
\(86\) 6.16165 + 3.36740i 0.664428 + 0.363116i
\(87\) −0.606935 −0.0650702
\(88\) 1.19570 + 16.9760i 0.127462 + 1.80965i
\(89\) 1.94765i 0.206451i −0.994658 0.103225i \(-0.967084\pi\)
0.994658 0.103225i \(-0.0329163\pi\)
\(90\) −0.503458 0.275145i −0.0530691 0.0290028i
\(91\) 9.08097 + 6.64968i 0.951944 + 0.697076i
\(92\) −8.75123 + 5.61516i −0.912379 + 0.585421i
\(93\) 4.72954i 0.490431i
\(94\) −4.79395 2.61994i −0.494458 0.270226i
\(95\) 4.53588i 0.465371i
\(96\) 5.44711 + 7.30389i 0.555943 + 0.745450i
\(97\) 3.14377i 0.319201i −0.987182 0.159601i \(-0.948979\pi\)
0.987182 0.159601i \(-0.0510206\pi\)
\(98\) 1.90334 9.71480i 0.192266 0.981343i
\(99\) −2.44098 −0.245327
\(100\) 1.08007 + 1.68329i 0.108007 + 0.168329i
\(101\) 16.3016 1.62207 0.811037 0.584995i \(-0.198904\pi\)
0.811037 + 0.584995i \(0.198904\pi\)
\(102\) 10.8361 + 5.92205i 1.07294 + 0.586370i
\(103\) 11.8940 1.17195 0.585974 0.810330i \(-0.300712\pi\)
0.585974 + 0.810330i \(0.300712\pi\)
\(104\) −0.845405 12.0027i −0.0828988 1.17696i
\(105\) −2.51769 + 3.43822i −0.245702 + 0.335536i
\(106\) −6.93293 + 12.6858i −0.673385 + 1.23216i
\(107\) 10.4794 1.01308 0.506542 0.862215i \(-0.330923\pi\)
0.506542 + 0.862215i \(0.330923\pi\)
\(108\) −9.23367 + 5.92471i −0.888510 + 0.570106i
\(109\) 0.676794i 0.0648251i −0.999475 0.0324126i \(-0.989681\pi\)
0.999475 0.0324126i \(-0.0103190\pi\)
\(110\) 7.46673 + 4.08064i 0.711925 + 0.389073i
\(111\) 0.599602 0.0569117
\(112\) −9.24193 + 5.15623i −0.873280 + 0.487218i
\(113\) −9.10537 −0.856562 −0.428281 0.903646i \(-0.640881\pi\)
−0.428281 + 0.903646i \(0.640881\pi\)
\(114\) −9.06645 4.95490i −0.849151 0.464069i
\(115\) 5.19890i 0.484800i
\(116\) −0.634292 + 0.406989i −0.0588925 + 0.0377880i
\(117\) 1.72587 0.159556
\(118\) 7.17784 13.1340i 0.660774 1.20908i
\(119\) −8.47403 + 11.5724i −0.776813 + 1.06084i
\(120\) 4.54445 0.320086i 0.414849 0.0292197i
\(121\) 25.2018 2.29107
\(122\) 6.92468 + 3.78440i 0.626931 + 0.342624i
\(123\) 9.27046 0.835889
\(124\) 3.17147 + 4.94273i 0.284806 + 0.443870i
\(125\) 1.00000 0.0894427
\(126\) −0.644615 1.37430i −0.0574269 0.122432i
\(127\) 3.74123i 0.331980i 0.986127 + 0.165990i \(0.0530820\pi\)
−0.986127 + 0.165990i \(0.946918\pi\)
\(128\) 10.5904 + 3.98047i 0.936065 + 0.351827i
\(129\) 7.99729i 0.704122i
\(130\) −5.27927 2.88517i −0.463023 0.253046i
\(131\) 17.5774i 1.53575i −0.640601 0.767874i \(-0.721315\pi\)
0.640601 0.767874i \(-0.278685\pi\)
\(132\) 16.3130 10.4671i 1.41986 0.911045i
\(133\) 7.09012 9.68244i 0.614791 0.839574i
\(134\) 0.971187 + 0.530763i 0.0838978 + 0.0458509i
\(135\) 5.48550i 0.472117i
\(136\) 15.2957 1.07734i 1.31159 0.0923815i
\(137\) −0.767338 −0.0655581 −0.0327791 0.999463i \(-0.510436\pi\)
−0.0327791 + 0.999463i \(0.510436\pi\)
\(138\) 10.3917 + 5.67917i 0.884601 + 0.483443i
\(139\) 2.01854i 0.171210i 0.996329 + 0.0856052i \(0.0272824\pi\)
−0.996329 + 0.0856052i \(0.972718\pi\)
\(140\) −0.325625 + 5.28147i −0.0275204 + 0.446366i
\(141\) 6.22213i 0.523998i
\(142\) −10.4310 + 19.0867i −0.875354 + 1.60172i
\(143\) −25.5961 −2.14045
\(144\) −0.676253 + 1.47515i −0.0563544 + 0.122930i
\(145\) 0.376818i 0.0312930i
\(146\) −5.94899 + 10.8854i −0.492342 + 0.900885i
\(147\) −10.7487 + 3.40390i −0.886538 + 0.280749i
\(148\) 0.626629 0.402072i 0.0515086 0.0330501i
\(149\) 4.23267i 0.346754i −0.984856 0.173377i \(-0.944532\pi\)
0.984856 0.173377i \(-0.0554679\pi\)
\(150\) 1.09238 1.99883i 0.0891924 0.163204i
\(151\) 0.625768i 0.0509243i 0.999676 + 0.0254622i \(0.00810573\pi\)
−0.999676 + 0.0254622i \(0.991894\pi\)
\(152\) −12.7977 + 0.901400i −1.03803 + 0.0731132i
\(153\) 2.19936i 0.177808i
\(154\) 9.56021 + 20.3820i 0.770384 + 1.64243i
\(155\) 2.93636 0.235854
\(156\) −11.5339 + 7.40066i −0.923454 + 0.592527i
\(157\) −2.91713 −0.232812 −0.116406 0.993202i \(-0.537137\pi\)
−0.116406 + 0.993202i \(0.537137\pi\)
\(158\) −5.93167 + 10.8537i −0.471898 + 0.863477i
\(159\) 16.4651 1.30577
\(160\) 4.53465 3.38186i 0.358495 0.267359i
\(161\) −8.12649 + 11.0977i −0.640457 + 0.874624i
\(162\) 9.45421 + 5.16681i 0.742793 + 0.405943i
\(163\) −7.14397 −0.559559 −0.279779 0.960064i \(-0.590261\pi\)
−0.279779 + 0.960064i \(0.590261\pi\)
\(164\) 9.68833 6.21644i 0.756531 0.485423i
\(165\) 9.69116i 0.754456i
\(166\) −5.71554 + 10.4583i −0.443612 + 0.811719i
\(167\) 6.26796 0.485029 0.242515 0.970148i \(-0.422028\pi\)
0.242515 + 0.970148i \(0.422028\pi\)
\(168\) 10.2011 + 6.42024i 0.787029 + 0.495332i
\(169\) 5.09746 0.392112
\(170\) 3.67672 6.72765i 0.281992 0.515987i
\(171\) 1.84018i 0.140722i
\(172\) −5.36270 8.35776i −0.408902 0.637274i
\(173\) 9.11366 0.692898 0.346449 0.938069i \(-0.387387\pi\)
0.346449 + 0.938069i \(0.387387\pi\)
\(174\) 0.753195 + 0.411628i 0.0570995 + 0.0312054i
\(175\) 2.13463 + 1.56312i 0.161363 + 0.118161i
\(176\) 10.0294 21.8778i 0.755996 1.64910i
\(177\) −17.0468 −1.28131
\(178\) −1.32091 + 2.41700i −0.0990067 + 0.181162i
\(179\) 10.9518 0.818579 0.409290 0.912405i \(-0.365777\pi\)
0.409290 + 0.912405i \(0.365777\pi\)
\(180\) 0.438177 + 0.682898i 0.0326598 + 0.0509002i
\(181\) −18.7975 −1.39721 −0.698603 0.715509i \(-0.746195\pi\)
−0.698603 + 0.715509i \(0.746195\pi\)
\(182\) −6.75945 14.4109i −0.501043 1.06821i
\(183\) 8.98763i 0.664385i
\(184\) 14.6684 1.03316i 1.08137 0.0761655i
\(185\) 0.372265i 0.0273695i
\(186\) 3.20761 5.86928i 0.235194 0.430356i
\(187\) 32.6185i 2.38530i
\(188\) 4.17234 + 6.50259i 0.304299 + 0.474250i
\(189\) −8.57449 + 11.7095i −0.623702 + 0.851743i
\(190\) −3.07627 + 5.62894i −0.223176 + 0.408366i
\(191\) 1.13019i 0.0817778i 0.999164 + 0.0408889i \(0.0130190\pi\)
−0.999164 + 0.0408889i \(0.986981\pi\)
\(192\) −1.80621 12.7583i −0.130352 0.920748i
\(193\) −3.27357 −0.235636 −0.117818 0.993035i \(-0.537590\pi\)
−0.117818 + 0.993035i \(0.537590\pi\)
\(194\) −2.13213 + 3.90136i −0.153078 + 0.280101i
\(195\) 6.85203i 0.490684i
\(196\) −8.95066 + 10.7650i −0.639333 + 0.768930i
\(197\) 21.2252i 1.51223i 0.654437 + 0.756116i \(0.272906\pi\)
−0.654437 + 0.756116i \(0.727094\pi\)
\(198\) 3.02920 + 1.65549i 0.215276 + 0.117650i
\(199\) −17.9614 −1.27325 −0.636626 0.771172i \(-0.719671\pi\)
−0.636626 + 0.771172i \(0.719671\pi\)
\(200\) −0.198727 2.82144i −0.0140521 0.199506i
\(201\) 1.26052i 0.0889099i
\(202\) −20.2300 11.0559i −1.42338 0.777890i
\(203\) −0.589011 + 0.804368i −0.0413404 + 0.0564556i
\(204\) −9.43105 14.6983i −0.660306 1.02909i
\(205\) 5.75560i 0.401989i
\(206\) −14.7602 8.06659i −1.02839 0.562026i
\(207\) 2.10916i 0.146597i
\(208\) −7.09120 + 15.4685i −0.491686 + 1.07255i
\(209\) 27.2915i 1.88779i
\(210\) 5.45624 2.55925i 0.376516 0.176605i
\(211\) −7.43642 −0.511944 −0.255972 0.966684i \(-0.582396\pi\)
−0.255972 + 0.966684i \(0.582396\pi\)
\(212\) 17.2073 11.0409i 1.18180 0.758293i
\(213\) 24.7728 1.69741
\(214\) −13.0048 7.10723i −0.888988 0.485840i
\(215\) −4.96515 −0.338620
\(216\) 15.4770 1.09011i 1.05308 0.0741729i
\(217\) 6.26804 + 4.58987i 0.425503 + 0.311581i
\(218\) −0.459007 + 0.839889i −0.0310879 + 0.0568845i
\(219\) 14.1283 0.954705
\(220\) −6.49855 10.1280i −0.438132 0.682829i
\(221\) 23.0625i 1.55135i
\(222\) −0.744095 0.406655i −0.0499404 0.0272929i
\(223\) −23.8641 −1.59806 −0.799029 0.601293i \(-0.794653\pi\)
−0.799029 + 0.601293i \(0.794653\pi\)
\(224\) 14.9661 0.130838i 0.999962 0.00874200i
\(225\) 0.405694 0.0270462
\(226\) 11.2996 + 6.17534i 0.751638 + 0.410777i
\(227\) 12.1282i 0.804974i −0.915426 0.402487i \(-0.868146\pi\)
0.915426 0.402487i \(-0.131854\pi\)
\(228\) 7.89084 + 12.2979i 0.522584 + 0.814447i
\(229\) −16.4001 −1.08375 −0.541875 0.840459i \(-0.682285\pi\)
−0.541875 + 0.840459i \(0.682285\pi\)
\(230\) 3.52593 6.45173i 0.232493 0.425415i
\(231\) 15.1484 20.6871i 0.996694 1.36111i
\(232\) 1.06317 0.0748837i 0.0698004 0.00491636i
\(233\) −26.4108 −1.73023 −0.865114 0.501575i \(-0.832754\pi\)
−0.865114 + 0.501575i \(0.832754\pi\)
\(234\) −2.14177 1.17050i −0.140012 0.0765177i
\(235\) 3.86303 0.251997
\(236\) −17.8151 + 11.4310i −1.15967 + 0.744092i
\(237\) 14.0872 0.915062
\(238\) 18.3646 8.61392i 1.19040 0.558357i
\(239\) 1.68909i 0.109258i −0.998507 0.0546292i \(-0.982602\pi\)
0.998507 0.0546292i \(-0.0173977\pi\)
\(240\) −5.85666 2.68486i −0.378046 0.173307i
\(241\) 5.25118i 0.338258i 0.985594 + 0.169129i \(0.0540955\pi\)
−0.985594 + 0.169129i \(0.945905\pi\)
\(242\) −31.2750 17.0921i −2.01043 1.09872i
\(243\) 4.18577i 0.268517i
\(244\) −6.02679 9.39275i −0.385826 0.601309i
\(245\) 2.11332 + 6.67337i 0.135015 + 0.426346i
\(246\) −11.5045 6.28730i −0.733498 0.400864i
\(247\) 19.2961i 1.22778i
\(248\) −0.583532 8.28474i −0.0370543 0.526082i
\(249\) 13.5739 0.860212
\(250\) −1.24098 0.678208i −0.0784865 0.0428936i
\(251\) 13.9692i 0.881730i −0.897574 0.440865i \(-0.854672\pi\)
0.897574 0.440865i \(-0.145328\pi\)
\(252\) −0.132104 + 2.14266i −0.00832178 + 0.134975i
\(253\) 31.2807i 1.96660i
\(254\) 2.53733 4.64280i 0.159206 0.291315i
\(255\) −8.73190 −0.546813
\(256\) −10.4429 12.1222i −0.652679 0.757635i
\(257\) 21.6938i 1.35322i 0.736341 + 0.676610i \(0.236552\pi\)
−0.736341 + 0.676610i \(0.763448\pi\)
\(258\) −5.42382 + 9.92448i −0.337672 + 0.617871i
\(259\) 0.581895 0.794650i 0.0361572 0.0493771i
\(260\) 4.59473 + 7.16089i 0.284953 + 0.444099i
\(261\) 0.152873i 0.00946257i
\(262\) −11.9212 + 21.8133i −0.736492 + 1.34763i
\(263\) 5.88968i 0.363173i 0.983375 + 0.181587i \(0.0581232\pi\)
−0.983375 + 0.181587i \(0.941877\pi\)
\(264\) −27.3430 + 1.92589i −1.68285 + 0.118530i
\(265\) 10.2224i 0.627958i
\(266\) −15.3654 + 7.20715i −0.942114 + 0.441899i
\(267\) 3.13706 0.191985
\(268\) −0.845257 1.31733i −0.0516323 0.0804689i
\(269\) 13.3475 0.813810 0.406905 0.913470i \(-0.366608\pi\)
0.406905 + 0.913470i \(0.366608\pi\)
\(270\) 3.72031 6.80740i 0.226411 0.414285i
\(271\) 24.7908 1.50593 0.752966 0.658059i \(-0.228622\pi\)
0.752966 + 0.658059i \(0.228622\pi\)
\(272\) −19.7123 9.03668i −1.19523 0.547929i
\(273\) −10.7105 + 14.6266i −0.648231 + 0.885241i
\(274\) 0.952252 + 0.520415i 0.0575277 + 0.0314394i
\(275\) −6.01679 −0.362826
\(276\) −9.04426 14.0955i −0.544400 0.848448i
\(277\) 2.09066i 0.125616i −0.998026 0.0628078i \(-0.979994\pi\)
0.998026 0.0628078i \(-0.0200055\pi\)
\(278\) 1.36899 2.50497i 0.0821065 0.150238i
\(279\) 1.19126 0.0713189
\(280\) 3.98603 6.33337i 0.238211 0.378491i
\(281\) −4.09181 −0.244097 −0.122048 0.992524i \(-0.538946\pi\)
−0.122048 + 0.992524i \(0.538946\pi\)
\(282\) 4.21990 7.72155i 0.251291 0.459811i
\(283\) 5.92294i 0.352082i 0.984383 + 0.176041i \(0.0563291\pi\)
−0.984383 + 0.176041i \(0.943671\pi\)
\(284\) 25.8895 16.6118i 1.53626 0.985728i
\(285\) 7.30587 0.432763
\(286\) 31.7643 + 17.3595i 1.87826 + 1.02649i
\(287\) 8.99669 12.2861i 0.531058 0.725226i
\(288\) 1.83968 1.37200i 0.108404 0.0808458i
\(289\) −12.3898 −0.728812
\(290\) 0.255561 0.467624i 0.0150070 0.0274598i
\(291\) 5.06362 0.296835
\(292\) 14.7652 9.47397i 0.864067 0.554422i
\(293\) 9.44316 0.551675 0.275838 0.961204i \(-0.411045\pi\)
0.275838 + 0.961204i \(0.411045\pi\)
\(294\) 15.6475 + 3.06568i 0.912580 + 0.178794i
\(295\) 10.5835i 0.616198i
\(296\) −1.05032 + 0.0739790i −0.0610488 + 0.00429994i
\(297\) 33.0051i 1.91515i
\(298\) −2.87063 + 5.25267i −0.166291 + 0.304279i
\(299\) 22.1167i 1.27904i
\(300\) −2.71124 + 1.73965i −0.156534 + 0.100439i
\(301\) −10.5988 7.76111i −0.610903 0.447343i
\(302\) 0.424401 0.776567i 0.0244215 0.0446864i
\(303\) 26.2568i 1.50841i
\(304\) 16.4930 + 7.56088i 0.945941 + 0.433646i
\(305\) −5.58001 −0.319510
\(306\) 1.49162 2.72937i 0.0852704 0.156027i
\(307\) 24.1204i 1.37663i 0.725414 + 0.688313i \(0.241649\pi\)
−0.725414 + 0.688313i \(0.758351\pi\)
\(308\) 1.95922 31.7775i 0.111637 1.81069i
\(309\) 19.1574i 1.08983i
\(310\) −3.64396 1.99146i −0.206963 0.113107i
\(311\) 16.5947 0.941001 0.470500 0.882400i \(-0.344073\pi\)
0.470500 + 0.882400i \(0.344073\pi\)
\(312\) 19.3326 1.36168i 1.09449 0.0770900i
\(313\) 11.3871i 0.643637i −0.946801 0.321819i \(-0.895706\pi\)
0.946801 0.321819i \(-0.104294\pi\)
\(314\) 3.62010 + 1.97842i 0.204294 + 0.111649i
\(315\) 0.866007 + 0.634147i 0.0487940 + 0.0357301i
\(316\) 14.7222 9.44638i 0.828187 0.531400i
\(317\) 26.7084i 1.50009i 0.661386 + 0.750046i \(0.269969\pi\)
−0.661386 + 0.750046i \(0.730031\pi\)
\(318\) −20.4329 11.1668i −1.14582 0.626201i
\(319\) 2.26723i 0.126941i
\(320\) −7.92102 + 1.12139i −0.442798 + 0.0626876i
\(321\) 16.8791i 0.942097i
\(322\) 17.6114 8.26064i 0.981445 0.460347i
\(323\) 24.5901 1.36823
\(324\) −8.22832 12.8238i −0.457129 0.712435i
\(325\) 4.25411 0.235976
\(326\) 8.86553 + 4.84510i 0.491016 + 0.268345i
\(327\) 1.09010 0.0602828
\(328\) −16.2391 + 1.14379i −0.896653 + 0.0631553i
\(329\) 8.24616 + 6.03838i 0.454626 + 0.332907i
\(330\) −6.57262 + 12.0265i −0.361811 + 0.662040i
\(331\) −3.25364 −0.178836 −0.0894182 0.995994i \(-0.528501\pi\)
−0.0894182 + 0.995994i \(0.528501\pi\)
\(332\) 14.1858 9.10219i 0.778545 0.499547i
\(333\) 0.151026i 0.00827615i
\(334\) −7.77842 4.25098i −0.425616 0.232603i
\(335\) −0.782596 −0.0427578
\(336\) −8.30507 14.8858i −0.453079 0.812089i
\(337\) −12.0157 −0.654539 −0.327270 0.944931i \(-0.606129\pi\)
−0.327270 + 0.944931i \(0.606129\pi\)
\(338\) −6.32585 3.45714i −0.344081 0.188043i
\(339\) 14.6659i 0.796542i
\(340\) −9.12549 + 5.85531i −0.494899 + 0.317549i
\(341\) −17.6675 −0.956746
\(342\) −1.24802 + 2.28363i −0.0674853 + 0.123484i
\(343\) −5.92010 + 17.5486i −0.319655 + 0.947534i
\(344\) 0.986707 + 14.0089i 0.0531997 + 0.755307i
\(345\) −8.37378 −0.450829
\(346\) −11.3099 6.18095i −0.608023 0.332290i
\(347\) −15.5740 −0.836057 −0.418028 0.908434i \(-0.637279\pi\)
−0.418028 + 0.908434i \(0.637279\pi\)
\(348\) −0.655531 1.02164i −0.0351401 0.0547659i
\(349\) 34.7705 1.86122 0.930610 0.366012i \(-0.119277\pi\)
0.930610 + 0.366012i \(0.119277\pi\)
\(350\) −1.58892 3.38753i −0.0849314 0.181071i
\(351\) 23.3359i 1.24558i
\(352\) −27.2840 + 20.3479i −1.45424 + 1.08455i
\(353\) 12.5154i 0.666126i −0.942905 0.333063i \(-0.891918\pi\)
0.942905 0.333063i \(-0.108082\pi\)
\(354\) 21.1547 + 11.5612i 1.12436 + 0.614473i
\(355\) 15.3803i 0.816302i
\(356\) 3.27846 2.10360i 0.173758 0.111491i
\(357\) −18.6394 13.6490i −0.986502 0.722382i
\(358\) −13.5910 7.42763i −0.718308 0.392562i
\(359\) 31.0752i 1.64009i −0.572301 0.820044i \(-0.693949\pi\)
0.572301 0.820044i \(-0.306051\pi\)
\(360\) −0.0806221 1.14464i −0.00424916 0.0603278i
\(361\) −1.57420 −0.0828526
\(362\) 23.3273 + 12.7486i 1.22606 + 0.670052i
\(363\) 40.5922i 2.13054i
\(364\) −1.38525 + 22.4680i −0.0726066 + 1.17764i
\(365\) 8.77164i 0.459129i
\(366\) −6.09548 + 11.1535i −0.318616 + 0.583002i
\(367\) −14.0542 −0.733624 −0.366812 0.930295i \(-0.619551\pi\)
−0.366812 + 0.930295i \(0.619551\pi\)
\(368\) −18.9039 8.66606i −0.985431 0.451750i
\(369\) 2.33501i 0.121556i
\(370\) −0.252473 + 0.461974i −0.0131255 + 0.0240169i
\(371\) 15.9789 21.8211i 0.829581 1.13290i
\(372\) −7.96118 + 5.10823i −0.412768 + 0.264849i
\(373\) 19.7598i 1.02312i 0.859247 + 0.511561i \(0.170933\pi\)
−0.859247 + 0.511561i \(0.829067\pi\)
\(374\) −22.1221 + 40.4789i −1.14391 + 2.09311i
\(375\) 1.61069i 0.0831754i
\(376\) −0.767688 10.8993i −0.0395905 0.562089i
\(377\) 1.60302i 0.0825600i
\(378\) 18.5823 8.71603i 0.955769 0.448304i
\(379\) −0.483016 −0.0248108 −0.0124054 0.999923i \(-0.503949\pi\)
−0.0124054 + 0.999923i \(0.503949\pi\)
\(380\) 7.63518 4.89906i 0.391677 0.251316i
\(381\) −6.02594 −0.308718
\(382\) 0.766505 1.40255i 0.0392178 0.0717605i
\(383\) −1.09585 −0.0559953 −0.0279977 0.999608i \(-0.508913\pi\)
−0.0279977 + 0.999608i \(0.508913\pi\)
\(384\) −6.41129 + 17.0577i −0.327175 + 0.870474i
\(385\) −12.8437 9.40496i −0.654573 0.479321i
\(386\) 4.06243 + 2.22016i 0.206772 + 0.113003i
\(387\) −2.01433 −0.102394
\(388\) 5.29186 3.39548i 0.268654 0.172380i
\(389\) 18.3250i 0.929114i 0.885543 + 0.464557i \(0.153786\pi\)
−0.885543 + 0.464557i \(0.846214\pi\)
\(390\) 4.64710 8.50324i 0.235315 0.430578i
\(391\) −28.1844 −1.42535
\(392\) 18.4085 7.28878i 0.929771 0.368139i
\(393\) 28.3117 1.42814
\(394\) 14.3951 26.3401i 0.725214 1.32699i
\(395\) 8.74609i 0.440064i
\(396\) −2.63642 4.10886i −0.132485 0.206478i
\(397\) 0.717950 0.0360329 0.0180164 0.999838i \(-0.494265\pi\)
0.0180164 + 0.999838i \(0.494265\pi\)
\(398\) 22.2898 + 12.1816i 1.11729 + 0.610608i
\(399\) 15.5954 + 11.4199i 0.780745 + 0.571712i
\(400\) −1.66690 + 3.63613i −0.0833452 + 0.181806i
\(401\) −21.1139 −1.05438 −0.527189 0.849748i \(-0.676754\pi\)
−0.527189 + 0.849748i \(0.676754\pi\)
\(402\) −0.854892 + 1.56428i −0.0426381 + 0.0780190i
\(403\) 12.4916 0.622250
\(404\) 17.6069 + 27.4403i 0.875975 + 1.36521i
\(405\) −7.61833 −0.378558
\(406\) 1.27648 0.598734i 0.0633506 0.0297147i
\(407\) 2.23984i 0.111025i
\(408\) 1.73526 + 24.6365i 0.0859083 + 1.21969i
\(409\) 1.08609i 0.0537038i 0.999639 + 0.0268519i \(0.00854825\pi\)
−0.999639 + 0.0268519i \(0.991452\pi\)
\(410\) −3.90349 + 7.14259i −0.192780 + 0.352748i
\(411\) 1.23594i 0.0609644i
\(412\) 12.8463 + 20.0210i 0.632892 + 0.986362i
\(413\) −16.5433 + 22.5920i −0.814044 + 1.11168i
\(414\) 1.43045 2.61743i 0.0703027 0.128639i
\(415\) 8.42742i 0.413686i
\(416\) 19.2909 14.3868i 0.945814 0.705371i
\(417\) −3.25123 −0.159214
\(418\) 18.5093 33.8682i 0.905318 1.65655i
\(419\) 0.208107i 0.0101667i −0.999987 0.00508334i \(-0.998382\pi\)
0.999987 0.00508334i \(-0.00161808\pi\)
\(420\) −8.50679 0.524480i −0.415089 0.0255920i
\(421\) 9.48511i 0.462276i −0.972921 0.231138i \(-0.925755\pi\)
0.972921 0.231138i \(-0.0742449\pi\)
\(422\) 9.22846 + 5.04344i 0.449234 + 0.245511i
\(423\) 1.56721 0.0762003
\(424\) −28.8419 + 2.03147i −1.40069 + 0.0986568i
\(425\) 5.42124i 0.262969i
\(426\) −30.7426 16.8011i −1.48948 0.814017i
\(427\) −11.9113 8.72221i −0.576427 0.422097i
\(428\) 11.3185 + 17.6399i 0.547100 + 0.852656i
\(429\) 41.2273i 1.99047i
\(430\) 6.16165 + 3.36740i 0.297141 + 0.162391i
\(431\) 13.6900i 0.659423i 0.944082 + 0.329711i \(0.106951\pi\)
−0.944082 + 0.329711i \(0.893049\pi\)
\(432\) −19.9460 9.14381i −0.959651 0.439932i
\(433\) 6.48406i 0.311604i −0.987788 0.155802i \(-0.950204\pi\)
0.987788 0.155802i \(-0.0497962\pi\)
\(434\) −4.66564 9.94698i −0.223958 0.477470i
\(435\) −0.606935 −0.0291003
\(436\) 1.13924 0.730984i 0.0545596 0.0350078i
\(437\) 23.5816 1.12806
\(438\) −17.5330 9.58196i −0.837760 0.457844i
\(439\) 9.04411 0.431652 0.215826 0.976432i \(-0.430756\pi\)
0.215826 + 0.976432i \(0.430756\pi\)
\(440\) 1.19570 + 16.9760i 0.0570026 + 0.809299i
\(441\) 0.857361 + 2.70734i 0.0408267 + 0.128921i
\(442\) 15.6412 28.6202i 0.743976 1.36132i
\(443\) 8.66264 0.411574 0.205787 0.978597i \(-0.434025\pi\)
0.205787 + 0.978597i \(0.434025\pi\)
\(444\) 0.647611 + 1.00930i 0.0307343 + 0.0478993i
\(445\) 1.94765i 0.0923277i
\(446\) 29.6149 + 16.1848i 1.40231 + 0.766373i
\(447\) 6.81750 0.322457
\(448\) −18.6613 9.98773i −0.881665 0.471876i
\(449\) −26.5808 −1.25443 −0.627213 0.778848i \(-0.715804\pi\)
−0.627213 + 0.778848i \(0.715804\pi\)
\(450\) −0.503458 0.275145i −0.0237332 0.0129704i
\(451\) 34.6303i 1.63068i
\(452\) −9.83443 15.3270i −0.462573 0.720919i
\(453\) −1.00792 −0.0473560
\(454\) −8.22541 + 15.0508i −0.386037 + 0.706369i
\(455\) 9.08097 + 6.64968i 0.425722 + 0.311742i
\(456\) −1.45187 20.6131i −0.0679901 0.965295i
\(457\) 33.4034 1.56254 0.781272 0.624191i \(-0.214571\pi\)
0.781272 + 0.624191i \(0.214571\pi\)
\(458\) 20.3522 + 11.1227i 0.950998 + 0.519729i
\(459\) −29.7382 −1.38806
\(460\) −8.75123 + 5.61516i −0.408028 + 0.261808i
\(461\) −9.70385 −0.451954 −0.225977 0.974133i \(-0.572557\pi\)
−0.225977 + 0.974133i \(0.572557\pi\)
\(462\) −32.8291 + 15.3985i −1.52735 + 0.716403i
\(463\) 28.6011i 1.32921i −0.747196 0.664604i \(-0.768600\pi\)
0.747196 0.664604i \(-0.231400\pi\)
\(464\) −1.37016 0.628119i −0.0636080 0.0291597i
\(465\) 4.72954i 0.219327i
\(466\) 32.7753 + 17.9120i 1.51829 + 0.829758i
\(467\) 8.61107i 0.398473i 0.979951 + 0.199236i \(0.0638462\pi\)
−0.979951 + 0.199236i \(0.936154\pi\)
\(468\) 1.86405 + 2.90513i 0.0861659 + 0.134289i
\(469\) −1.67056 1.22329i −0.0771391 0.0564863i
\(470\) −4.79395 2.61994i −0.221129 0.120849i
\(471\) 4.69857i 0.216499i
\(472\) 29.8608 2.10323i 1.37445 0.0968091i
\(473\) 29.8743 1.37362
\(474\) −17.4819 9.55405i −0.802973 0.438832i
\(475\) 4.53588i 0.208120i
\(476\) −28.6321 1.76529i −1.31235 0.0809120i
\(477\) 4.14717i 0.189886i
\(478\) −1.14556 + 2.09613i −0.0523965 + 0.0958749i
\(479\) −6.75741 −0.308754 −0.154377 0.988012i \(-0.549337\pi\)
−0.154377 + 0.988012i \(0.549337\pi\)
\(480\) 5.44711 + 7.30389i 0.248625 + 0.333375i
\(481\) 1.58366i 0.0722086i
\(482\) 3.56139 6.51661i 0.162217 0.296824i
\(483\) −17.8750 13.0892i −0.813339 0.595580i
\(484\) 27.2197 + 42.4219i 1.23726 + 1.92827i
\(485\) 3.14377i 0.142751i
\(486\) 2.83882 5.19446i 0.128771 0.235625i
\(487\) 7.72534i 0.350069i −0.984562 0.175034i \(-0.943996\pi\)
0.984562 0.175034i \(-0.0560036\pi\)
\(488\) 1.10890 + 15.7436i 0.0501974 + 0.712681i
\(489\) 11.5067i 0.520350i
\(490\) 1.90334 9.71480i 0.0859841 0.438870i
\(491\) −33.1648 −1.49671 −0.748354 0.663300i \(-0.769156\pi\)
−0.748354 + 0.663300i \(0.769156\pi\)
\(492\) 10.0127 + 15.6048i 0.451409 + 0.703521i
\(493\) −2.04282 −0.0920039
\(494\) −13.0868 + 23.9461i −0.588802 + 1.07739i
\(495\) −2.44098 −0.109714
\(496\) −4.89463 + 10.6770i −0.219775 + 0.479410i
\(497\) 24.0412 32.8313i 1.07840 1.47269i
\(498\) −16.8450 9.20594i −0.754841 0.412528i
\(499\) −9.13507 −0.408942 −0.204471 0.978873i \(-0.565547\pi\)
−0.204471 + 0.978873i \(0.565547\pi\)
\(500\) 1.08007 + 1.68329i 0.0483021 + 0.0752788i
\(501\) 10.0957i 0.451043i
\(502\) −9.47404 + 17.3355i −0.422847 + 0.773723i
\(503\) 13.9338 0.621277 0.310639 0.950528i \(-0.399457\pi\)
0.310639 + 0.950528i \(0.399457\pi\)
\(504\) 1.61711 2.56941i 0.0720317 0.114450i
\(505\) 16.3016 0.725413
\(506\) −21.2148 + 38.8187i −0.943113 + 1.72570i
\(507\) 8.21040i 0.364637i
\(508\) −6.29756 + 4.04078i −0.279409 + 0.179281i
\(509\) −11.4366 −0.506918 −0.253459 0.967346i \(-0.581568\pi\)
−0.253459 + 0.967346i \(0.581568\pi\)
\(510\) 10.8361 + 5.92205i 0.479832 + 0.262233i
\(511\) 13.7111 18.7242i 0.606544 0.828311i
\(512\) 4.73805 + 22.1258i 0.209394 + 0.977831i
\(513\) 24.8816 1.09855
\(514\) 14.7129 26.9216i 0.648958 1.18746i
\(515\) 11.8940 0.524111
\(516\) 13.4617 8.63762i 0.592619 0.380250i
\(517\) −23.2431 −1.02223
\(518\) −1.26106 + 0.591500i −0.0554077 + 0.0259890i
\(519\) 14.6792i 0.644347i
\(520\) −0.845405 12.0027i −0.0370735 0.526353i
\(521\) 13.5526i 0.593751i −0.954916 0.296875i \(-0.904055\pi\)
0.954916 0.296875i \(-0.0959446\pi\)
\(522\) 0.103679 0.189712i 0.00453792 0.00830347i
\(523\) 16.3634i 0.715522i −0.933813 0.357761i \(-0.883540\pi\)
0.933813 0.357761i \(-0.116460\pi\)
\(524\) 29.5879 18.9848i 1.29255 0.829357i
\(525\) −2.51769 + 3.43822i −0.109881 + 0.150056i
\(526\) 3.99443 7.30898i 0.174165 0.318687i
\(527\) 15.9187i 0.693429i
\(528\) 35.2383 + 16.1542i 1.53355 + 0.703023i
\(529\) −4.02852 −0.175153
\(530\) −6.93293 + 12.6858i −0.301147 + 0.551037i
\(531\) 4.29368i 0.186330i
\(532\) 23.9561 + 1.47700i 1.03863 + 0.0640359i
\(533\) 24.4850i 1.06056i
\(534\) −3.89303 2.12758i −0.168468 0.0920693i
\(535\) 10.4794 0.453065
\(536\) 0.155523 + 2.20805i 0.00671756 + 0.0953731i
\(537\) 17.6400i 0.761221i
\(538\) −16.5640 9.05236i −0.714123 0.390275i
\(539\) −12.7154 40.1523i −0.547692 1.72948i
\(540\) −9.23367 + 5.92471i −0.397354 + 0.254959i
\(541\) 23.4050i 1.00626i −0.864211 0.503129i \(-0.832182\pi\)
0.864211 0.503129i \(-0.167818\pi\)
\(542\) −30.7649 16.8133i −1.32146 0.722193i
\(543\) 30.2768i 1.29930i
\(544\) 18.3339 + 24.5834i 0.786058 + 1.05400i
\(545\) 0.676794i 0.0289907i
\(546\) 23.2114 10.8873i 0.993358 0.465935i
\(547\) 21.2928 0.910416 0.455208 0.890385i \(-0.349565\pi\)
0.455208 + 0.890385i \(0.349565\pi\)
\(548\) −0.828778 1.29165i −0.0354036 0.0551765i
\(549\) −2.26377 −0.0966155
\(550\) 7.46673 + 4.08064i 0.318382 + 0.173999i
\(551\) 1.70920 0.0728144
\(552\) 1.66409 + 23.6261i 0.0708285 + 1.00559i
\(553\) 13.6712 18.6697i 0.581358 0.793917i
\(554\) −1.41790 + 2.59447i −0.0602409 + 0.110228i
\(555\) 0.599602 0.0254517
\(556\) −3.39778 + 2.18016i −0.144098 + 0.0924594i
\(557\) 2.06871i 0.0876541i −0.999039 0.0438270i \(-0.986045\pi\)
0.999039 0.0438270i \(-0.0139551\pi\)
\(558\) −1.47833 0.807922i −0.0625828 0.0342021i
\(559\) −21.1223 −0.893378
\(560\) −9.24193 + 5.15623i −0.390543 + 0.217891i
\(561\) 52.5381 2.21816
\(562\) 5.07785 + 2.77509i 0.214196 + 0.117060i
\(563\) 25.5312i 1.07601i 0.842941 + 0.538006i \(0.180822\pi\)
−0.842941 + 0.538006i \(0.819178\pi\)
\(564\) −10.4736 + 6.72033i −0.441019 + 0.282977i
\(565\) −9.10537 −0.383066
\(566\) 4.01698 7.35025i 0.168846 0.308954i
\(567\) −16.2623 11.9084i −0.682954 0.500104i
\(568\) −43.3946 + 3.05648i −1.82080 + 0.128247i
\(569\) 26.3859 1.10616 0.553078 0.833130i \(-0.313453\pi\)
0.553078 + 0.833130i \(0.313453\pi\)
\(570\) −9.06645 4.95490i −0.379752 0.207538i
\(571\) 17.6202 0.737384 0.368692 0.929552i \(-0.379806\pi\)
0.368692 + 0.929552i \(0.379806\pi\)
\(572\) −27.6455 43.0856i −1.15592 1.80150i
\(573\) −1.82038 −0.0760476
\(574\) −19.4972 + 9.14520i −0.813799 + 0.381713i
\(575\) 5.19890i 0.216809i
\(576\) −3.21351 + 0.454941i −0.133896 + 0.0189559i
\(577\) 29.5306i 1.22938i 0.788770 + 0.614688i \(0.210718\pi\)
−0.788770 + 0.614688i \(0.789282\pi\)
\(578\) 15.3755 + 8.40286i 0.639537 + 0.349513i
\(579\) 5.27268i 0.219125i
\(580\) −0.634292 + 0.406989i −0.0263375 + 0.0168993i
\(581\) 13.1731 17.9895i 0.546510 0.746328i
\(582\) −6.28386 3.43419i −0.260474 0.142352i
\(583\) 61.5062i 2.54733i
\(584\) −24.7486 + 1.74316i −1.02411 + 0.0721324i
\(585\) 1.72587 0.0713558
\(586\) −11.7188 6.40442i −0.484098 0.264564i
\(587\) 5.32153i 0.219643i 0.993951 + 0.109822i \(0.0350279\pi\)
−0.993951 + 0.109822i \(0.964972\pi\)
\(588\) −17.3391 14.4167i −0.715051 0.594534i
\(589\) 13.3190i 0.548798i
\(590\) 7.17784 13.1340i 0.295507 0.540717i
\(591\) −34.1871 −1.40627
\(592\) 1.35360 + 0.620531i 0.0556328 + 0.0255037i
\(593\) 45.6864i 1.87611i 0.346481 + 0.938057i \(0.387377\pi\)
−0.346481 + 0.938057i \(0.612623\pi\)
\(594\) −22.3843 + 40.9587i −0.918440 + 1.68056i
\(595\) −8.47403 + 11.5724i −0.347401 + 0.474420i
\(596\) 7.12480 4.57158i 0.291843 0.187259i
\(597\) 28.9302i 1.18404i
\(598\) 14.9997 27.4464i 0.613384 1.12237i
\(599\) 22.5049i 0.919525i −0.888042 0.459762i \(-0.847935\pi\)
0.888042 0.459762i \(-0.152065\pi\)
\(600\) 4.54445 0.320086i 0.185526 0.0130675i
\(601\) 4.49699i 0.183436i 0.995785 + 0.0917181i \(0.0292359\pi\)
−0.995785 + 0.0917181i \(0.970764\pi\)
\(602\) 7.88923 + 16.8196i 0.321541 + 0.685514i
\(603\) −0.317494 −0.0129294
\(604\) −1.05335 + 0.675873i −0.0428601 + 0.0275009i
\(605\) 25.2018 1.02460
\(606\) 17.8076 32.5842i 0.723383 1.32364i
\(607\) 10.8910 0.442051 0.221025 0.975268i \(-0.429060\pi\)
0.221025 + 0.975268i \(0.429060\pi\)
\(608\) −15.3397 20.5686i −0.622107 0.834167i
\(609\) −1.29558 0.948711i −0.0524997 0.0384437i
\(610\) 6.92468 + 3.78440i 0.280372 + 0.153226i
\(611\) 16.4338 0.664839
\(612\) −3.70215 + 2.37546i −0.149651 + 0.0960223i
\(613\) 30.5045i 1.23206i −0.787721 0.616032i \(-0.788739\pi\)
0.787721 0.616032i \(-0.211261\pi\)
\(614\) 16.3587 29.9330i 0.660182 1.20800i
\(615\) 9.27046 0.373821
\(616\) −23.9831 + 38.1066i −0.966308 + 1.53536i
\(617\) −39.6859 −1.59769 −0.798847 0.601534i \(-0.794557\pi\)
−0.798847 + 0.601534i \(0.794557\pi\)
\(618\) 12.9927 23.7740i 0.522644 0.956332i
\(619\) 13.7231i 0.551579i 0.961218 + 0.275789i \(0.0889392\pi\)
−0.961218 + 0.275789i \(0.911061\pi\)
\(620\) 3.17147 + 4.94273i 0.127369 + 0.198505i
\(621\) −28.5185 −1.14441
\(622\) −20.5937 11.2547i −0.825734 0.451271i
\(623\) 3.04441 4.15753i 0.121972 0.166568i
\(624\) −24.9149 11.4217i −0.997393 0.457233i
\(625\) 1.00000 0.0400000
\(626\) −7.72283 + 14.1312i −0.308666 + 0.564796i
\(627\) −43.9579 −1.75551
\(628\) −3.15070 4.91036i −0.125726 0.195945i
\(629\) 2.01814 0.0804684
\(630\) −0.644615 1.37430i −0.0256821 0.0547533i
\(631\) 36.7721i 1.46387i 0.681373 + 0.731936i \(0.261383\pi\)
−0.681373 + 0.731936i \(0.738617\pi\)
\(632\) −24.6766 + 1.73808i −0.981580 + 0.0691372i
\(633\) 11.9777i 0.476072i
\(634\) 18.1138 33.1446i 0.719392 1.31634i
\(635\) 3.74123i 0.148466i
\(636\) 17.7834 + 27.7155i 0.705159 + 1.09899i
\(637\) 8.99031 + 28.3893i 0.356209 + 1.12482i
\(638\) −1.53766 + 2.81360i −0.0608764 + 0.111391i
\(639\) 6.23969i 0.246838i
\(640\) 10.5904 + 3.98047i 0.418621 + 0.157342i
\(641\) −40.2483 −1.58971 −0.794855 0.606799i \(-0.792453\pi\)
−0.794855 + 0.606799i \(0.792453\pi\)
\(642\) 11.4475 20.9466i 0.451797 0.826696i
\(643\) 12.3361i 0.486487i −0.969965 0.243243i \(-0.921789\pi\)
0.969965 0.243243i \(-0.0782114\pi\)
\(644\) −27.4578 1.69289i −1.08199 0.0667093i
\(645\) 7.99729i 0.314893i
\(646\) −30.5158 16.6772i −1.20063 0.656155i
\(647\) −47.9622 −1.88559 −0.942794 0.333376i \(-0.891812\pi\)
−0.942794 + 0.333376i \(0.891812\pi\)
\(648\) 1.51397 + 21.4946i 0.0594742 + 0.844389i
\(649\) 63.6790i 2.49962i
\(650\) −5.27927 2.88517i −0.207070 0.113166i
\(651\) −7.39284 + 10.0958i −0.289748 + 0.395687i
\(652\) −7.71598 12.0253i −0.302181 0.470949i
\(653\) 36.7504i 1.43815i 0.694930 + 0.719077i \(0.255435\pi\)
−0.694930 + 0.719077i \(0.744565\pi\)
\(654\) −1.35280 0.739316i −0.0528985 0.0289095i
\(655\) 17.5774i 0.686808i
\(656\) 20.9281 + 9.59404i 0.817105 + 0.374584i
\(657\) 3.55860i 0.138834i
\(658\) −6.13806 13.0861i −0.239286 0.510150i
\(659\) 15.4039 0.600050 0.300025 0.953931i \(-0.403005\pi\)
0.300025 + 0.953931i \(0.403005\pi\)
\(660\) 16.3130 10.4671i 0.634983 0.407432i
\(661\) −6.20639 −0.241400 −0.120700 0.992689i \(-0.538514\pi\)
−0.120700 + 0.992689i \(0.538514\pi\)
\(662\) 4.03771 + 2.20665i 0.156930 + 0.0857638i
\(663\) −37.1465 −1.44265
\(664\) −23.7774 + 1.67475i −0.922743 + 0.0649930i
\(665\) 7.09012 9.68244i 0.274943 0.375469i
\(666\) −0.102427 + 0.187420i −0.00396896 + 0.00726238i
\(667\) −1.95904 −0.0758542
\(668\) 6.76983 + 10.5508i 0.261932 + 0.408222i
\(669\) 38.4375i 1.48608i
\(670\) 0.971187 + 0.530763i 0.0375202 + 0.0205052i
\(671\) 33.5738 1.29610
\(672\) 0.210739 + 24.1056i 0.00812945 + 0.929894i
\(673\) −46.2742 −1.78374 −0.891870 0.452291i \(-0.850607\pi\)
−0.891870 + 0.452291i \(0.850607\pi\)
\(674\) 14.9113 + 8.14917i 0.574362 + 0.313894i
\(675\) 5.48550i 0.211137i
\(676\) 5.50560 + 8.58048i 0.211754 + 0.330019i
\(677\) −0.112071 −0.00430726 −0.00215363 0.999998i \(-0.500686\pi\)
−0.00215363 + 0.999998i \(0.500686\pi\)
\(678\) −9.94652 + 18.2001i −0.381994 + 0.698970i
\(679\) 4.91408 6.71079i 0.188585 0.257537i
\(680\) 15.2957 1.07734i 0.586562 0.0413143i
\(681\) 19.5346 0.748569
\(682\) 21.9250 + 11.9822i 0.839551 + 0.458822i
\(683\) 0.561153 0.0214719 0.0107360 0.999942i \(-0.496583\pi\)
0.0107360 + 0.999942i \(0.496583\pi\)
\(684\) 3.09754 1.98752i 0.118438 0.0759946i
\(685\) −0.767338 −0.0293185
\(686\) 19.2483 17.7624i 0.734904 0.678171i
\(687\) 26.4154i 1.00781i
\(688\) 8.27643 18.0539i 0.315536 0.688299i
\(689\) 43.4873i 1.65673i
\(690\) 10.3917 + 5.67917i 0.395606 + 0.216202i
\(691\) 39.1762i 1.49033i 0.666879 + 0.745166i \(0.267630\pi\)
−0.666879 + 0.745166i \(0.732370\pi\)
\(692\) 9.84337 + 15.3409i 0.374189 + 0.583173i
\(693\) −5.21059 3.81553i −0.197934 0.144940i
\(694\) 19.3271 + 10.5624i 0.733645 + 0.400944i
\(695\) 2.01854i 0.0765676i
\(696\) 0.120614 + 1.71243i 0.00457187 + 0.0649094i
\(697\) 31.2025 1.18188
\(698\) −43.1495 23.5816i −1.63323 0.892577i
\(699\) 42.5395i 1.60899i
\(700\) −0.325625 + 5.28147i −0.0123075 + 0.199621i
\(701\) 49.6478i 1.87517i −0.347753 0.937586i \(-0.613055\pi\)
0.347753 0.937586i \(-0.386945\pi\)
\(702\) 15.8266 28.9594i 0.597337 1.09300i
\(703\) −1.68855 −0.0636849
\(704\) 47.6591 6.74717i 1.79622 0.254294i
\(705\) 6.22213i 0.234339i
\(706\) −8.48803 + 15.5313i −0.319451 + 0.584530i
\(707\) 34.7980 + 25.4814i 1.30871 + 0.958326i
\(708\) −18.4117 28.6946i −0.691953 1.07841i
\(709\) 13.0064i 0.488465i 0.969717 + 0.244233i \(0.0785360\pi\)
−0.969717 + 0.244233i \(0.921464\pi\)
\(710\) −10.4310 + 19.0867i −0.391470 + 0.716310i
\(711\) 3.54823i 0.133069i
\(712\) −5.49518 + 0.387051i −0.205941 + 0.0145053i
\(713\) 15.2658i 0.571709i
\(714\) 13.8743 + 29.5795i 0.519233 + 1.10699i
\(715\) −25.5961 −0.957240
\(716\) 11.8287 + 18.4351i 0.442061 + 0.688952i
\(717\) 2.72060 0.101603
\(718\) −21.0755 + 38.5638i −0.786529 + 1.43919i
\(719\) 12.4976 0.466081 0.233041 0.972467i \(-0.425132\pi\)
0.233041 + 0.972467i \(0.425132\pi\)
\(720\) −0.676253 + 1.47515i −0.0252024 + 0.0549757i
\(721\) 25.3893 + 18.5917i 0.945546 + 0.692391i
\(722\) 1.95355 + 1.06763i 0.0727037 + 0.0397332i
\(723\) −8.45800 −0.314556
\(724\) −20.3026 31.6415i −0.754539 1.17595i
\(725\) 0.376818i 0.0139947i
\(726\) 27.5299 50.3741i 1.02173 1.86956i
\(727\) 49.8167 1.84760 0.923800 0.382875i \(-0.125066\pi\)
0.923800 + 0.382875i \(0.125066\pi\)
\(728\) 16.9570 26.9428i 0.628469 0.998568i
\(729\) −29.5969 −1.09618
\(730\) −5.94899 + 10.8854i −0.220182 + 0.402888i
\(731\) 26.9172i 0.995570i
\(732\) 15.1288 9.70726i 0.559175 0.358791i
\(733\) −48.8875 −1.80570 −0.902850 0.429955i \(-0.858529\pi\)
−0.902850 + 0.429955i \(0.858529\pi\)
\(734\) 17.4410 + 9.53168i 0.643760 + 0.351821i
\(735\) −10.7487 + 3.40390i −0.396472 + 0.125555i
\(736\) 17.5819 + 23.5752i 0.648079 + 0.868992i
\(737\) 4.70872 0.173448
\(738\) −1.58362 + 2.89770i −0.0582940 + 0.106666i
\(739\) −39.3743 −1.44841 −0.724204 0.689585i \(-0.757793\pi\)
−0.724204 + 0.689585i \(0.757793\pi\)
\(740\) 0.626629 0.402072i 0.0230353 0.0147805i
\(741\) 31.0800 1.14175
\(742\) −34.6287 + 16.2426i −1.27126 + 0.596285i
\(743\) 35.6179i 1.30669i 0.757059 + 0.653346i \(0.226635\pi\)
−0.757059 + 0.653346i \(0.773365\pi\)
\(744\) 13.3441 0.939887i 0.489219 0.0344579i
\(745\) 4.23267i 0.155073i
\(746\) 13.4012 24.5215i 0.490654 0.897797i
\(747\) 3.41895i 0.125093i
\(748\) 54.9062 35.2302i 2.00757 1.28814i
\(749\) 22.3697 + 16.3806i 0.817373 + 0.598534i
\(750\) 1.09238 1.99883i 0.0398880 0.0729869i
\(751\) 13.2839i 0.484738i −0.970184 0.242369i \(-0.922076\pi\)
0.970184 0.242369i \(-0.0779245\pi\)
\(752\) −6.43931 + 14.0465i −0.234817 + 0.512223i
\(753\) 22.5000 0.819946
\(754\) 1.08718 1.98932i 0.0395929 0.0724469i
\(755\) 0.625768i 0.0227740i
\(756\) −28.9715 1.78622i −1.05368 0.0649641i
\(757\) 20.0483i 0.728666i 0.931269 + 0.364333i \(0.118703\pi\)
−0.931269 + 0.364333i \(0.881297\pi\)
\(758\) 0.599413 + 0.327585i 0.0217717 + 0.0118984i
\(759\) 50.3833 1.82880
\(760\) −12.7977 + 0.901400i −0.464221 + 0.0326972i
\(761\) 28.5860i 1.03624i 0.855307 + 0.518121i \(0.173368\pi\)
−0.855307 + 0.518121i \(0.826632\pi\)
\(762\) 7.47808 + 4.08684i 0.270902 + 0.148051i
\(763\) 1.05791 1.44471i 0.0382989 0.0523019i
\(764\) −1.90244 + 1.22068i −0.0688277 + 0.0441628i
\(765\) 2.19936i 0.0795181i
\(766\) 1.35993 + 0.743214i 0.0491363 + 0.0268534i
\(767\) 45.0236i 1.62571i
\(768\) 19.5250 16.8202i 0.704547 0.606945i
\(769\) 26.3204i 0.949137i −0.880219 0.474569i \(-0.842604\pi\)
0.880219 0.474569i \(-0.157396\pi\)
\(770\) 9.56021 + 20.3820i 0.344526 + 0.734518i
\(771\) −34.9418 −1.25840
\(772\) −3.53568 5.51035i −0.127252 0.198322i
\(773\) 0.586223 0.0210850 0.0105425 0.999944i \(-0.496644\pi\)
0.0105425 + 0.999944i \(0.496644\pi\)
\(774\) 2.49974 + 1.36613i 0.0898514 + 0.0491046i
\(775\) 2.93636 0.105477
\(776\) −8.86994 + 0.624750i −0.318412 + 0.0224272i
\(777\) 1.27993 + 0.937249i 0.0459173 + 0.0336236i
\(778\) 12.4282 22.7410i 0.445571 0.815303i
\(779\) −26.1067 −0.935370
\(780\) −11.5339 + 7.40066i −0.412981 + 0.264986i
\(781\) 92.5401i 3.31135i
\(782\) 34.9764 + 19.1149i 1.25075 + 0.683548i
\(783\) −2.06703 −0.0738698
\(784\) −27.7879 3.43956i −0.992426 0.122842i
\(785\) −2.91713 −0.104117
\(786\) −35.1343 19.2012i −1.25320 0.684885i
\(787\) 12.7886i 0.455864i 0.973677 + 0.227932i \(0.0731964\pi\)
−0.973677 + 0.227932i \(0.926804\pi\)
\(788\) −35.7281 + 22.9247i −1.27276 + 0.816657i
\(789\) −9.48642 −0.337725
\(790\) −5.93167 + 10.8537i −0.211039 + 0.386159i
\(791\) −19.4366 14.2328i −0.691087 0.506059i
\(792\) 0.485087 + 6.88706i 0.0172368 + 0.244721i
\(793\) −23.7380 −0.842960
\(794\) −0.890962 0.486919i −0.0316191 0.0172801i
\(795\) 16.4651 0.583957
\(796\) −19.3996 30.2342i −0.687600 1.07162i
\(797\) −27.5991 −0.977609 −0.488805 0.872393i \(-0.662567\pi\)
−0.488805 + 0.872393i \(0.662567\pi\)
\(798\) −11.6085 24.7488i −0.410935 0.876099i
\(799\) 20.9424i 0.740890i
\(800\) 4.53465 3.38186i 0.160324 0.119567i
\(801\) 0.790151i 0.0279186i
\(802\) 26.2020 + 14.3196i 0.925223 + 0.505643i
\(803\) 52.7771i 1.86247i
\(804\) 2.12181 1.36144i 0.0748304 0.0480144i
\(805\) −8.12649 + 11.0977i −0.286421 + 0.391144i
\(806\) −15.5018 8.47189i −0.546028 0.298410i
\(807\) 21.4986i 0.756786i
\(808\) −3.23957 45.9940i −0.113968 1.61806i
\(809\) −19.2283 −0.676030 −0.338015 0.941141i \(-0.609755\pi\)
−0.338015 + 0.941141i \(0.609755\pi\)
\(810\) 9.45421 + 5.16681i 0.332187 + 0.181543i
\(811\) 7.93942i 0.278791i 0.990237 + 0.139395i \(0.0445159\pi\)
−0.990237 + 0.139395i \(0.955484\pi\)
\(812\) −1.99015 0.122701i −0.0698407 0.00430597i
\(813\) 39.9301i 1.40041i
\(814\) 1.51908 2.77960i 0.0532437 0.0974250i
\(815\) −7.14397 −0.250242
\(816\) 14.5553 31.7503i 0.509536 1.11148i
\(817\) 22.5213i 0.787921i
\(818\) 0.736596 1.34782i 0.0257545 0.0471254i
\(819\) 3.68409 + 2.69773i 0.128733 + 0.0942664i
\(820\) 9.68833 6.21644i 0.338331 0.217088i
\(821\) 26.3775i 0.920582i 0.887768 + 0.460291i \(0.152255\pi\)
−0.887768 + 0.460291i \(0.847745\pi\)
\(822\) −0.838224 + 1.53378i −0.0292364 + 0.0534967i
\(823\) 21.7419i 0.757875i −0.925422 0.378938i \(-0.876289\pi\)
0.925422 0.378938i \(-0.123711\pi\)
\(824\) −2.36365 33.5581i −0.0823416 1.16905i
\(825\) 9.69116i 0.337403i
\(826\) 35.8520 16.8164i 1.24745 0.585118i
\(827\) 57.4711 1.99846 0.999232 0.0391762i \(-0.0124734\pi\)
0.999232 + 0.0391762i \(0.0124734\pi\)
\(828\) −3.55032 + 2.27804i −0.123382 + 0.0791672i
\(829\) 7.16668 0.248909 0.124455 0.992225i \(-0.460282\pi\)
0.124455 + 0.992225i \(0.460282\pi\)
\(830\) −5.71554 + 10.4583i −0.198389 + 0.363012i
\(831\) 3.36740 0.116814
\(832\) −33.6969 + 4.77051i −1.16823 + 0.165388i
\(833\) −36.1779 + 11.4568i −1.25349 + 0.396955i
\(834\) 4.03472 + 2.20501i 0.139711 + 0.0763533i
\(835\) 6.26796 0.216912
\(836\) −45.9393 + 29.4766i −1.58884 + 1.01947i
\(837\) 16.1074i 0.556753i
\(838\) −0.141140 + 0.258257i −0.00487559 + 0.00892133i
\(839\) 12.0764 0.416922 0.208461 0.978031i \(-0.433155\pi\)
0.208461 + 0.978031i \(0.433155\pi\)
\(840\) 10.2011 + 6.42024i 0.351970 + 0.221519i
\(841\) 28.8580 0.995104
\(842\) −6.43288 + 11.7708i −0.221692 + 0.405650i
\(843\) 6.59061i 0.226993i
\(844\) −8.03184 12.5176i −0.276467 0.430874i
\(845\) 5.09746 0.175358
\(846\) −1.94488 1.06289i −0.0668662 0.0365430i
\(847\) 53.7966 + 39.3934i 1.84847 + 1.35357i
\(848\) 37.1700 + 17.0398i 1.27642 + 0.585149i
\(849\) −9.53998 −0.327411
\(850\) 3.67672 6.72765i 0.126111 0.230757i
\(851\) 1.93537 0.0663436
\(852\) 26.7563 + 41.6998i 0.916657 + 1.42861i
\(853\) 40.3302 1.38088 0.690440 0.723390i \(-0.257417\pi\)
0.690440 + 0.723390i \(0.257417\pi\)
\(854\) 8.86619 + 18.9024i 0.303395 + 0.646827i
\(855\) 1.84018i 0.0629327i
\(856\) −2.08254 29.5671i −0.0711798 1.01058i
\(857\) 13.5485i 0.462810i 0.972858 + 0.231405i \(0.0743322\pi\)
−0.972858 + 0.231405i \(0.925668\pi\)
\(858\) −27.9607 + 51.1623i −0.954561 + 1.74665i
\(859\) 24.4181i 0.833136i 0.909105 + 0.416568i \(0.136767\pi\)
−0.909105 + 0.416568i \(0.863233\pi\)
\(860\) −5.36270 8.35776i −0.182866 0.284997i
\(861\) 19.7890 + 14.4908i 0.674409 + 0.493846i
\(862\) 9.28465 16.9890i 0.316236 0.578648i
\(863\) 33.4276i 1.13789i −0.822376 0.568945i \(-0.807352\pi\)
0.822376 0.568945i \(-0.192648\pi\)
\(864\) 18.5512 + 24.8748i 0.631124 + 0.846258i
\(865\) 9.11366 0.309874
\(866\) −4.39754 + 8.04659i −0.149434 + 0.273434i
\(867\) 19.9561i 0.677743i
\(868\) −0.956152 + 15.5083i −0.0324539 + 0.526386i
\(869\) 52.6234i 1.78513i
\(870\) 0.753195 + 0.411628i 0.0255357 + 0.0139555i
\(871\) −3.32925 −0.112807
\(872\) −1.90953 + 0.134497i −0.0646649 + 0.00455464i
\(873\) 1.27541i 0.0431660i
\(874\) −29.2643 15.9932i −0.989879 0.540978i
\(875\) 2.13463 + 1.56312i 0.0721638 + 0.0528430i
\(876\) 15.2596 + 23.7821i 0.515573 + 0.803521i
\(877\) 33.1528i 1.11949i −0.828664 0.559746i \(-0.810899\pi\)
0.828664 0.559746i \(-0.189101\pi\)
\(878\) −11.2236 6.13378i −0.378777 0.207005i
\(879\) 15.2100i 0.513019i
\(880\) 10.0294 21.8778i 0.338092 0.737502i
\(881\) 52.3710i 1.76442i −0.470853 0.882212i \(-0.656054\pi\)
0.470853 0.882212i \(-0.343946\pi\)
\(882\) 0.772173 3.94123i 0.0260004 0.132708i
\(883\) 3.17165 0.106735 0.0533673 0.998575i \(-0.483005\pi\)
0.0533673 + 0.998575i \(0.483005\pi\)
\(884\) −38.8209 + 24.9091i −1.30569 + 0.837784i
\(885\) −17.0468 −0.573020
\(886\) −10.7502 5.87507i −0.361159 0.197377i
\(887\) −36.3723 −1.22126 −0.610632 0.791915i \(-0.709084\pi\)
−0.610632 + 0.791915i \(0.709084\pi\)
\(888\) −0.119157 1.69174i −0.00399864 0.0567711i
\(889\) −5.84798 + 7.98615i −0.196135 + 0.267847i
\(890\) −1.32091 + 2.41700i −0.0442771 + 0.0810181i
\(891\) 45.8379 1.53563
\(892\) −25.7749 40.1701i −0.863006 1.34499i
\(893\) 17.5223i 0.586360i
\(894\) −8.46039 4.62368i −0.282958 0.154639i
\(895\) 10.9518 0.366080
\(896\) 16.3846 + 25.0508i 0.547371 + 0.836890i
\(897\) −35.6230 −1.18942
\(898\) 32.9863 + 18.0273i 1.10077 + 0.601579i
\(899\) 1.10647i 0.0369029i
\(900\) 0.438177 + 0.682898i 0.0146059 + 0.0227633i
\(901\) 55.4182 1.84625
\(902\) 23.4865 42.9755i 0.782016 1.43093i
\(903\) 12.5007 17.0713i 0.415998 0.568097i
\(904\) 1.80948 + 25.6902i 0.0601824 + 0.854445i
\(905\) −18.7975 −0.624850
\(906\) 1.25080 + 0.683576i 0.0415552 + 0.0227103i
\(907\) −13.5038 −0.448388 −0.224194 0.974545i \(-0.571975\pi\)
−0.224194 + 0.974545i \(0.571975\pi\)
\(908\) 20.4152 13.0992i 0.677501 0.434713i
\(909\) 6.61347 0.219355
\(910\) −6.75945 14.4109i −0.224073 0.477717i
\(911\) 6.93039i 0.229614i 0.993388 + 0.114807i \(0.0366250\pi\)
−0.993388 + 0.114807i \(0.963375\pi\)
\(912\) −12.1782 + 26.5651i −0.403260 + 0.879658i
\(913\) 50.7060i 1.67813i
\(914\) −41.4529 22.6544i −1.37114 0.749342i
\(915\) 8.98763i 0.297122i
\(916\) −17.7133 27.6061i −0.585262 0.912131i
\(917\) 27.4756 37.5214i 0.907325 1.23907i
\(918\) 36.9045 + 20.1687i 1.21803 + 0.665665i
\(919\) 18.9826i 0.626178i 0.949724 + 0.313089i \(0.101364\pi\)
−0.949724 + 0.313089i \(0.898636\pi\)
\(920\) 14.6684 1.03316i 0.483601 0.0340622i
\(921\) −38.8504 −1.28017
\(922\) 12.0423 + 6.58123i 0.396592 + 0.216741i
\(923\) 65.4295i 2.15364i
\(924\) 51.1836 + 3.15569i 1.68382 + 0.103814i
\(925\) 0.372265i 0.0122400i
\(926\) −19.3975 + 35.4935i −0.637442 + 1.16639i
\(927\) 4.82531 0.158484
\(928\) 1.27434 + 1.70874i 0.0418324 + 0.0560920i
\(929\) 55.6476i 1.82574i 0.408250 + 0.912870i \(0.366139\pi\)
−0.408250 + 0.912870i \(0.633861\pi\)
\(930\) 3.20761 5.86928i 0.105182 0.192461i
\(931\) 30.2696 9.58577i 0.992046 0.314161i
\(932\) −28.5255 44.4569i −0.934383 1.45624i
\(933\) 26.7289i 0.875064i
\(934\) 5.84009 10.6862i 0.191094 0.349662i
\(935\) 32.6185i 1.06674i
\(936\) −0.342975 4.86942i −0.0112105 0.159162i
\(937\) 30.8690i 1.00845i −0.863574 0.504223i \(-0.831779\pi\)
0.863574 0.504223i \(-0.168221\pi\)
\(938\) 1.24348 + 2.65106i 0.0406012 + 0.0865603i
\(939\) 18.3410 0.598537
\(940\) 4.17234 + 6.50259i 0.136087 + 0.212091i
\(941\) 14.1430 0.461048 0.230524 0.973067i \(-0.425956\pi\)
0.230524 + 0.973067i \(0.425956\pi\)
\(942\) −3.18661 + 5.83084i −0.103825 + 0.189979i
\(943\) 29.9228 0.974420
\(944\) −38.4831 17.6418i −1.25252 0.574190i
\(945\) −8.57449 + 11.7095i −0.278928 + 0.380911i
\(946\) −37.0734 20.2610i −1.20536 0.658741i
\(947\) 10.5002 0.341212 0.170606 0.985339i \(-0.445428\pi\)
0.170606 + 0.985339i \(0.445428\pi\)
\(948\) 15.2151 + 23.7128i 0.494165 + 0.770156i
\(949\) 37.3155i 1.21131i
\(950\) −3.07627 + 5.62894i −0.0998073 + 0.182627i
\(951\) −43.0188 −1.39498
\(952\) 34.3347 + 21.6092i 1.11279 + 0.700359i
\(953\) 36.8415 1.19341 0.596706 0.802460i \(-0.296476\pi\)
0.596706 + 0.802460i \(0.296476\pi\)
\(954\) −2.81264 + 5.14656i −0.0910627 + 0.166626i
\(955\) 1.13019i 0.0365721i
\(956\) 2.84323 1.82434i 0.0919566 0.0590033i
\(957\) 3.65180 0.118046
\(958\) 8.38581 + 4.58293i 0.270933 + 0.148068i
\(959\) −1.63799 1.19944i −0.0528933 0.0387319i
\(960\) −1.80621 12.7583i −0.0582950 0.411771i
\(961\) −22.3778 −0.721865
\(962\) −1.07405 + 1.96529i −0.0346287 + 0.0633635i
\(963\) 4.25144 0.137001
\(964\) −8.83924 + 5.67163i −0.284693 + 0.182671i
\(965\) −3.27357 −0.105380
\(966\) 13.3053 + 28.3664i 0.428090 + 0.912674i
\(967\) 48.0941i 1.54660i −0.634040 0.773301i \(-0.718604\pi\)
0.634040 0.773301i \(-0.281396\pi\)
\(968\) −5.00827 71.1053i −0.160972 2.28541i
\(969\) 39.6069i 1.27236i
\(970\) −2.13213 + 3.90136i −0.0684585 + 0.125265i
\(971\) 13.7904i 0.442555i 0.975211 + 0.221277i \(0.0710226\pi\)
−0.975211 + 0.221277i \(0.928977\pi\)
\(972\) −7.04584 + 4.52091i −0.225996 + 0.145008i
\(973\) −3.15522 + 4.30884i −0.101152 + 0.138135i
\(974\) −5.23939 + 9.58700i −0.167881 + 0.307187i
\(975\) 6.85203i 0.219441i
\(976\) 9.30134 20.2896i 0.297729 0.649455i
\(977\) 19.9730 0.638992 0.319496 0.947588i \(-0.396486\pi\)
0.319496 + 0.947588i \(0.396486\pi\)
\(978\) −7.80393 + 14.2796i −0.249542 + 0.456611i
\(979\) 11.7186i 0.374529i
\(980\) −8.95066 + 10.7650i −0.285918 + 0.343876i
\(981\) 0.274571i 0.00876638i
\(982\) 41.1569 + 22.4926i 1.31337 + 0.717769i
\(983\) 50.8845 1.62296 0.811482 0.584377i \(-0.198661\pi\)
0.811482 + 0.584377i \(0.198661\pi\)
\(984\) −1.84229 26.1560i −0.0587300 0.833824i
\(985\) 21.2252i 0.676291i
\(986\) 2.53510 + 1.38546i 0.0807340 + 0.0441219i
\(987\) −9.72593 + 13.2820i −0.309580 + 0.422770i
\(988\) 32.4809 20.8411i 1.03336 0.663045i
\(989\) 25.8133i 0.820815i
\(990\) 3.02920 + 1.65549i 0.0962744 + 0.0526149i
\(991\) 41.0233i 1.30315i 0.758585 + 0.651574i \(0.225891\pi\)
−0.758585 + 0.651574i \(0.774109\pi\)
\(992\) 13.3153 9.93034i 0.422763 0.315289i
\(993\) 5.24060i 0.166305i
\(994\) −52.1012 + 24.4381i −1.65255 + 0.775129i
\(995\) −17.9614 −0.569416
\(996\) 14.6608 + 22.8488i 0.464544 + 0.723992i
\(997\) −29.5605 −0.936189 −0.468095 0.883678i \(-0.655059\pi\)
−0.468095 + 0.883678i \(0.655059\pi\)
\(998\) 11.3365 + 6.19548i 0.358849 + 0.196114i
\(999\) 2.04206 0.0646079
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 280.2.h.b.251.3 yes 16
4.3 odd 2 1120.2.h.b.111.5 16
7.6 odd 2 280.2.h.a.251.3 16
8.3 odd 2 280.2.h.a.251.4 yes 16
8.5 even 2 1120.2.h.a.111.5 16
28.27 even 2 1120.2.h.a.111.12 16
56.13 odd 2 1120.2.h.b.111.12 16
56.27 even 2 inner 280.2.h.b.251.4 yes 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
280.2.h.a.251.3 16 7.6 odd 2
280.2.h.a.251.4 yes 16 8.3 odd 2
280.2.h.b.251.3 yes 16 1.1 even 1 trivial
280.2.h.b.251.4 yes 16 56.27 even 2 inner
1120.2.h.a.111.5 16 8.5 even 2
1120.2.h.a.111.12 16 28.27 even 2
1120.2.h.b.111.5 16 4.3 odd 2
1120.2.h.b.111.12 16 56.13 odd 2