Properties

Label 280.2.b.c.141.4
Level $280$
Weight $2$
Character 280.141
Analytic conductor $2.236$
Analytic rank $0$
Dimension $8$
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(141,280)]
 
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([0, 1, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("280.141");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 280.b (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: \(8\)
Coefficient field: 8.0.18939904.2
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 4x^{7} + 14x^{6} - 28x^{5} + 43x^{4} - 44x^{3} + 30x^{2} - 12x + 2 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 141.4
Root \(0.500000 - 0.691860i\) of defining polynomial
Character \(\chi\) \(=\) 280.141
Dual form 280.2.b.c.141.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.635665 + 1.26330i) q^{2} -0.414214i q^{3} +(-1.19186 - 1.60607i) q^{4} +1.00000i q^{5} +(0.523276 + 0.263301i) q^{6} -1.00000 q^{7} +(2.78658 - 0.484753i) q^{8} +2.82843 q^{9} +O(q^{10})\) \(q+(-0.635665 + 1.26330i) q^{2} -0.414214i q^{3} +(-1.19186 - 1.60607i) q^{4} +1.00000i q^{5} +(0.523276 + 0.263301i) q^{6} -1.00000 q^{7} +(2.78658 - 0.484753i) q^{8} +2.82843 q^{9} +(-1.26330 - 0.635665i) q^{10} +6.37109i q^{11} +(-0.665257 + 0.493684i) q^{12} -0.573155i q^{13} +(0.635665 - 1.26330i) q^{14} +0.414214 q^{15} +(-1.15894 + 3.82843i) q^{16} +0.638991 q^{17} +(-1.79793 + 3.57316i) q^{18} +6.11582i q^{19} +(1.60607 - 1.19186i) q^{20} +0.414214i q^{21} +(-8.04860 - 4.04988i) q^{22} +4.62636 q^{23} +(-0.200791 - 1.15424i) q^{24} -1.00000 q^{25} +(0.724068 + 0.364335i) q^{26} -2.41421i q^{27} +(1.19186 + 1.60607i) q^{28} +1.60850i q^{29} +(-0.263301 + 0.523276i) q^{30} -4.08370 q^{31} +(-4.09976 - 3.89769i) q^{32} +2.63899 q^{33} +(-0.406184 + 0.807238i) q^{34} -1.00000i q^{35} +(-3.37109 - 4.54266i) q^{36} -2.96951i q^{37} +(-7.72612 - 3.88761i) q^{38} -0.237409 q^{39} +(0.484753 + 2.78658i) q^{40} +8.11582 q^{41} +(-0.523276 - 0.263301i) q^{42} -2.08370i q^{43} +(10.2324 - 7.59344i) q^{44} +2.82843i q^{45} +(-2.94082 + 5.84449i) q^{46} -8.45479 q^{47} +(1.58579 + 0.480049i) q^{48} +1.00000 q^{49} +(0.635665 - 1.26330i) q^{50} -0.264679i q^{51} +(-0.920529 + 0.683121i) q^{52} -0.317883i q^{53} +(3.04988 + 1.53463i) q^{54} -6.37109 q^{55} +(-2.78658 + 0.484753i) q^{56} +2.53325 q^{57} +(-2.03202 - 1.02247i) q^{58} -6.37887i q^{59} +(-0.493684 - 0.665257i) q^{60} -8.44700i q^{61} +(2.59587 - 5.15894i) q^{62} -2.82843 q^{63} +(7.53003 - 2.70160i) q^{64} +0.573155 q^{65} +(-1.67751 + 3.33384i) q^{66} +4.31788i q^{67} +(-0.761588 - 1.02627i) q^{68} -1.91630i q^{69} +(1.26330 + 0.635665i) q^{70} +13.1917 q^{71} +(7.88163 - 1.37109i) q^{72} +15.1917 q^{73} +(3.75138 + 1.88761i) q^{74} +0.414214i q^{75} +(9.82245 - 7.28919i) q^{76} -6.37109i q^{77} +(0.150912 - 0.299919i) q^{78} -3.80801 q^{79} +(-3.82843 - 1.15894i) q^{80} +7.48528 q^{81} +(-5.15894 + 10.2527i) q^{82} -12.4243i q^{83} +(0.665257 - 0.493684i) q^{84} +0.638991i q^{85} +(2.63234 + 1.32453i) q^{86} +0.666261 q^{87} +(3.08840 + 17.7535i) q^{88} -6.54011 q^{89} +(-3.57316 - 1.79793i) q^{90} +0.573155i q^{91} +(-5.51397 - 7.43027i) q^{92} +1.69152i q^{93} +(5.37441 - 10.6809i) q^{94} -6.11582 q^{95} +(-1.61448 + 1.69818i) q^{96} -17.3559 q^{97} +(-0.635665 + 1.26330i) q^{98} +18.0202i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 4 q^{4} - 8 q^{7} + 12 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 4 q^{4} - 8 q^{7} + 12 q^{8} - 4 q^{10} - 12 q^{12} - 8 q^{15} - 8 q^{17} + 8 q^{18} - 4 q^{20} - 4 q^{22} - 8 q^{23} + 20 q^{24} - 8 q^{25} - 20 q^{26} + 4 q^{28} + 4 q^{30} - 8 q^{31} + 8 q^{33} + 4 q^{34} + 16 q^{36} + 16 q^{38} - 32 q^{39} + 4 q^{40} + 24 q^{41} + 20 q^{44} + 24 q^{48} + 8 q^{49} - 12 q^{52} + 8 q^{54} - 8 q^{55} - 12 q^{56} - 8 q^{57} - 32 q^{58} + 12 q^{60} - 24 q^{62} + 8 q^{64} - 16 q^{65} + 4 q^{66} - 20 q^{68} + 4 q^{70} + 16 q^{71} + 16 q^{72} + 32 q^{73} + 16 q^{74} + 8 q^{76} - 4 q^{78} + 48 q^{79} - 8 q^{80} - 8 q^{81} - 32 q^{82} + 12 q^{84} + 24 q^{86} - 32 q^{87} + 4 q^{88} + 56 q^{89} - 8 q^{90} - 8 q^{94} - 8 q^{95} - 48 q^{96} + 24 q^{97}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.635665 + 1.26330i −0.449483 + 0.893289i
\(3\) 0.414214i 0.239146i −0.992825 0.119573i \(-0.961847\pi\)
0.992825 0.119573i \(-0.0381526\pi\)
\(4\) −1.19186 1.60607i −0.595930 0.803037i
\(5\) 1.00000i 0.447214i
\(6\) 0.523276 + 0.263301i 0.213627 + 0.107492i
\(7\) −1.00000 −0.377964
\(8\) 2.78658 0.484753i 0.985204 0.171386i
\(9\) 2.82843 0.942809
\(10\) −1.26330 0.635665i −0.399491 0.201015i
\(11\) 6.37109i 1.92096i 0.278357 + 0.960478i \(0.410210\pi\)
−0.278357 + 0.960478i \(0.589790\pi\)
\(12\) −0.665257 + 0.493684i −0.192043 + 0.142514i
\(13\) 0.573155i 0.158965i −0.996836 0.0794823i \(-0.974673\pi\)
0.996836 0.0794823i \(-0.0253267\pi\)
\(14\) 0.635665 1.26330i 0.169889 0.337631i
\(15\) 0.414214 0.106949
\(16\) −1.15894 + 3.82843i −0.289735 + 0.957107i
\(17\) 0.638991 0.154978 0.0774890 0.996993i \(-0.475310\pi\)
0.0774890 + 0.996993i \(0.475310\pi\)
\(18\) −1.79793 + 3.57316i −0.423777 + 0.842201i
\(19\) 6.11582i 1.40306i 0.712638 + 0.701532i \(0.247500\pi\)
−0.712638 + 0.701532i \(0.752500\pi\)
\(20\) 1.60607 1.19186i 0.359129 0.266508i
\(21\) 0.414214i 0.0903888i
\(22\) −8.04860 4.04988i −1.71597 0.863437i
\(23\) 4.62636 0.964663 0.482331 0.875989i \(-0.339790\pi\)
0.482331 + 0.875989i \(0.339790\pi\)
\(24\) −0.200791 1.15424i −0.0409863 0.235608i
\(25\) −1.00000 −0.200000
\(26\) 0.724068 + 0.364335i 0.142001 + 0.0714519i
\(27\) 2.41421i 0.464616i
\(28\) 1.19186 + 1.60607i 0.225240 + 0.303519i
\(29\) 1.60850i 0.298690i 0.988785 + 0.149345i \(0.0477166\pi\)
−0.988785 + 0.149345i \(0.952283\pi\)
\(30\) −0.263301 + 0.523276i −0.0480720 + 0.0955368i
\(31\) −4.08370 −0.733454 −0.366727 0.930329i \(-0.619522\pi\)
−0.366727 + 0.930329i \(0.619522\pi\)
\(32\) −4.09976 3.89769i −0.724742 0.689021i
\(33\) 2.63899 0.459389
\(34\) −0.406184 + 0.807238i −0.0696600 + 0.138440i
\(35\) 1.00000i 0.169031i
\(36\) −3.37109 4.54266i −0.561848 0.757110i
\(37\) 2.96951i 0.488184i −0.969752 0.244092i \(-0.921510\pi\)
0.969752 0.244092i \(-0.0784898\pi\)
\(38\) −7.72612 3.88761i −1.25334 0.630654i
\(39\) −0.237409 −0.0380158
\(40\) 0.484753 + 2.78658i 0.0766461 + 0.440597i
\(41\) 8.11582 1.26748 0.633739 0.773547i \(-0.281519\pi\)
0.633739 + 0.773547i \(0.281519\pi\)
\(42\) −0.523276 0.263301i −0.0807433 0.0406282i
\(43\) 2.08370i 0.317761i −0.987298 0.158881i \(-0.949212\pi\)
0.987298 0.158881i \(-0.0507885\pi\)
\(44\) 10.2324 7.59344i 1.54260 1.14475i
\(45\) 2.82843i 0.421637i
\(46\) −2.94082 + 5.84449i −0.433600 + 0.861722i
\(47\) −8.45479 −1.23326 −0.616629 0.787254i \(-0.711502\pi\)
−0.616629 + 0.787254i \(0.711502\pi\)
\(48\) 1.58579 + 0.480049i 0.228889 + 0.0692892i
\(49\) 1.00000 0.142857
\(50\) 0.635665 1.26330i 0.0898966 0.178658i
\(51\) 0.264679i 0.0370624i
\(52\) −0.920529 + 0.683121i −0.127654 + 0.0947318i
\(53\) 0.317883i 0.0436646i −0.999762 0.0218323i \(-0.993050\pi\)
0.999762 0.0218323i \(-0.00694999\pi\)
\(54\) 3.04988 + 1.53463i 0.415036 + 0.208837i
\(55\) −6.37109 −0.859077
\(56\) −2.78658 + 0.484753i −0.372372 + 0.0647778i
\(57\) 2.53325 0.335538
\(58\) −2.03202 1.02247i −0.266817 0.134256i
\(59\) 6.37887i 0.830458i −0.909717 0.415229i \(-0.863701\pi\)
0.909717 0.415229i \(-0.136299\pi\)
\(60\) −0.493684 0.665257i −0.0637344 0.0858843i
\(61\) 8.44700i 1.08153i −0.841174 0.540764i \(-0.818135\pi\)
0.841174 0.540764i \(-0.181865\pi\)
\(62\) 2.59587 5.15894i 0.329675 0.655186i
\(63\) −2.82843 −0.356348
\(64\) 7.53003 2.70160i 0.941254 0.337700i
\(65\) 0.573155 0.0710912
\(66\) −1.67751 + 3.33384i −0.206488 + 0.410367i
\(67\) 4.31788i 0.527513i 0.964589 + 0.263757i \(0.0849616\pi\)
−0.964589 + 0.263757i \(0.915038\pi\)
\(68\) −0.761588 1.02627i −0.0923561 0.124453i
\(69\) 1.91630i 0.230696i
\(70\) 1.26330 + 0.635665i 0.150993 + 0.0759765i
\(71\) 13.1917 1.56557 0.782785 0.622292i \(-0.213798\pi\)
0.782785 + 0.622292i \(0.213798\pi\)
\(72\) 7.88163 1.37109i 0.928859 0.161584i
\(73\) 15.1917 1.77806 0.889029 0.457851i \(-0.151381\pi\)
0.889029 + 0.457851i \(0.151381\pi\)
\(74\) 3.75138 + 1.88761i 0.436089 + 0.219430i
\(75\) 0.414214i 0.0478293i
\(76\) 9.82245 7.28919i 1.12671 0.836128i
\(77\) 6.37109i 0.726053i
\(78\) 0.150912 0.299919i 0.0170875 0.0339591i
\(79\) −3.80801 −0.428435 −0.214217 0.976786i \(-0.568720\pi\)
−0.214217 + 0.976786i \(0.568720\pi\)
\(80\) −3.82843 1.15894i −0.428031 0.129574i
\(81\) 7.48528 0.831698
\(82\) −5.15894 + 10.2527i −0.569710 + 1.13222i
\(83\) 12.4243i 1.36374i −0.731472 0.681872i \(-0.761166\pi\)
0.731472 0.681872i \(-0.238834\pi\)
\(84\) 0.665257 0.493684i 0.0725855 0.0538654i
\(85\) 0.638991i 0.0693083i
\(86\) 2.63234 + 1.32453i 0.283852 + 0.142828i
\(87\) 0.666261 0.0714307
\(88\) 3.08840 + 17.7535i 0.329225 + 1.89253i
\(89\) −6.54011 −0.693250 −0.346625 0.938004i \(-0.612672\pi\)
−0.346625 + 0.938004i \(0.612672\pi\)
\(90\) −3.57316 1.79793i −0.376644 0.189519i
\(91\) 0.573155i 0.0600830i
\(92\) −5.51397 7.43027i −0.574871 0.774659i
\(93\) 1.69152i 0.175403i
\(94\) 5.37441 10.6809i 0.554328 1.10166i
\(95\) −6.11582 −0.627469
\(96\) −1.61448 + 1.69818i −0.164777 + 0.173319i
\(97\) −17.3559 −1.76223 −0.881113 0.472907i \(-0.843205\pi\)
−0.881113 + 0.472907i \(0.843205\pi\)
\(98\) −0.635665 + 1.26330i −0.0642119 + 0.127613i
\(99\) 18.0202i 1.81109i
\(100\) 1.19186 + 1.60607i 0.119186 + 0.160607i
\(101\) 13.3617i 1.32954i −0.747049 0.664768i \(-0.768530\pi\)
0.747049 0.664768i \(-0.231470\pi\)
\(102\) 0.334369 + 0.168247i 0.0331075 + 0.0166589i
\(103\) −14.8181 −1.46007 −0.730035 0.683410i \(-0.760496\pi\)
−0.730035 + 0.683410i \(0.760496\pi\)
\(104\) −0.277839 1.59714i −0.0272443 0.156613i
\(105\) −0.414214 −0.0404231
\(106\) 0.401582 + 0.202067i 0.0390051 + 0.0196265i
\(107\) 2.57153i 0.248599i 0.992245 + 0.124300i \(0.0396684\pi\)
−0.992245 + 0.124300i \(0.960332\pi\)
\(108\) −3.87740 + 2.87740i −0.373103 + 0.276878i
\(109\) 13.6442i 1.30688i 0.756979 + 0.653440i \(0.226675\pi\)
−0.756979 + 0.653440i \(0.773325\pi\)
\(110\) 4.04988 8.04860i 0.386141 0.767404i
\(111\) −1.23001 −0.116747
\(112\) 1.15894 3.82843i 0.109510 0.361752i
\(113\) 1.83005 0.172157 0.0860783 0.996288i \(-0.472566\pi\)
0.0860783 + 0.996288i \(0.472566\pi\)
\(114\) −1.61030 + 3.20026i −0.150819 + 0.299732i
\(115\) 4.62636i 0.431410i
\(116\) 2.58336 1.91710i 0.239859 0.177998i
\(117\) 1.62113i 0.149873i
\(118\) 8.05844 + 4.05483i 0.741839 + 0.373277i
\(119\) −0.638991 −0.0585762
\(120\) 1.15424 0.200791i 0.105367 0.0183296i
\(121\) −29.5908 −2.69007
\(122\) 10.6711 + 5.36947i 0.966117 + 0.486129i
\(123\) 3.36168i 0.303113i
\(124\) 4.86720 + 6.55872i 0.437087 + 0.588990i
\(125\) 1.00000i 0.0894427i
\(126\) 1.79793 3.57316i 0.160173 0.318322i
\(127\) 3.91375 0.347289 0.173645 0.984808i \(-0.444446\pi\)
0.173645 + 0.984808i \(0.444446\pi\)
\(128\) −1.37364 + 11.2300i −0.121414 + 0.992602i
\(129\) −0.863096 −0.0759914
\(130\) −0.364335 + 0.724068i −0.0319543 + 0.0635049i
\(131\) 10.1970i 0.890913i −0.895304 0.445456i \(-0.853041\pi\)
0.895304 0.445456i \(-0.146959\pi\)
\(132\) −3.14531 4.23841i −0.273764 0.368906i
\(133\) 6.11582i 0.530308i
\(134\) −5.45479 2.74473i −0.471222 0.237108i
\(135\) 2.41421 0.207782
\(136\) 1.78060 0.309753i 0.152685 0.0265611i
\(137\) −3.51217 −0.300065 −0.150032 0.988681i \(-0.547938\pi\)
−0.150032 + 0.988681i \(0.547938\pi\)
\(138\) 2.42087 + 1.21813i 0.206078 + 0.103694i
\(139\) 1.87802i 0.159292i −0.996823 0.0796459i \(-0.974621\pi\)
0.996823 0.0796459i \(-0.0253790\pi\)
\(140\) −1.60607 + 1.19186i −0.135738 + 0.100731i
\(141\) 3.50209i 0.294929i
\(142\) −8.38552 + 16.6651i −0.703698 + 1.39851i
\(143\) 3.65162 0.305364
\(144\) −3.27798 + 10.8284i −0.273165 + 0.902369i
\(145\) −1.60850 −0.133578
\(146\) −9.65685 + 19.1917i −0.799207 + 1.58832i
\(147\) 0.414214i 0.0341638i
\(148\) −4.76924 + 3.53923i −0.392029 + 0.290923i
\(149\) 8.99907i 0.737233i 0.929582 + 0.368616i \(0.120168\pi\)
−0.929582 + 0.368616i \(0.879832\pi\)
\(150\) −0.523276 0.263301i −0.0427253 0.0214984i
\(151\) −10.8732 −0.884846 −0.442423 0.896806i \(-0.645881\pi\)
−0.442423 + 0.896806i \(0.645881\pi\)
\(152\) 2.96466 + 17.0422i 0.240466 + 1.38230i
\(153\) 1.80734 0.146115
\(154\) 8.04860 + 4.04988i 0.648575 + 0.326349i
\(155\) 4.08370i 0.328011i
\(156\) 0.282958 + 0.381296i 0.0226548 + 0.0305281i
\(157\) 11.3390i 0.904948i 0.891777 + 0.452474i \(0.149459\pi\)
−0.891777 + 0.452474i \(0.850541\pi\)
\(158\) 2.42062 4.81067i 0.192574 0.382716i
\(159\) −0.131672 −0.0104422
\(160\) 3.89769 4.09976i 0.308139 0.324114i
\(161\) −4.62636 −0.364608
\(162\) −4.75813 + 9.45616i −0.373834 + 0.742946i
\(163\) 24.0656i 1.88496i −0.334260 0.942481i \(-0.608486\pi\)
0.334260 0.942481i \(-0.391514\pi\)
\(164\) −9.67291 13.0346i −0.755328 1.01783i
\(165\) 2.63899i 0.205445i
\(166\) 15.6956 + 7.89769i 1.21822 + 0.612980i
\(167\) 13.7328 1.06267 0.531337 0.847161i \(-0.321690\pi\)
0.531337 + 0.847161i \(0.321690\pi\)
\(168\) 0.200791 + 1.15424i 0.0154914 + 0.0890514i
\(169\) 12.6715 0.974730
\(170\) −0.807238 0.406184i −0.0619123 0.0311529i
\(171\) 17.2981i 1.32282i
\(172\) −3.34657 + 2.48348i −0.255174 + 0.189363i
\(173\) 19.1648i 1.45708i 0.685005 + 0.728538i \(0.259800\pi\)
−0.685005 + 0.728538i \(0.740200\pi\)
\(174\) −0.423519 + 0.841688i −0.0321069 + 0.0638082i
\(175\) 1.00000 0.0755929
\(176\) −24.3912 7.38372i −1.83856 0.556569i
\(177\) −2.64222 −0.198601
\(178\) 4.15732 8.26213i 0.311604 0.619273i
\(179\) 8.08115i 0.604013i 0.953306 + 0.302007i \(0.0976565\pi\)
−0.953306 + 0.302007i \(0.902344\pi\)
\(180\) 4.54266 3.37109i 0.338590 0.251266i
\(181\) 18.4243i 1.36947i −0.728794 0.684733i \(-0.759919\pi\)
0.728794 0.684733i \(-0.240081\pi\)
\(182\) −0.724068 0.364335i −0.0536715 0.0270063i
\(183\) −3.49886 −0.258643
\(184\) 12.8917 2.24264i 0.950390 0.165330i
\(185\) 2.96951 0.218322
\(186\) −2.13690 1.07524i −0.156685 0.0788406i
\(187\) 4.07107i 0.297706i
\(188\) 10.0769 + 13.5790i 0.734935 + 0.990351i
\(189\) 2.41421i 0.175608i
\(190\) 3.88761 7.72612i 0.282037 0.560511i
\(191\) 17.0860 1.23630 0.618150 0.786061i \(-0.287883\pi\)
0.618150 + 0.786061i \(0.287883\pi\)
\(192\) −1.11904 3.11904i −0.0807598 0.225097i
\(193\) 20.5975 1.48264 0.741320 0.671152i \(-0.234200\pi\)
0.741320 + 0.671152i \(0.234200\pi\)
\(194\) 11.0325 21.9257i 0.792091 1.57418i
\(195\) 0.237409i 0.0170012i
\(196\) −1.19186 1.60607i −0.0851328 0.114720i
\(197\) 15.0662i 1.07342i −0.843766 0.536712i \(-0.819666\pi\)
0.843766 0.536712i \(-0.180334\pi\)
\(198\) −22.7649 11.4548i −1.61783 0.814056i
\(199\) −13.4032 −0.950128 −0.475064 0.879951i \(-0.657575\pi\)
−0.475064 + 0.879951i \(0.657575\pi\)
\(200\) −2.78658 + 0.484753i −0.197041 + 0.0342772i
\(201\) 1.78853 0.126153
\(202\) 16.8798 + 8.49356i 1.18766 + 0.597604i
\(203\) 1.60850i 0.112894i
\(204\) −0.425093 + 0.315460i −0.0297625 + 0.0220866i
\(205\) 8.11582i 0.566833i
\(206\) 9.41934 18.7197i 0.656277 1.30426i
\(207\) 13.0853 0.909493
\(208\) 2.19428 + 0.664253i 0.152146 + 0.0460577i
\(209\) −38.9644 −2.69522
\(210\) 0.263301 0.523276i 0.0181695 0.0361095i
\(211\) 5.54266i 0.381573i −0.981632 0.190786i \(-0.938896\pi\)
0.981632 0.190786i \(-0.0611037\pi\)
\(212\) −0.510544 + 0.378872i −0.0350643 + 0.0260211i
\(213\) 5.46419i 0.374400i
\(214\) −3.24862 1.63463i −0.222071 0.111741i
\(215\) 2.08370 0.142107
\(216\) −1.17030 6.72739i −0.0796286 0.457741i
\(217\) 4.08370 0.277220
\(218\) −17.2368 8.67316i −1.16742 0.587420i
\(219\) 6.29262i 0.425216i
\(220\) 7.59344 + 10.2324i 0.511950 + 0.689870i
\(221\) 0.366241i 0.0246360i
\(222\) 0.781874 1.55387i 0.0524760 0.104289i
\(223\) 18.0052 1.20572 0.602860 0.797847i \(-0.294028\pi\)
0.602860 + 0.797847i \(0.294028\pi\)
\(224\) 4.09976 + 3.89769i 0.273927 + 0.260425i
\(225\) −2.82843 −0.188562
\(226\) −1.16330 + 2.31190i −0.0773815 + 0.153786i
\(227\) 10.3532i 0.687168i 0.939122 + 0.343584i \(0.111641\pi\)
−0.939122 + 0.343584i \(0.888359\pi\)
\(228\) −3.01928 4.06859i −0.199957 0.269449i
\(229\) 18.2089i 1.20328i −0.798768 0.601640i \(-0.794514\pi\)
0.798768 0.601640i \(-0.205486\pi\)
\(230\) −5.84449 2.94082i −0.385374 0.193912i
\(231\) −2.63899 −0.173633
\(232\) 0.779723 + 4.48220i 0.0511913 + 0.294271i
\(233\) −21.8243 −1.42975 −0.714877 0.699250i \(-0.753517\pi\)
−0.714877 + 0.699250i \(0.753517\pi\)
\(234\) 2.04797 + 1.03049i 0.133880 + 0.0673655i
\(235\) 8.45479i 0.551529i
\(236\) −10.2449 + 7.60272i −0.666888 + 0.494895i
\(237\) 1.57733i 0.102459i
\(238\) 0.406184 0.807238i 0.0263290 0.0523255i
\(239\) 19.1924 1.24145 0.620727 0.784027i \(-0.286838\pi\)
0.620727 + 0.784027i \(0.286838\pi\)
\(240\) −0.480049 + 1.58579i −0.0309871 + 0.102362i
\(241\) 10.5369 0.678739 0.339370 0.940653i \(-0.389786\pi\)
0.339370 + 0.940653i \(0.389786\pi\)
\(242\) 18.8098 37.3820i 1.20914 2.40301i
\(243\) 10.3431i 0.663513i
\(244\) −13.5665 + 10.0676i −0.868506 + 0.644515i
\(245\) 1.00000i 0.0638877i
\(246\) 4.24682 + 2.13690i 0.270767 + 0.136244i
\(247\) 3.50531 0.223038
\(248\) −11.3795 + 1.97958i −0.722602 + 0.125704i
\(249\) −5.14631 −0.326134
\(250\) 1.26330 + 0.635665i 0.0798982 + 0.0402030i
\(251\) 6.57153i 0.414791i 0.978257 + 0.207396i \(0.0664988\pi\)
−0.978257 + 0.207396i \(0.933501\pi\)
\(252\) 3.37109 + 4.54266i 0.212359 + 0.286161i
\(253\) 29.4749i 1.85307i
\(254\) −2.48783 + 4.94424i −0.156101 + 0.310229i
\(255\) 0.264679 0.0165748
\(256\) −13.3137 8.87385i −0.832107 0.554615i
\(257\) 19.3779 1.20876 0.604381 0.796695i \(-0.293420\pi\)
0.604381 + 0.796695i \(0.293420\pi\)
\(258\) 0.548640 1.09035i 0.0341569 0.0678823i
\(259\) 2.96951i 0.184516i
\(260\) −0.683121 0.920529i −0.0423653 0.0570888i
\(261\) 4.54952i 0.281608i
\(262\) 12.8818 + 6.48185i 0.795842 + 0.400450i
\(263\) 17.5096 1.07969 0.539845 0.841765i \(-0.318483\pi\)
0.539845 + 0.841765i \(0.318483\pi\)
\(264\) 7.35375 1.27926i 0.452592 0.0787329i
\(265\) 0.317883 0.0195274
\(266\) 7.72612 + 3.88761i 0.473719 + 0.238365i
\(267\) 2.70900i 0.165788i
\(268\) 6.93484 5.14631i 0.423613 0.314361i
\(269\) 0.661029i 0.0403037i 0.999797 + 0.0201518i \(0.00641496\pi\)
−0.999797 + 0.0201518i \(0.993585\pi\)
\(270\) −1.53463 + 3.04988i −0.0933947 + 0.185610i
\(271\) 10.5722 0.642217 0.321108 0.947042i \(-0.395945\pi\)
0.321108 + 0.947042i \(0.395945\pi\)
\(272\) −0.740553 + 2.44633i −0.0449026 + 0.148331i
\(273\) 0.237409 0.0143686
\(274\) 2.23256 4.43692i 0.134874 0.268044i
\(275\) 6.37109i 0.384191i
\(276\) −3.07772 + 2.28396i −0.185257 + 0.137478i
\(277\) 15.0211i 0.902530i −0.892390 0.451265i \(-0.850973\pi\)
0.892390 0.451265i \(-0.149027\pi\)
\(278\) 2.37251 + 1.19379i 0.142294 + 0.0715990i
\(279\) −11.5504 −0.691507
\(280\) −0.484753 2.78658i −0.0289695 0.166530i
\(281\) −1.97567 −0.117858 −0.0589292 0.998262i \(-0.518769\pi\)
−0.0589292 + 0.998262i \(0.518769\pi\)
\(282\) −4.42419 2.22616i −0.263457 0.132566i
\(283\) 19.0669i 1.13341i −0.823921 0.566705i \(-0.808218\pi\)
0.823921 0.566705i \(-0.191782\pi\)
\(284\) −15.7227 21.1869i −0.932970 1.25721i
\(285\) 2.53325i 0.150057i
\(286\) −2.32121 + 4.61310i −0.137256 + 0.272778i
\(287\) −8.11582 −0.479061
\(288\) −11.5959 11.0243i −0.683293 0.649615i
\(289\) −16.5917 −0.975982
\(290\) 1.02247 2.03202i 0.0600412 0.119324i
\(291\) 7.18905i 0.421430i
\(292\) −18.1064 24.3990i −1.05960 1.42785i
\(293\) 28.7640i 1.68041i 0.542270 + 0.840204i \(0.317565\pi\)
−0.542270 + 0.840204i \(0.682435\pi\)
\(294\) 0.523276 + 0.263301i 0.0305181 + 0.0153560i
\(295\) 6.37887 0.371392
\(296\) −1.43948 8.27476i −0.0836678 0.480961i
\(297\) 15.3812 0.892506
\(298\) −11.3685 5.72040i −0.658562 0.331374i
\(299\) 2.65162i 0.153347i
\(300\) 0.665257 0.493684i 0.0384086 0.0285029i
\(301\) 2.08370i 0.120102i
\(302\) 6.91170 13.7361i 0.397724 0.790423i
\(303\) −5.53459 −0.317954
\(304\) −23.4140 7.08787i −1.34288 0.406517i
\(305\) 8.44700 0.483674
\(306\) −1.14886 + 2.28321i −0.0656761 + 0.130523i
\(307\) 12.5142i 0.714222i −0.934062 0.357111i \(-0.883762\pi\)
0.934062 0.357111i \(-0.116238\pi\)
\(308\) −10.2324 + 7.59344i −0.583047 + 0.432677i
\(309\) 6.13785i 0.349170i
\(310\) 5.15894 + 2.59587i 0.293008 + 0.147435i
\(311\) 18.0617 1.02418 0.512092 0.858931i \(-0.328871\pi\)
0.512092 + 0.858931i \(0.328871\pi\)
\(312\) −0.661558 + 0.115085i −0.0374533 + 0.00651538i
\(313\) −15.7853 −0.892238 −0.446119 0.894974i \(-0.647194\pi\)
−0.446119 + 0.894974i \(0.647194\pi\)
\(314\) −14.3245 7.20779i −0.808380 0.406759i
\(315\) 2.82843i 0.159364i
\(316\) 4.53861 + 6.11594i 0.255317 + 0.344049i
\(317\) 28.0844i 1.57738i 0.614793 + 0.788688i \(0.289239\pi\)
−0.614793 + 0.788688i \(0.710761\pi\)
\(318\) 0.0836990 0.166341i 0.00469361 0.00932793i
\(319\) −10.2479 −0.573771
\(320\) 2.70160 + 7.53003i 0.151024 + 0.420941i
\(321\) 1.06516 0.0594516
\(322\) 2.94082 5.84449i 0.163885 0.325700i
\(323\) 3.90795i 0.217444i
\(324\) −8.92140 12.0219i −0.495634 0.667884i
\(325\) 0.573155i 0.0317929i
\(326\) 30.4021 + 15.2977i 1.68382 + 0.847258i
\(327\) 5.65162 0.312535
\(328\) 22.6154 3.93416i 1.24872 0.217228i
\(329\) 8.45479 0.466127
\(330\) −3.33384 1.67751i −0.183522 0.0923441i
\(331\) 15.8852i 0.873132i 0.899672 + 0.436566i \(0.143805\pi\)
−0.899672 + 0.436566i \(0.856195\pi\)
\(332\) −19.9543 + 14.8080i −1.09514 + 0.812695i
\(333\) 8.39903i 0.460264i
\(334\) −8.72944 + 17.3486i −0.477654 + 0.949274i
\(335\) −4.31788 −0.235911
\(336\) −1.58579 0.480049i −0.0865117 0.0261888i
\(337\) −8.44311 −0.459925 −0.229963 0.973199i \(-0.573860\pi\)
−0.229963 + 0.973199i \(0.573860\pi\)
\(338\) −8.05483 + 16.0079i −0.438125 + 0.870716i
\(339\) 0.758031i 0.0411706i
\(340\) 1.02627 0.761588i 0.0556571 0.0413029i
\(341\) 26.0176i 1.40893i
\(342\) −21.8528 10.9958i −1.18166 0.594586i
\(343\) −1.00000 −0.0539949
\(344\) −1.01008 5.80639i −0.0544598 0.313060i
\(345\) 1.91630 0.103170
\(346\) −24.2110 12.1824i −1.30159 0.654931i
\(347\) 2.89656i 0.155495i 0.996973 + 0.0777477i \(0.0247729\pi\)
−0.996973 + 0.0777477i \(0.975227\pi\)
\(348\) −0.794090 1.07006i −0.0425677 0.0573615i
\(349\) 4.86671i 0.260509i 0.991481 + 0.130254i \(0.0415794\pi\)
−0.991481 + 0.130254i \(0.958421\pi\)
\(350\) −0.635665 + 1.26330i −0.0339777 + 0.0675263i
\(351\) −1.38372 −0.0738575
\(352\) 24.8325 26.1199i 1.32358 1.39220i
\(353\) −3.46742 −0.184552 −0.0922760 0.995733i \(-0.529414\pi\)
−0.0922760 + 0.995733i \(0.529414\pi\)
\(354\) 1.67956 3.33791i 0.0892678 0.177408i
\(355\) 13.1917i 0.700144i
\(356\) 7.79489 + 10.5039i 0.413128 + 0.556705i
\(357\) 0.264679i 0.0140083i
\(358\) −10.2089 5.13690i −0.539558 0.271494i
\(359\) 33.8444 1.78624 0.893120 0.449819i \(-0.148511\pi\)
0.893120 + 0.449819i \(0.148511\pi\)
\(360\) 1.37109 + 7.88163i 0.0722627 + 0.415398i
\(361\) −18.4032 −0.968590
\(362\) 23.2754 + 11.7117i 1.22333 + 0.615552i
\(363\) 12.2569i 0.643320i
\(364\) 0.920529 0.683121i 0.0482488 0.0358052i
\(365\) 15.1917i 0.795172i
\(366\) 2.22411 4.42012i 0.116256 0.231043i
\(367\) −0.762206 −0.0397868 −0.0198934 0.999802i \(-0.506333\pi\)
−0.0198934 + 0.999802i \(0.506333\pi\)
\(368\) −5.36168 + 17.7117i −0.279497 + 0.923285i
\(369\) 22.9550 1.19499
\(370\) −1.88761 + 3.75138i −0.0981322 + 0.195025i
\(371\) 0.317883i 0.0165037i
\(372\) 2.71671 2.01606i 0.140855 0.104528i
\(373\) 19.2621i 0.997355i −0.866788 0.498678i \(-0.833819\pi\)
0.866788 0.498678i \(-0.166181\pi\)
\(374\) −5.14298 2.58784i −0.265937 0.133814i
\(375\) −0.414214 −0.0213899
\(376\) −23.5599 + 4.09848i −1.21501 + 0.211363i
\(377\) 0.921918 0.0474812
\(378\) −3.04988 1.53463i −0.156869 0.0789329i
\(379\) 0.317883i 0.0163286i −0.999967 0.00816428i \(-0.997401\pi\)
0.999967 0.00816428i \(-0.00259880\pi\)
\(380\) 7.28919 + 9.82245i 0.373928 + 0.503881i
\(381\) 1.62113i 0.0830529i
\(382\) −10.8610 + 21.5848i −0.555696 + 1.10437i
\(383\) −34.9835 −1.78757 −0.893787 0.448492i \(-0.851961\pi\)
−0.893787 + 0.448492i \(0.851961\pi\)
\(384\) 4.65162 + 0.568980i 0.237377 + 0.0290357i
\(385\) 6.37109 0.324701
\(386\) −13.0931 + 26.0208i −0.666422 + 1.32443i
\(387\) 5.89359i 0.299588i
\(388\) 20.6858 + 27.8749i 1.05016 + 1.41513i
\(389\) 25.9718i 1.31682i −0.752658 0.658411i \(-0.771229\pi\)
0.752658 0.658411i \(-0.228771\pi\)
\(390\) 0.299919 + 0.150912i 0.0151870 + 0.00764175i
\(391\) 2.95620 0.149502
\(392\) 2.78658 0.484753i 0.140743 0.0244837i
\(393\) −4.22372 −0.213059
\(394\) 19.0332 + 9.57707i 0.958877 + 0.482486i
\(395\) 3.80801i 0.191602i
\(396\) 28.9417 21.4775i 1.45437 1.07928i
\(397\) 24.9314i 1.25127i −0.780116 0.625634i \(-0.784840\pi\)
0.780116 0.625634i \(-0.215160\pi\)
\(398\) 8.51995 16.9323i 0.427067 0.848739i
\(399\) −2.53325 −0.126821
\(400\) 1.15894 3.82843i 0.0579471 0.191421i
\(401\) −7.53905 −0.376482 −0.188241 0.982123i \(-0.560279\pi\)
−0.188241 + 0.982123i \(0.560279\pi\)
\(402\) −1.13690 + 2.25945i −0.0567036 + 0.112691i
\(403\) 2.34059i 0.116593i
\(404\) −21.4598 + 15.9252i −1.06767 + 0.792311i
\(405\) 7.48528i 0.371947i
\(406\) 2.03202 + 1.02247i 0.100847 + 0.0507441i
\(407\) 18.9190 0.937779
\(408\) −0.128304 0.737548i −0.00635198 0.0365141i
\(409\) 16.7064 0.826081 0.413040 0.910713i \(-0.364467\pi\)
0.413040 + 0.910713i \(0.364467\pi\)
\(410\) −10.2527 5.15894i −0.506346 0.254782i
\(411\) 1.45479i 0.0717593i
\(412\) 17.6611 + 23.7989i 0.870099 + 1.17249i
\(413\) 6.37887i 0.313884i
\(414\) −8.31788 + 16.5307i −0.408802 + 0.812440i
\(415\) 12.4243 0.609885
\(416\) −2.23398 + 2.34980i −0.109530 + 0.115208i
\(417\) −0.777902 −0.0380940
\(418\) 24.7683 49.2238i 1.21146 2.40761i
\(419\) 1.40320i 0.0685510i −0.999412 0.0342755i \(-0.989088\pi\)
0.999412 0.0342755i \(-0.0109124\pi\)
\(420\) 0.493684 + 0.665257i 0.0240893 + 0.0324612i
\(421\) 12.5538i 0.611835i 0.952058 + 0.305917i \(0.0989631\pi\)
−0.952058 + 0.305917i \(0.901037\pi\)
\(422\) 7.00205 + 3.52328i 0.340854 + 0.171510i
\(423\) −23.9137 −1.16273
\(424\) −0.154095 0.885806i −0.00748351 0.0430186i
\(425\) −0.638991 −0.0309956
\(426\) 6.90292 + 3.47340i 0.334448 + 0.168287i
\(427\) 8.44700i 0.408779i
\(428\) 4.13007 3.06491i 0.199634 0.148148i
\(429\) 1.51255i 0.0730267i
\(430\) −1.32453 + 2.63234i −0.0638747 + 0.126943i
\(431\) −2.28283 −0.109960 −0.0549800 0.998487i \(-0.517510\pi\)
−0.0549800 + 0.998487i \(0.517510\pi\)
\(432\) 9.24264 + 2.79793i 0.444687 + 0.134616i
\(433\) 20.0357 0.962856 0.481428 0.876486i \(-0.340118\pi\)
0.481428 + 0.876486i \(0.340118\pi\)
\(434\) −2.59587 + 5.15894i −0.124606 + 0.247637i
\(435\) 0.666261i 0.0319448i
\(436\) 21.9136 16.2620i 1.04947 0.778808i
\(437\) 28.2940i 1.35348i
\(438\) 7.94948 + 4.00000i 0.379841 + 0.191127i
\(439\) −7.05681 −0.336803 −0.168402 0.985718i \(-0.553861\pi\)
−0.168402 + 0.985718i \(0.553861\pi\)
\(440\) −17.7535 + 3.08840i −0.846366 + 0.147234i
\(441\) 2.82843 0.134687
\(442\) 0.462673 + 0.232807i 0.0220071 + 0.0110735i
\(443\) 6.36075i 0.302208i −0.988518 0.151104i \(-0.951717\pi\)
0.988518 0.151104i \(-0.0482829\pi\)
\(444\) 1.46600 + 1.97549i 0.0695732 + 0.0937524i
\(445\) 6.54011i 0.310031i
\(446\) −11.4453 + 22.7460i −0.541951 + 1.07706i
\(447\) 3.72754 0.176306
\(448\) −7.53003 + 2.70160i −0.355760 + 0.127639i
\(449\) −1.29907 −0.0613069 −0.0306534 0.999530i \(-0.509759\pi\)
−0.0306534 + 0.999530i \(0.509759\pi\)
\(450\) 1.79793 3.57316i 0.0847554 0.168440i
\(451\) 51.7066i 2.43477i
\(452\) −2.18116 2.93919i −0.102593 0.138248i
\(453\) 4.50382i 0.211608i
\(454\) −13.0792 6.58118i −0.613839 0.308870i
\(455\) −0.573155 −0.0268699
\(456\) 7.05911 1.22800i 0.330573 0.0575065i
\(457\) −9.46809 −0.442899 −0.221449 0.975172i \(-0.571079\pi\)
−0.221449 + 0.975172i \(0.571079\pi\)
\(458\) 23.0034 + 11.5748i 1.07488 + 0.540854i
\(459\) 1.54266i 0.0720052i
\(460\) 7.43027 5.51397i 0.346438 0.257090i
\(461\) 41.7160i 1.94291i 0.237230 + 0.971454i \(0.423761\pi\)
−0.237230 + 0.971454i \(0.576239\pi\)
\(462\) 1.67751 3.33384i 0.0780450 0.155104i
\(463\) −20.6108 −0.957865 −0.478932 0.877852i \(-0.658976\pi\)
−0.478932 + 0.877852i \(0.658976\pi\)
\(464\) −6.15801 1.86415i −0.285879 0.0865412i
\(465\) −1.69152 −0.0784425
\(466\) 13.8729 27.5706i 0.642650 1.27718i
\(467\) 4.26373i 0.197302i −0.995122 0.0986509i \(-0.968547\pi\)
0.995122 0.0986509i \(-0.0314527\pi\)
\(468\) −2.60365 + 1.93216i −0.120354 + 0.0893140i
\(469\) 4.31788i 0.199381i
\(470\) 10.6809 + 5.37441i 0.492675 + 0.247903i
\(471\) 4.69676 0.216415
\(472\) −3.09218 17.7752i −0.142329 0.818171i
\(473\) 13.2754 0.610405
\(474\) −1.99264 1.00265i −0.0915251 0.0460534i
\(475\) 6.11582i 0.280613i
\(476\) 0.761588 + 1.02627i 0.0349073 + 0.0470388i
\(477\) 0.899110i 0.0411674i
\(478\) −12.1999 + 24.2458i −0.558012 + 1.10898i
\(479\) −28.6080 −1.30713 −0.653565 0.756870i \(-0.726728\pi\)
−0.653565 + 0.756870i \(0.726728\pi\)
\(480\) −1.69818 1.61448i −0.0775107 0.0736904i
\(481\) −1.70199 −0.0776040
\(482\) −6.69792 + 13.3112i −0.305082 + 0.606310i
\(483\) 1.91630i 0.0871947i
\(484\) 35.2680 + 47.5249i 1.60309 + 2.16022i
\(485\) 17.3559i 0.788091i
\(486\) 13.0665 + 6.57478i 0.592709 + 0.298238i
\(487\) −21.2949 −0.964964 −0.482482 0.875906i \(-0.660265\pi\)
−0.482482 + 0.875906i \(0.660265\pi\)
\(488\) −4.09471 23.5382i −0.185359 1.06553i
\(489\) −9.96829 −0.450782
\(490\) −1.26330 0.635665i −0.0570701 0.0287164i
\(491\) 20.9018i 0.943285i −0.881790 0.471642i \(-0.843661\pi\)
0.881790 0.471642i \(-0.156339\pi\)
\(492\) −5.39911 + 4.00665i −0.243410 + 0.180634i
\(493\) 1.02781i 0.0462905i
\(494\) −2.22820 + 4.42826i −0.100252 + 0.199237i
\(495\) −18.0202 −0.809946
\(496\) 4.73277 15.6341i 0.212508 0.701994i
\(497\) −13.1917 −0.591730
\(498\) 3.27133 6.50134i 0.146592 0.291332i
\(499\) 37.2449i 1.66731i −0.552284 0.833656i \(-0.686244\pi\)
0.552284 0.833656i \(-0.313756\pi\)
\(500\) −1.60607 + 1.19186i −0.0718258 + 0.0533016i
\(501\) 5.68830i 0.254134i
\(502\) −8.30182 4.17729i −0.370529 0.186442i
\(503\) −2.27182 −0.101295 −0.0506477 0.998717i \(-0.516129\pi\)
−0.0506477 + 0.998717i \(0.516129\pi\)
\(504\) −7.88163 + 1.37109i −0.351076 + 0.0610731i
\(505\) 13.3617 0.594587
\(506\) −37.2357 18.7362i −1.65533 0.832926i
\(507\) 5.24870i 0.233103i
\(508\) −4.66464 6.28577i −0.206960 0.278886i
\(509\) 11.1716i 0.495171i 0.968866 + 0.247586i \(0.0796372\pi\)
−0.968866 + 0.247586i \(0.920363\pi\)
\(510\) −0.168247 + 0.334369i −0.00745011 + 0.0148061i
\(511\) −15.1917 −0.672043
\(512\) 19.6734 11.1784i 0.869450 0.494021i
\(513\) 14.7649 0.651886
\(514\) −12.3179 + 24.4802i −0.543319 + 1.07977i
\(515\) 14.8181i 0.652963i
\(516\) 1.02869 + 1.38620i 0.0452855 + 0.0610239i
\(517\) 53.8662i 2.36903i
\(518\) −3.75138 1.88761i −0.164826 0.0829369i
\(519\) 7.93834 0.348454
\(520\) 1.59714 0.277839i 0.0700393 0.0121840i
\(521\) −26.9593 −1.18111 −0.590554 0.806998i \(-0.701091\pi\)
−0.590554 + 0.806998i \(0.701091\pi\)
\(522\) −5.74741 2.89197i −0.251557 0.126578i
\(523\) 16.5339i 0.722979i 0.932376 + 0.361489i \(0.117732\pi\)
−0.932376 + 0.361489i \(0.882268\pi\)
\(524\) −16.3771 + 12.1533i −0.715436 + 0.530921i
\(525\) 0.414214i 0.0180778i
\(526\) −11.1303 + 22.1199i −0.485302 + 0.964474i
\(527\) −2.60945 −0.113669
\(528\) −3.05844 + 10.1032i −0.133101 + 0.439685i
\(529\) −1.59680 −0.0694259
\(530\) −0.202067 + 0.401582i −0.00877724 + 0.0174436i
\(531\) 18.0422i 0.782964i
\(532\) −9.82245 + 7.28919i −0.425857 + 0.316027i
\(533\) 4.65162i 0.201484i
\(534\) −3.42228 1.72202i −0.148097 0.0745190i
\(535\) −2.57153 −0.111177
\(536\) 2.09311 + 12.0321i 0.0904084 + 0.519708i
\(537\) 3.34732 0.144448
\(538\) −0.835079 0.420193i −0.0360028 0.0181158i
\(539\) 6.37109i 0.274422i
\(540\) −2.87740 3.87740i −0.123824 0.166857i
\(541\) 19.9011i 0.855616i −0.903870 0.427808i \(-0.859286\pi\)
0.903870 0.427808i \(-0.140714\pi\)
\(542\) −6.72040 + 13.3559i −0.288666 + 0.573685i
\(543\) −7.63159 −0.327503
\(544\) −2.61971 2.49059i −0.112319 0.106783i
\(545\) −13.6442 −0.584454
\(546\) −0.150912 + 0.299919i −0.00645846 + 0.0128353i
\(547\) 5.29610i 0.226445i 0.993570 + 0.113223i \(0.0361173\pi\)
−0.993570 + 0.113223i \(0.963883\pi\)
\(548\) 4.18601 + 5.64080i 0.178817 + 0.240963i
\(549\) 23.8917i 1.01967i
\(550\) 8.04860 + 4.04988i 0.343194 + 0.172687i
\(551\) −9.83727 −0.419082
\(552\) −0.928932 5.33992i −0.0395380 0.227282i
\(553\) 3.80801 0.161933
\(554\) 18.9762 + 9.54838i 0.806220 + 0.405672i
\(555\) 1.23001i 0.0522110i
\(556\) −3.01624 + 2.23834i −0.127917 + 0.0949267i
\(557\) 0.114759i 0.00486248i −0.999997 0.00243124i \(-0.999226\pi\)
0.999997 0.00243124i \(-0.000773889\pi\)
\(558\) 7.34222 14.5917i 0.310821 0.617716i
\(559\) −1.19428 −0.0505128
\(560\) 3.82843 + 1.15894i 0.161781 + 0.0489742i
\(561\) 1.68629 0.0711953
\(562\) 1.25586 2.49586i 0.0529754 0.105282i
\(563\) 6.67149i 0.281170i 0.990069 + 0.140585i \(0.0448983\pi\)
−0.990069 + 0.140585i \(0.955102\pi\)
\(564\) 5.62461 4.17400i 0.236839 0.175757i
\(565\) 1.83005i 0.0769908i
\(566\) 24.0872 + 12.1202i 1.01246 + 0.509448i
\(567\) −7.48528 −0.314352
\(568\) 36.7598 6.39473i 1.54241 0.268317i
\(569\) 22.9536 0.962267 0.481134 0.876647i \(-0.340225\pi\)
0.481134 + 0.876647i \(0.340225\pi\)
\(570\) −3.20026 1.61030i −0.134044 0.0674481i
\(571\) 18.4294i 0.771246i −0.922656 0.385623i \(-0.873986\pi\)
0.922656 0.385623i \(-0.126014\pi\)
\(572\) −4.35222 5.86477i −0.181975 0.245218i
\(573\) 7.07725i 0.295656i
\(574\) 5.15894 10.2527i 0.215330 0.427940i
\(575\) −4.62636 −0.192933
\(576\) 21.2981 7.64129i 0.887422 0.318387i
\(577\) 10.7201 0.446285 0.223143 0.974786i \(-0.428368\pi\)
0.223143 + 0.974786i \(0.428368\pi\)
\(578\) 10.5468 20.9603i 0.438687 0.871834i
\(579\) 8.53176i 0.354568i
\(580\) 1.91710 + 2.58336i 0.0796033 + 0.107268i
\(581\) 12.4243i 0.515447i
\(582\) −9.08194 4.56983i −0.376458 0.189426i
\(583\) 2.02526 0.0838778
\(584\) 42.3329 7.36423i 1.75175 0.304734i
\(585\) 1.62113 0.0670254
\(586\) −36.3375 18.2842i −1.50109 0.755315i
\(587\) 33.8444i 1.39691i 0.715655 + 0.698454i \(0.246128\pi\)
−0.715655 + 0.698454i \(0.753872\pi\)
\(588\) −0.665257 + 0.493684i −0.0274347 + 0.0203592i
\(589\) 24.9752i 1.02908i
\(590\) −4.05483 + 8.05844i −0.166935 + 0.331761i
\(591\) −6.24063 −0.256705
\(592\) 11.3685 + 3.44148i 0.467244 + 0.141444i
\(593\) −2.26336 −0.0929452 −0.0464726 0.998920i \(-0.514798\pi\)
−0.0464726 + 0.998920i \(0.514798\pi\)
\(594\) −9.77727 + 19.4310i −0.401166 + 0.797265i
\(595\) 0.638991i 0.0261961i
\(596\) 14.4532 10.7256i 0.592025 0.439339i
\(597\) 5.55179i 0.227220i
\(598\) 3.34980 + 1.68554i 0.136983 + 0.0689270i
\(599\) −26.3290 −1.07577 −0.537887 0.843017i \(-0.680777\pi\)
−0.537887 + 0.843017i \(0.680777\pi\)
\(600\) 0.200791 + 1.15424i 0.00819727 + 0.0471216i
\(601\) −1.06516 −0.0434489 −0.0217245 0.999764i \(-0.506916\pi\)
−0.0217245 + 0.999764i \(0.506916\pi\)
\(602\) −2.63234 1.32453i −0.107286 0.0539840i
\(603\) 12.2128i 0.497344i
\(604\) 12.9593 + 17.4631i 0.527306 + 0.710564i
\(605\) 29.5908i 1.20304i
\(606\) 3.51815 6.99185i 0.142915 0.284025i
\(607\) −6.42494 −0.260780 −0.130390 0.991463i \(-0.541623\pi\)
−0.130390 + 0.991463i \(0.541623\pi\)
\(608\) 23.8376 25.0734i 0.966741 1.01686i
\(609\) −0.666261 −0.0269983
\(610\) −5.36947 + 10.6711i −0.217403 + 0.432061i
\(611\) 4.84591i 0.196044i
\(612\) −2.15409 2.90272i −0.0870741 0.117335i
\(613\) 5.46419i 0.220697i 0.993893 + 0.110348i \(0.0351966\pi\)
−0.993893 + 0.110348i \(0.964803\pi\)
\(614\) 15.8092 + 7.95482i 0.638006 + 0.321031i
\(615\) 3.36168 0.135556
\(616\) −3.08840 17.7535i −0.124435 0.715310i
\(617\) −34.9485 −1.40698 −0.703488 0.710707i \(-0.748375\pi\)
−0.703488 + 0.710707i \(0.748375\pi\)
\(618\) −7.75396 3.90162i −0.311910 0.156946i
\(619\) 1.00848i 0.0405341i 0.999795 + 0.0202671i \(0.00645165\pi\)
−0.999795 + 0.0202671i \(0.993548\pi\)
\(620\) −6.55872 + 4.86720i −0.263405 + 0.195471i
\(621\) 11.1690i 0.448197i
\(622\) −11.4812 + 22.8173i −0.460353 + 0.914892i
\(623\) 6.54011 0.262024
\(624\) 0.275143 0.908902i 0.0110145 0.0363852i
\(625\) 1.00000 0.0400000
\(626\) 10.0342 19.9416i 0.401046 0.797026i
\(627\) 16.1396i 0.644553i
\(628\) 18.2112 13.5145i 0.726707 0.539286i
\(629\) 1.89749i 0.0756578i
\(630\) 3.57316 + 1.79793i 0.142358 + 0.0716314i
\(631\) −38.7566 −1.54287 −0.771437 0.636306i \(-0.780462\pi\)
−0.771437 + 0.636306i \(0.780462\pi\)
\(632\) −10.6113 + 1.84594i −0.422096 + 0.0734277i
\(633\) −2.29585 −0.0912517
\(634\) −35.4790 17.8523i −1.40905 0.709004i
\(635\) 3.91375i 0.155312i
\(636\) 0.156934 + 0.211474i 0.00622284 + 0.00838550i
\(637\) 0.573155i 0.0227092i
\(638\) 6.51422 12.9461i 0.257900 0.512543i
\(639\) 37.3118 1.47603
\(640\) −11.2300 1.37364i −0.443905 0.0542979i
\(641\) 25.5096 1.00757 0.503785 0.863829i \(-0.331941\pi\)
0.503785 + 0.863829i \(0.331941\pi\)
\(642\) −0.677088 + 1.34562i −0.0267225 + 0.0531075i
\(643\) 28.9041i 1.13987i 0.821691 + 0.569933i \(0.193031\pi\)
−0.821691 + 0.569933i \(0.806969\pi\)
\(644\) 5.51397 + 7.43027i 0.217281 + 0.292794i
\(645\) 0.863096i 0.0339844i
\(646\) −4.93692 2.48415i −0.194240 0.0977375i
\(647\) −36.9077 −1.45099 −0.725496 0.688226i \(-0.758390\pi\)
−0.725496 + 0.688226i \(0.758390\pi\)
\(648\) 20.8583 3.62851i 0.819392 0.142541i
\(649\) 40.6404 1.59527
\(650\) −0.724068 0.364335i −0.0284003 0.0142904i
\(651\) 1.69152i 0.0662960i
\(652\) −38.6511 + 28.6828i −1.51369 + 1.12330i
\(653\) 26.8139i 1.04931i 0.851315 + 0.524655i \(0.175806\pi\)
−0.851315 + 0.524655i \(0.824194\pi\)
\(654\) −3.59254 + 7.13970i −0.140479 + 0.279184i
\(655\) 10.1970 0.398428
\(656\) −9.40576 + 31.0708i −0.367233 + 1.21311i
\(657\) 42.9687 1.67637
\(658\) −5.37441 + 10.6809i −0.209516 + 0.416386i
\(659\) 29.6783i 1.15610i −0.816000 0.578052i \(-0.803813\pi\)
0.816000 0.578052i \(-0.196187\pi\)
\(660\) 4.23841 3.14531i 0.164980 0.122431i
\(661\) 32.6812i 1.27115i −0.772039 0.635575i \(-0.780763\pi\)
0.772039 0.635575i \(-0.219237\pi\)
\(662\) −20.0678 10.0977i −0.779959 0.392458i
\(663\) −0.151702 −0.00589162
\(664\) −6.02271 34.6213i −0.233726 1.34357i
\(665\) 6.11582 0.237161
\(666\) 10.6105 + 5.33897i 0.411149 + 0.206881i
\(667\) 7.44148i 0.288135i
\(668\) −16.3675 22.0558i −0.633279 0.853366i
\(669\) 7.45801i 0.288343i
\(670\) 2.74473 5.45479i 0.106038 0.210737i
\(671\) 53.8166 2.07757
\(672\) 1.61448 1.69818i 0.0622798 0.0655085i
\(673\) −33.6084 −1.29551 −0.647754 0.761850i \(-0.724291\pi\)
−0.647754 + 0.761850i \(0.724291\pi\)
\(674\) 5.36699 10.6662i 0.206729 0.410846i
\(675\) 2.41421i 0.0929231i
\(676\) −15.1026 20.3513i −0.580871 0.782744i
\(677\) 18.5122i 0.711480i 0.934585 + 0.355740i \(0.115771\pi\)
−0.934585 + 0.355740i \(0.884229\pi\)
\(678\) 0.957622 + 0.481854i 0.0367772 + 0.0185055i
\(679\) 17.3559 0.666058
\(680\) 0.309753 + 1.78060i 0.0118785 + 0.0682828i
\(681\) 4.28845 0.164334
\(682\) 32.8681 + 16.5385i 1.25858 + 0.633291i
\(683\) 37.9217i 1.45103i −0.688205 0.725516i \(-0.741601\pi\)
0.688205 0.725516i \(-0.258399\pi\)
\(684\) 27.7821 20.6170i 1.06227 0.788309i
\(685\) 3.51217i 0.134193i
\(686\) 0.635665 1.26330i 0.0242698 0.0482331i
\(687\) −7.54238 −0.287760
\(688\) 7.97729 + 2.41489i 0.304131 + 0.0920667i
\(689\) −0.182196 −0.00694113
\(690\) −1.21813 + 2.42087i −0.0463733 + 0.0921608i
\(691\) 12.2822i 0.467235i 0.972329 + 0.233618i \(0.0750564\pi\)
−0.972329 + 0.233618i \(0.924944\pi\)
\(692\) 30.7801 22.8418i 1.17009 0.868315i
\(693\) 18.0202i 0.684529i
\(694\) −3.65922 1.84124i −0.138902 0.0698925i
\(695\) 1.87802 0.0712374
\(696\) 1.85659 0.322972i 0.0703738 0.0122422i
\(697\) 5.18593 0.196431
\(698\) −6.14812 3.09360i −0.232710 0.117094i
\(699\) 9.03990i 0.341920i
\(700\) −1.19186 1.60607i −0.0450481 0.0607039i
\(701\) 33.4919i 1.26497i −0.774572 0.632485i \(-0.782035\pi\)
0.774572 0.632485i \(-0.217965\pi\)
\(702\) 0.879582 1.74805i 0.0331977 0.0659760i
\(703\) 18.1609 0.684953
\(704\) 17.2121 + 47.9745i 0.648707 + 1.80811i
\(705\) −3.50209 −0.131896
\(706\) 2.20412 4.38039i 0.0829530 0.164858i
\(707\) 13.3617i 0.502518i
\(708\) 3.14915 + 4.24359i 0.118352 + 0.159484i
\(709\) 24.2644i 0.911269i 0.890167 + 0.455635i \(0.150588\pi\)
−0.890167 + 0.455635i \(0.849412\pi\)
\(710\) −16.6651 8.38552i −0.625431 0.314703i
\(711\) −10.7707 −0.403932
\(712\) −18.2245 + 3.17034i −0.682993 + 0.118813i
\(713\) −18.8927 −0.707536
\(714\) −0.334369 0.168247i −0.0125134 0.00629649i
\(715\) 3.65162i 0.136563i
\(716\) 12.9789 9.63159i 0.485045 0.359949i
\(717\) 7.94975i 0.296889i
\(718\) −21.5137 + 42.7557i −0.802885 + 1.59563i
\(719\) 48.3258 1.80225 0.901124 0.433561i \(-0.142743\pi\)
0.901124 + 0.433561i \(0.142743\pi\)
\(720\) −10.8284 3.27798i −0.403552 0.122163i
\(721\) 14.8181 0.551855
\(722\) 11.6983 23.2488i 0.435365 0.865230i
\(723\) 4.36451i 0.162318i
\(724\) −29.5908 + 21.9592i −1.09973 + 0.816106i
\(725\) 1.60850i 0.0597381i
\(726\) −15.4841 7.79128i −0.574671 0.289162i
\(727\) −21.6926 −0.804533 −0.402267 0.915523i \(-0.631778\pi\)
−0.402267 + 0.915523i \(0.631778\pi\)
\(728\) 0.277839 + 1.59714i 0.0102974 + 0.0591940i
\(729\) 18.1716 0.673021
\(730\) −19.1917 9.65685i −0.710318 0.357416i
\(731\) 1.33146i 0.0492460i
\(732\) 4.17015 + 5.61943i 0.154133 + 0.207700i
\(733\) 39.6832i 1.46573i 0.680372 + 0.732867i \(0.261818\pi\)
−0.680372 + 0.732867i \(0.738182\pi\)
\(734\) 0.484508 0.962896i 0.0178835 0.0355411i
\(735\) 0.414214 0.0152785
\(736\) −18.9670 18.0321i −0.699131 0.664673i
\(737\) −27.5096 −1.01333
\(738\) −14.5917 + 28.9991i −0.537128 + 1.06747i
\(739\) 7.62891i 0.280634i 0.990107 + 0.140317i \(0.0448122\pi\)
−0.990107 + 0.140317i \(0.955188\pi\)
\(740\) −3.53923 4.76924i −0.130105 0.175321i
\(741\) 1.45195i 0.0533386i
\(742\) −0.401582 0.202067i −0.0147426 0.00741813i
\(743\) −18.0916 −0.663717 −0.331858 0.943329i \(-0.607676\pi\)
−0.331858 + 0.943329i \(0.607676\pi\)
\(744\) 0.819971 + 4.71356i 0.0300616 + 0.172808i
\(745\) −8.99907 −0.329700
\(746\) 24.3339 + 12.2443i 0.890926 + 0.448294i
\(747\) 35.1412i 1.28575i
\(748\) 6.53843 4.85214i 0.239069 0.177412i
\(749\) 2.57153i 0.0939618i
\(750\) 0.263301 0.523276i 0.00961440 0.0191074i
\(751\) −46.8933 −1.71116 −0.855581 0.517669i \(-0.826800\pi\)
−0.855581 + 0.517669i \(0.826800\pi\)
\(752\) 9.79860 32.3685i 0.357318 1.18036i
\(753\) 2.72202 0.0991959
\(754\) −0.586031 + 1.16466i −0.0213420 + 0.0424144i
\(755\) 10.8732i 0.395715i
\(756\) 3.87740 2.87740i 0.141020 0.104650i
\(757\) 14.0299i 0.509924i −0.966951 0.254962i \(-0.917937\pi\)
0.966951 0.254962i \(-0.0820629\pi\)
\(758\) 0.401582 + 0.202067i 0.0145861 + 0.00733942i
\(759\) 12.2089 0.443156
\(760\) −17.0422 + 2.96466i −0.618185 + 0.107539i
\(761\) 39.9447 1.44799 0.723996 0.689804i \(-0.242303\pi\)
0.723996 + 0.689804i \(0.242303\pi\)
\(762\) 2.04797 + 1.03049i 0.0741902 + 0.0373309i
\(763\) 13.6442i 0.493954i
\(764\) −20.3641 27.4414i −0.736747 0.992793i
\(765\) 1.80734i 0.0653445i
\(766\) 22.2378 44.1947i 0.803484 1.59682i
\(767\) −3.65608 −0.132014
\(768\) −3.67567 + 5.51472i −0.132634 + 0.198995i
\(769\) 21.6005 0.778932 0.389466 0.921041i \(-0.372660\pi\)
0.389466 + 0.921041i \(0.372660\pi\)
\(770\) −4.04988 + 8.04860i −0.145947 + 0.290052i
\(771\) 8.02661i 0.289071i
\(772\) −24.5493 33.0811i −0.883549 1.19061i
\(773\) 7.55852i 0.271861i −0.990718 0.135930i \(-0.956598\pi\)
0.990718 0.135930i \(-0.0434024\pi\)
\(774\) 7.44538 + 3.74635i 0.267619 + 0.134660i
\(775\) 4.08370 0.146691
\(776\) −48.3636 + 8.41332i −1.73615 + 0.302021i
\(777\) 1.23001 0.0441263
\(778\) 32.8102 + 16.5094i 1.17630 + 0.591890i
\(779\) 49.6348i 1.77835i
\(780\) −0.381296 + 0.282958i −0.0136526 + 0.0101315i
\(781\) 84.0457i 3.00739i
\(782\) −1.87915 + 3.73457i −0.0671984 + 0.133548i
\(783\) 3.88325 0.138776
\(784\) −1.15894 + 3.82843i −0.0413908 + 0.136730i
\(785\) −11.3390 −0.404705
\(786\) 2.68487 5.33583i 0.0957662 0.190323i
\(787\) 33.0164i 1.17691i −0.808531 0.588453i \(-0.799737\pi\)
0.808531 0.588453i \(-0.200263\pi\)
\(788\) −24.1975 + 17.9568i −0.861999 + 0.639685i
\(789\) 7.25272i 0.258204i
\(790\) 4.81067 + 2.42062i 0.171156 + 0.0861218i
\(791\) −1.83005 −0.0650691
\(792\) 8.73532 + 50.2146i 0.310396 + 1.78430i
\(793\) −4.84144 −0.171925
\(794\) 31.4958 + 15.8480i 1.11774 + 0.562424i
\(795\) 0.131672i 0.00466991i
\(796\) 15.9747 + 21.5265i 0.566210 + 0.762988i
\(797\) 52.2029i 1.84912i 0.381035 + 0.924561i \(0.375568\pi\)
−0.381035 + 0.924561i \(0.624432\pi\)
\(798\) 1.61030 3.20026i 0.0570040 0.113288i
\(799\) −5.40253 −0.191128
\(800\) 4.09976 + 3.89769i 0.144948 + 0.137804i
\(801\) −18.4982 −0.653602
\(802\) 4.79231 9.52409i 0.169222 0.336307i
\(803\) 96.7879i 3.41557i
\(804\) −2.13167 2.87250i −0.0751783 0.101305i
\(805\) 4.62636i 0.163058i
\(806\) −2.95687 1.48783i −0.104151 0.0524067i
\(807\) 0.273807 0.00963847
\(808\) −6.47711 37.2334i −0.227864 1.30987i
\(809\) 24.8852 0.874918 0.437459 0.899238i \(-0.355878\pi\)
0.437459 + 0.899238i \(0.355878\pi\)
\(810\) −9.45616 4.75813i −0.332256 0.167184i
\(811\) 29.2632i 1.02757i −0.857919 0.513785i \(-0.828243\pi\)
0.857919 0.513785i \(-0.171757\pi\)
\(812\) −2.58336 + 1.91710i −0.0906583 + 0.0672771i
\(813\) 4.37916i 0.153584i
\(814\) −12.0261 + 23.9004i −0.421516 + 0.837708i
\(815\) 24.0656 0.842980
\(816\) 1.01330 + 0.306747i 0.0354727 + 0.0107383i
\(817\) 12.7435 0.445839
\(818\) −10.6197 + 21.1053i −0.371309 + 0.737929i
\(819\) 1.62113i 0.0566468i
\(820\) 13.0346 9.67291i 0.455188 0.337793i
\(821\) 10.7833i 0.376340i 0.982136 + 0.188170i \(0.0602556\pi\)
−0.982136 + 0.188170i \(0.939744\pi\)
\(822\) −1.83783 0.924757i −0.0641018 0.0322546i
\(823\) 17.2874 0.602600 0.301300 0.953529i \(-0.402579\pi\)
0.301300 + 0.953529i \(0.402579\pi\)
\(824\) −41.2918 + 7.18311i −1.43847 + 0.250236i
\(825\) −2.63899 −0.0918779
\(826\) −8.05844 4.05483i −0.280389 0.141085i
\(827\) 8.53905i 0.296932i −0.988918 0.148466i \(-0.952566\pi\)
0.988918 0.148466i \(-0.0474335\pi\)
\(828\) −15.5959 21.0160i −0.541994 0.730356i
\(829\) 48.6955i 1.69127i 0.533765 + 0.845633i \(0.320777\pi\)
−0.533765 + 0.845633i \(0.679223\pi\)
\(830\) −7.89769 + 15.6956i −0.274133 + 0.544803i
\(831\) −6.22194 −0.215837
\(832\) −1.54844 4.31588i −0.0536824 0.149626i
\(833\) 0.638991 0.0221397
\(834\) 0.494485 0.982725i 0.0171226 0.0340290i
\(835\) 13.7328i 0.475242i
\(836\) 46.4401 + 62.5797i 1.60616 + 2.16436i
\(837\) 9.85892i 0.340774i
\(838\) 1.77267 + 0.891968i 0.0612359 + 0.0308125i
\(839\) −4.54882 −0.157043 −0.0785214 0.996912i \(-0.525020\pi\)
−0.0785214 + 0.996912i \(0.525020\pi\)
\(840\) −1.15424 + 0.200791i −0.0398250 + 0.00692795i
\(841\) 26.4127 0.910784
\(842\) −15.8592 7.98001i −0.546545 0.275009i
\(843\) 0.818348i 0.0281854i
\(844\) −8.90192 + 6.60607i −0.306417 + 0.227390i
\(845\) 12.6715i 0.435913i
\(846\) 15.2011 30.2103i 0.522626 1.03865i
\(847\) 29.5908 1.01675
\(848\) 1.21699 + 0.368408i 0.0417917 + 0.0126512i
\(849\) −7.89777 −0.271051
\(850\) 0.406184 0.807238i 0.0139320 0.0276880i
\(851\) 13.7380i 0.470933i
\(852\) −8.77589 + 6.51255i −0.300657 + 0.223116i
\(853\) 33.4183i 1.14422i 0.820177 + 0.572110i \(0.193875\pi\)
−0.820177 + 0.572110i \(0.806125\pi\)
\(854\) −10.6711 5.36947i −0.365158 0.183739i
\(855\) −17.2981 −0.591584
\(856\) 1.24656 + 7.16578i 0.0426065 + 0.244921i
\(857\) −16.4925 −0.563373 −0.281687 0.959506i \(-0.590894\pi\)
−0.281687 + 0.959506i \(0.590894\pi\)
\(858\) 1.91081 + 0.961476i 0.0652339 + 0.0328243i
\(859\) 22.4600i 0.766326i −0.923681 0.383163i \(-0.874835\pi\)
0.923681 0.383163i \(-0.125165\pi\)
\(860\) −2.48348 3.34657i −0.0846858 0.114117i
\(861\) 3.36168i 0.114566i
\(862\) 1.45111 2.88390i 0.0494252 0.0982260i
\(863\) 35.0034 1.19153 0.595764 0.803159i \(-0.296849\pi\)
0.595764 + 0.803159i \(0.296849\pi\)
\(864\) −9.40986 + 9.89769i −0.320130 + 0.336726i
\(865\) −19.1648 −0.651624
\(866\) −12.7360 + 25.3112i −0.432787 + 0.860108i
\(867\) 6.87250i 0.233402i
\(868\) −4.86720 6.55872i −0.165203 0.222617i
\(869\) 24.2612i 0.823004i
\(870\) −0.841688 0.423519i −0.0285359 0.0143586i
\(871\) 2.47482 0.0838560
\(872\) 6.61407 + 38.0207i 0.223981 + 1.28754i
\(873\) −49.0899 −1.66144
\(874\) −35.7438 17.9855i −1.20905 0.608368i
\(875\) 1.00000i 0.0338062i
\(876\) −10.1064 + 7.49992i −0.341464 + 0.253399i
\(877\) 13.9841i 0.472211i 0.971727 + 0.236106i \(0.0758711\pi\)
−0.971727 + 0.236106i \(0.924129\pi\)
\(878\) 4.48577 8.91488i 0.151387 0.300863i
\(879\) 11.9144 0.401863
\(880\) 7.38372 24.3912i 0.248905 0.822229i
\(881\) −4.22514 −0.142349 −0.0711743 0.997464i \(-0.522675\pi\)
−0.0711743 + 0.997464i \(0.522675\pi\)
\(882\) −1.79793 + 3.57316i −0.0605395 + 0.120314i
\(883\) 15.4565i 0.520154i 0.965588 + 0.260077i \(0.0837479\pi\)
−0.965588 + 0.260077i \(0.916252\pi\)
\(884\) −0.588210 + 0.436508i −0.0197836 + 0.0146813i
\(885\) 2.64222i 0.0888171i
\(886\) 8.03554 + 4.04331i 0.269959 + 0.135838i
\(887\) 26.5127 0.890208 0.445104 0.895479i \(-0.353167\pi\)
0.445104 + 0.895479i \(0.353167\pi\)
\(888\) −3.42752 + 0.596250i −0.115020 + 0.0200089i
\(889\) −3.91375 −0.131263
\(890\) 8.26213 + 4.15732i 0.276947 + 0.139354i
\(891\) 47.6894i 1.59765i
\(892\) −21.4597 28.9177i −0.718524 0.968237i
\(893\) 51.7079i 1.73034i
\(894\) −2.36947 + 4.70900i −0.0792468 + 0.157493i
\(895\) −8.08115 −0.270123
\(896\) 1.37364 11.2300i 0.0458901 0.375168i
\(897\) −1.09834 −0.0366724
\(898\) 0.825773 1.64112i 0.0275564 0.0547648i
\(899\) 6.56862i 0.219076i
\(900\) 3.37109 + 4.54266i 0.112370 + 0.151422i
\(901\) 0.203125i 0.00676706i
\(902\) −65.3210 32.8681i −2.17495 1.09439i
\(903\) 0.863096 0.0287220
\(904\) 5.09958 0.887122i 0.169609 0.0295052i
\(905\) 18.4243 0.612444
\(906\) −5.68968 2.86292i −0.189027 0.0951141i
\(907\) 41.8112i 1.38832i 0.719821 + 0.694160i \(0.244224\pi\)
−0.719821 + 0.694160i \(0.755776\pi\)
\(908\) 16.6280 12.3396i 0.551821 0.409504i
\(909\) 37.7925i 1.25350i
\(910\) 0.364335 0.724068i 0.0120776 0.0240026i
\(911\) −8.07470 −0.267527 −0.133763 0.991013i \(-0.542706\pi\)
−0.133763 + 0.991013i \(0.542706\pi\)
\(912\) −2.93589 + 9.69838i −0.0972171 + 0.321145i
\(913\) 79.1563 2.61969
\(914\) 6.01854 11.9610i 0.199075 0.395636i
\(915\) 3.49886i 0.115669i
\(916\) −29.2449 + 21.7025i −0.966277 + 0.717070i
\(917\) 10.1970i 0.336733i
\(918\) 1.94885 + 0.980616i 0.0643215 + 0.0323651i
\(919\) −12.7176 −0.419514 −0.209757 0.977754i \(-0.567267\pi\)
−0.209757 + 0.977754i \(0.567267\pi\)
\(920\) 2.24264 + 12.8917i 0.0739377 + 0.425027i
\(921\) −5.18354 −0.170803
\(922\) −52.6998 26.5174i −1.73558 0.873304i
\(923\) 7.56091i 0.248870i
\(924\) 3.14531 + 4.23841i 0.103473 + 0.139434i
\(925\) 2.96951i 0.0976367i
\(926\) 13.1016 26.0376i 0.430544 0.855650i
\(927\) −41.9119 −1.37657
\(928\) 6.26942 6.59445i 0.205804 0.216473i
\(929\) −40.7169 −1.33588 −0.667939 0.744216i \(-0.732823\pi\)
−0.667939 + 0.744216i \(0.732823\pi\)
\(930\) 1.07524 2.13690i 0.0352586 0.0700718i
\(931\) 6.11582i 0.200438i
\(932\) 26.0114 + 35.0513i 0.852033 + 1.14814i
\(933\) 7.48139i 0.244930i
\(934\) 5.38637 + 2.71030i 0.176248 + 0.0886838i
\(935\) −4.07107 −0.133138
\(936\) −0.785846 4.51740i −0.0256862 0.147656i
\(937\) −3.65363 −0.119359 −0.0596794 0.998218i \(-0.519008\pi\)
−0.0596794 + 0.998218i \(0.519008\pi\)
\(938\) 5.45479 + 2.74473i 0.178105 + 0.0896185i
\(939\) 6.53849i 0.213375i
\(940\) −13.5790 + 10.0769i −0.442898 + 0.328673i
\(941\) 12.5502i 0.409124i −0.978854 0.204562i \(-0.934423\pi\)
0.978854 0.204562i \(-0.0655770\pi\)
\(942\) −2.98556 + 5.93342i −0.0972749 + 0.193321i
\(943\) 37.5467 1.22269
\(944\) 24.4210 + 7.39274i 0.794837 + 0.240613i
\(945\) −2.41421 −0.0785344
\(946\) −8.43873 + 16.7709i −0.274367 + 0.545268i
\(947\) 50.0396i 1.62607i −0.582215 0.813035i \(-0.697814\pi\)
0.582215 0.813035i \(-0.302186\pi\)
\(948\) 2.53331 1.87996i 0.0822780 0.0610581i
\(949\) 8.70722i 0.282648i
\(950\) 7.72612 + 3.88761i 0.250668 + 0.126131i
\(951\) 11.6329 0.377224
\(952\) −1.78060 + 0.309753i −0.0577095 + 0.0100391i
\(953\) −37.1736 −1.20417 −0.602086 0.798431i \(-0.705663\pi\)
−0.602086 + 0.798431i \(0.705663\pi\)
\(954\) 1.13585 + 0.571533i 0.0367744 + 0.0185041i
\(955\) 17.0860i 0.552890i
\(956\) −22.8746 30.8244i −0.739819 0.996932i
\(957\) 4.24481i 0.137215i
\(958\) 18.1851 36.1405i 0.587533 1.16765i
\(959\) 3.51217 0.113414
\(960\) 3.11904 1.11904i 0.100667 0.0361169i
\(961\) −14.3234 −0.462045
\(962\) 1.08189 2.15012i 0.0348817 0.0693227i
\(963\) 7.27339i 0.234382i
\(964\) −12.5585 16.9230i −0.404481 0.545052i
\(965\) 20.5975i 0.663057i
\(966\) −2.42087 1.21813i −0.0778901 0.0391926i
\(967\) 36.9518 1.18829 0.594145 0.804358i \(-0.297491\pi\)
0.594145 + 0.804358i \(0.297491\pi\)
\(968\) −82.4570 + 14.3442i −2.65027 + 0.461040i
\(969\) 1.61873 0.0520010
\(970\) 21.9257 + 11.0325i 0.703993 + 0.354234i
\(971\) 15.1668i 0.486724i −0.969935 0.243362i \(-0.921750\pi\)
0.969935 0.243362i \(-0.0782504\pi\)
\(972\) −16.6118 + 12.3276i −0.532825 + 0.395407i
\(973\) 1.87802i 0.0602066i
\(974\) 13.5364 26.9019i 0.433735 0.861991i
\(975\) 0.237409 0.00760316
\(976\) 32.3387 + 9.78958i 1.03514 + 0.313357i
\(977\) −32.5314 −1.04077 −0.520386 0.853931i \(-0.674212\pi\)
−0.520386 + 0.853931i \(0.674212\pi\)
\(978\) 6.33649 12.5930i 0.202619 0.402678i
\(979\) 41.6676i 1.33170i
\(980\) 1.60607 1.19186i 0.0513041 0.0380726i
\(981\) 38.5917i 1.23214i
\(982\) 26.4053 + 13.2865i 0.842626 + 0.423991i
\(983\) 25.7172 0.820251 0.410126 0.912029i \(-0.365485\pi\)
0.410126 + 0.912029i \(0.365485\pi\)
\(984\) −1.62958 9.36759i −0.0519492 0.298628i
\(985\) 15.0662 0.480050
\(986\) −1.29844 0.653346i −0.0413507 0.0208068i
\(987\) 3.50209i 0.111473i
\(988\) −4.17784 5.62979i −0.132915 0.179107i
\(989\) 9.63994i 0.306532i
\(990\) 11.4548 22.7649i 0.364057 0.723516i
\(991\) −6.65917 −0.211535 −0.105768 0.994391i \(-0.533730\pi\)
−0.105768 + 0.994391i \(0.533730\pi\)
\(992\) 16.7422 + 15.9170i 0.531565 + 0.505365i
\(993\) 6.57988 0.208806
\(994\) 8.38552 16.6651i 0.265973 0.528586i
\(995\) 13.4032i 0.424910i
\(996\) 6.13368 + 8.26535i 0.194353 + 0.261898i
\(997\) 5.50077i 0.174211i 0.996199 + 0.0871056i \(0.0277618\pi\)
−0.996199 + 0.0871056i \(0.972238\pi\)
\(998\) 47.0516 + 23.6753i 1.48939 + 0.749429i
\(999\) −7.16902 −0.226818
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.b.c.141.4 yes 8
4.3 odd 2 1120.2.b.c.561.5 8
8.3 odd 2 1120.2.b.c.561.4 8
8.5 even 2 inner 280.2.b.c.141.3 8
16.3 odd 4 8960.2.a.bv.1.1 4
16.5 even 4 8960.2.a.bu.1.1 4
16.11 odd 4 8960.2.a.bs.1.4 4
16.13 even 4 8960.2.a.bt.1.4 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
280.2.b.c.141.3 8 8.5 even 2 inner
280.2.b.c.141.4 yes 8 1.1 even 1 trivial
1120.2.b.c.561.4 8 8.3 odd 2
1120.2.b.c.561.5 8 4.3 odd 2
8960.2.a.bs.1.4 4 16.11 odd 4
8960.2.a.bt.1.4 4 16.13 even 4
8960.2.a.bu.1.1 4 16.5 even 4
8960.2.a.bv.1.1 4 16.3 odd 4