Properties

Label 390.2.x.b.49.3
Level $390$
Weight $2$
Character 390.49
Analytic conductor $3.114$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [390,2,Mod(49,390)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(390, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 3, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("390.49");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 390 = 2 \cdot 3 \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 390.x (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.11416567883\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 2 x^{11} - 8 x^{10} + 34 x^{9} + 8 x^{8} - 134 x^{7} + 98 x^{6} + 154 x^{5} + 104 x^{4} + 190 x^{3} - 1196 x^{2} - 338 x + 2197 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 49.3
Root \(-0.330925 + 1.46916i\) of defining polynomial
Character \(\chi\) \(=\) 390.49
Dual form 390.2.x.b.199.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.571769 - 2.16173i) q^{5} +(-0.866025 - 0.500000i) q^{6} +(0.603137 - 1.04466i) q^{7} -1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.571769 - 2.16173i) q^{5} +(-0.866025 - 0.500000i) q^{6} +(0.603137 - 1.04466i) q^{7} -1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +(2.15800 - 0.585699i) q^{10} +(4.46182 - 2.57603i) q^{11} -1.00000i q^{12} +(2.24511 + 2.82126i) q^{13} +1.20627 q^{14} +(0.585699 + 2.15800i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(4.10150 + 2.36800i) q^{17} +1.00000 q^{18} +(-1.84474 - 1.06506i) q^{19} +(1.58623 + 1.57603i) q^{20} +1.20627i q^{21} +(4.46182 + 2.57603i) q^{22} +(-1.88293 + 1.08711i) q^{23} +(0.866025 - 0.500000i) q^{24} +(-4.34616 - 2.47202i) q^{25} +(-1.32073 + 3.35495i) q^{26} +1.00000i q^{27} +(0.603137 + 1.04466i) q^{28} +(2.38346 + 4.12828i) q^{29} +(-1.57603 + 1.58623i) q^{30} -5.91046i q^{31} +(0.500000 - 0.866025i) q^{32} +(-2.57603 + 4.46182i) q^{33} +4.73601i q^{34} +(-1.91343 - 1.90113i) q^{35} +(0.500000 + 0.866025i) q^{36} +(-2.20034 - 3.81110i) q^{37} -2.13012i q^{38} +(-3.35495 - 1.32073i) q^{39} +(-0.571769 + 2.16173i) q^{40} +(4.10150 - 2.36800i) q^{41} +(-1.04466 + 0.603137i) q^{42} +(1.70944 + 0.986944i) q^{43} +5.15206i q^{44} +(-1.58623 - 1.57603i) q^{45} +(-1.88293 - 1.08711i) q^{46} +0.852296 q^{47} +(0.866025 + 0.500000i) q^{48} +(2.77245 + 4.80203i) q^{49} +(-0.0322474 - 4.99990i) q^{50} -4.73601 q^{51} +(-3.56583 + 0.533691i) q^{52} +4.48042i q^{53} +(-0.866025 + 0.500000i) q^{54} +(-3.01756 - 11.1181i) q^{55} +(-0.603137 + 1.04466i) q^{56} +2.13012 q^{57} +(-2.38346 + 4.12828i) q^{58} +(1.68133 + 0.970715i) q^{59} +(-2.16173 - 0.571769i) q^{60} +(-1.53795 + 2.66381i) q^{61} +(5.11861 - 2.95523i) q^{62} +(-0.603137 - 1.04466i) q^{63} +1.00000 q^{64} +(7.38248 - 3.24021i) q^{65} -5.15206 q^{66} +(-7.02765 - 12.1723i) q^{67} +(-4.10150 + 2.36800i) q^{68} +(1.08711 - 1.88293i) q^{69} +(0.689710 - 2.60764i) q^{70} +(-0.298707 - 0.172459i) q^{71} +(-0.500000 + 0.866025i) q^{72} -15.7228 q^{73} +(2.20034 - 3.81110i) q^{74} +(4.99990 - 0.0322474i) q^{75} +(1.84474 - 1.06506i) q^{76} -6.21480i q^{77} +(-0.533691 - 3.56583i) q^{78} -13.5863 q^{79} +(-2.15800 + 0.585699i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(4.10150 + 2.36800i) q^{82} -10.2045 q^{83} +(-1.04466 - 0.603137i) q^{84} +(7.46410 - 7.51240i) q^{85} +1.97389i q^{86} +(-4.12828 - 2.38346i) q^{87} +(-4.46182 + 2.57603i) q^{88} +(14.1941 - 8.19497i) q^{89} +(0.571769 - 2.16173i) q^{90} +(4.30137 - 0.643777i) q^{91} -2.17422i q^{92} +(2.95523 + 5.11861i) q^{93} +(0.426148 + 0.738110i) q^{94} +(-3.35713 + 3.37886i) q^{95} +1.00000i q^{96} +(-4.24139 + 7.34631i) q^{97} +(-2.77245 + 4.80203i) q^{98} -5.15206i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 6 q^{2} - 6 q^{4} + 2 q^{5} + 2 q^{7} - 12 q^{8} + 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 6 q^{2} - 6 q^{4} + 2 q^{5} + 2 q^{7} - 12 q^{8} + 6 q^{9} + 4 q^{10} + 6 q^{11} + 8 q^{13} + 4 q^{14} + 6 q^{15} - 6 q^{16} - 18 q^{17} + 12 q^{18} - 6 q^{19} + 2 q^{20} + 6 q^{22} - 6 q^{23} - 10 q^{25} - 2 q^{26} + 2 q^{28} + 14 q^{29} + 6 q^{30} + 6 q^{32} - 6 q^{33} - 22 q^{35} + 6 q^{36} + 12 q^{37} - 2 q^{39} - 2 q^{40} - 18 q^{41} + 12 q^{42} + 36 q^{43} - 2 q^{45} - 6 q^{46} - 16 q^{47} + 8 q^{49} - 20 q^{50} + 16 q^{51} - 10 q^{52} + 8 q^{55} - 2 q^{56} + 8 q^{57} - 14 q^{58} - 36 q^{59} + 10 q^{61} - 6 q^{62} - 2 q^{63} + 12 q^{64} - 44 q^{65} - 12 q^{66} - 4 q^{67} + 18 q^{68} + 16 q^{69} + 4 q^{70} - 12 q^{71} - 6 q^{72} - 28 q^{73} - 12 q^{74} + 16 q^{75} + 6 q^{76} + 2 q^{78} + 4 q^{79} - 4 q^{80} - 6 q^{81} - 18 q^{82} - 72 q^{83} + 12 q^{84} + 48 q^{85} - 6 q^{87} - 6 q^{88} + 18 q^{89} + 2 q^{90} + 2 q^{91} + 16 q^{93} - 8 q^{94} + 18 q^{95} + 48 q^{97} - 8 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/390\mathbb{Z}\right)^\times\).

\(n\) \(131\) \(157\) \(301\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{5}{6}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 + 0.866025i 0.353553 + 0.612372i
\(3\) −0.866025 + 0.500000i −0.500000 + 0.288675i
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) 0.571769 2.16173i 0.255703 0.966755i
\(6\) −0.866025 0.500000i −0.353553 0.204124i
\(7\) 0.603137 1.04466i 0.227964 0.394846i −0.729240 0.684258i \(-0.760126\pi\)
0.957205 + 0.289412i \(0.0934597\pi\)
\(8\) −1.00000 −0.353553
\(9\) 0.500000 0.866025i 0.166667 0.288675i
\(10\) 2.15800 0.585699i 0.682419 0.185214i
\(11\) 4.46182 2.57603i 1.34529 0.776703i 0.357711 0.933832i \(-0.383557\pi\)
0.987578 + 0.157130i \(0.0502240\pi\)
\(12\) 1.00000i 0.288675i
\(13\) 2.24511 + 2.82126i 0.622681 + 0.782476i
\(14\) 1.20627 0.322390
\(15\) 0.585699 + 2.15800i 0.151227 + 0.557193i
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 4.10150 + 2.36800i 0.994761 + 0.574326i 0.906694 0.421789i \(-0.138598\pi\)
0.0880670 + 0.996115i \(0.471931\pi\)
\(18\) 1.00000 0.235702
\(19\) −1.84474 1.06506i −0.423212 0.244341i 0.273239 0.961946i \(-0.411905\pi\)
−0.696450 + 0.717605i \(0.745238\pi\)
\(20\) 1.58623 + 1.57603i 0.354692 + 0.352411i
\(21\) 1.20627i 0.263231i
\(22\) 4.46182 + 2.57603i 0.951263 + 0.549212i
\(23\) −1.88293 + 1.08711i −0.392618 + 0.226678i −0.683294 0.730144i \(-0.739453\pi\)
0.290676 + 0.956822i \(0.406120\pi\)
\(24\) 0.866025 0.500000i 0.176777 0.102062i
\(25\) −4.34616 2.47202i −0.869232 0.494404i
\(26\) −1.32073 + 3.35495i −0.259016 + 0.657960i
\(27\) 1.00000i 0.192450i
\(28\) 0.603137 + 1.04466i 0.113982 + 0.197423i
\(29\) 2.38346 + 4.12828i 0.442598 + 0.766602i 0.997881 0.0650589i \(-0.0207235\pi\)
−0.555283 + 0.831661i \(0.687390\pi\)
\(30\) −1.57603 + 1.58623i −0.287743 + 0.289605i
\(31\) 5.91046i 1.06155i −0.847513 0.530775i \(-0.821901\pi\)
0.847513 0.530775i \(-0.178099\pi\)
\(32\) 0.500000 0.866025i 0.0883883 0.153093i
\(33\) −2.57603 + 4.46182i −0.448430 + 0.776703i
\(34\) 4.73601i 0.812219i
\(35\) −1.91343 1.90113i −0.323428 0.321349i
\(36\) 0.500000 + 0.866025i 0.0833333 + 0.144338i
\(37\) −2.20034 3.81110i −0.361734 0.626541i 0.626513 0.779411i \(-0.284482\pi\)
−0.988246 + 0.152870i \(0.951148\pi\)
\(38\) 2.13012i 0.345551i
\(39\) −3.35495 1.32073i −0.537222 0.211486i
\(40\) −0.571769 + 2.16173i −0.0904046 + 0.341800i
\(41\) 4.10150 2.36800i 0.640547 0.369820i −0.144278 0.989537i \(-0.546086\pi\)
0.784825 + 0.619717i \(0.212753\pi\)
\(42\) −1.04466 + 0.603137i −0.161195 + 0.0930660i
\(43\) 1.70944 + 0.986944i 0.260687 + 0.150508i 0.624648 0.780907i \(-0.285243\pi\)
−0.363961 + 0.931414i \(0.618576\pi\)
\(44\) 5.15206i 0.776703i
\(45\) −1.58623 1.57603i −0.236461 0.234941i
\(46\) −1.88293 1.08711i −0.277623 0.160285i
\(47\) 0.852296 0.124320 0.0621600 0.998066i \(-0.480201\pi\)
0.0621600 + 0.998066i \(0.480201\pi\)
\(48\) 0.866025 + 0.500000i 0.125000 + 0.0721688i
\(49\) 2.77245 + 4.80203i 0.396065 + 0.686004i
\(50\) −0.0322474 4.99990i −0.00456046 0.707092i
\(51\) −4.73601 −0.663174
\(52\) −3.56583 + 0.533691i −0.494492 + 0.0740096i
\(53\) 4.48042i 0.615433i 0.951478 + 0.307716i \(0.0995648\pi\)
−0.951478 + 0.307716i \(0.900435\pi\)
\(54\) −0.866025 + 0.500000i −0.117851 + 0.0680414i
\(55\) −3.01756 11.1181i −0.406888 1.49917i
\(56\) −0.603137 + 1.04466i −0.0805976 + 0.139599i
\(57\) 2.13012 0.282141
\(58\) −2.38346 + 4.12828i −0.312964 + 0.542070i
\(59\) 1.68133 + 0.970715i 0.218890 + 0.126376i 0.605436 0.795894i \(-0.292999\pi\)
−0.386546 + 0.922270i \(0.626332\pi\)
\(60\) −2.16173 0.571769i −0.279078 0.0738150i
\(61\) −1.53795 + 2.66381i −0.196915 + 0.341066i −0.947527 0.319677i \(-0.896426\pi\)
0.750612 + 0.660744i \(0.229759\pi\)
\(62\) 5.11861 2.95523i 0.650064 0.375315i
\(63\) −0.603137 1.04466i −0.0759881 0.131615i
\(64\) 1.00000 0.125000
\(65\) 7.38248 3.24021i 0.915684 0.401899i
\(66\) −5.15206 −0.634175
\(67\) −7.02765 12.1723i −0.858564 1.48708i −0.873298 0.487186i \(-0.838023\pi\)
0.0147340 0.999891i \(-0.495310\pi\)
\(68\) −4.10150 + 2.36800i −0.497380 + 0.287163i
\(69\) 1.08711 1.88293i 0.130873 0.226678i
\(70\) 0.689710 2.60764i 0.0824361 0.311673i
\(71\) −0.298707 0.172459i −0.0354500 0.0204671i 0.482170 0.876078i \(-0.339849\pi\)
−0.517620 + 0.855610i \(0.673182\pi\)
\(72\) −0.500000 + 0.866025i −0.0589256 + 0.102062i
\(73\) −15.7228 −1.84022 −0.920109 0.391662i \(-0.871900\pi\)
−0.920109 + 0.391662i \(0.871900\pi\)
\(74\) 2.20034 3.81110i 0.255784 0.443031i
\(75\) 4.99990 0.0322474i 0.577338 0.00372360i
\(76\) 1.84474 1.06506i 0.211606 0.122171i
\(77\) 6.21480i 0.708242i
\(78\) −0.533691 3.56583i −0.0604286 0.403751i
\(79\) −13.5863 −1.52858 −0.764290 0.644873i \(-0.776910\pi\)
−0.764290 + 0.644873i \(0.776910\pi\)
\(80\) −2.15800 + 0.585699i −0.241272 + 0.0654831i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 4.10150 + 2.36800i 0.452935 + 0.261502i
\(83\) −10.2045 −1.12009 −0.560046 0.828462i \(-0.689216\pi\)
−0.560046 + 0.828462i \(0.689216\pi\)
\(84\) −1.04466 0.603137i −0.113982 0.0658076i
\(85\) 7.46410 7.51240i 0.809595 0.814834i
\(86\) 1.97389i 0.212850i
\(87\) −4.12828 2.38346i −0.442598 0.255534i
\(88\) −4.46182 + 2.57603i −0.475631 + 0.274606i
\(89\) 14.1941 8.19497i 1.50457 0.868665i 0.504586 0.863361i \(-0.331645\pi\)
0.999986 0.00530346i \(-0.00168815\pi\)
\(90\) 0.571769 2.16173i 0.0602697 0.227866i
\(91\) 4.30137 0.643777i 0.450906 0.0674862i
\(92\) 2.17422i 0.226678i
\(93\) 2.95523 + 5.11861i 0.306443 + 0.530775i
\(94\) 0.426148 + 0.738110i 0.0439538 + 0.0761302i
\(95\) −3.35713 + 3.37886i −0.344435 + 0.346663i
\(96\) 1.00000i 0.102062i
\(97\) −4.24139 + 7.34631i −0.430648 + 0.745904i −0.996929 0.0783078i \(-0.975048\pi\)
0.566281 + 0.824212i \(0.308382\pi\)
\(98\) −2.77245 + 4.80203i −0.280060 + 0.485078i
\(99\) 5.15206i 0.517802i
\(100\) 4.31391 2.52788i 0.431391 0.252788i
\(101\) 6.79121 + 11.7627i 0.675751 + 1.17044i 0.976249 + 0.216653i \(0.0695139\pi\)
−0.300498 + 0.953783i \(0.597153\pi\)
\(102\) −2.36800 4.10150i −0.234467 0.406109i
\(103\) 2.15696i 0.212531i 0.994338 + 0.106266i \(0.0338894\pi\)
−0.994338 + 0.106266i \(0.966111\pi\)
\(104\) −2.24511 2.82126i −0.220151 0.276647i
\(105\) 2.60764 + 0.689710i 0.254480 + 0.0673088i
\(106\) −3.88016 + 2.24021i −0.376874 + 0.217588i
\(107\) −7.00959 + 4.04699i −0.677642 + 0.391237i −0.798966 0.601376i \(-0.794619\pi\)
0.121324 + 0.992613i \(0.461286\pi\)
\(108\) −0.866025 0.500000i −0.0833333 0.0481125i
\(109\) 16.8839i 1.61718i 0.588370 + 0.808592i \(0.299770\pi\)
−0.588370 + 0.808592i \(0.700230\pi\)
\(110\) 8.11982 8.17235i 0.774194 0.779203i
\(111\) 3.81110 + 2.20034i 0.361734 + 0.208847i
\(112\) −1.20627 −0.113982
\(113\) −4.28771 2.47551i −0.403354 0.232876i 0.284576 0.958653i \(-0.408147\pi\)
−0.687930 + 0.725777i \(0.741480\pi\)
\(114\) 1.06506 + 1.84474i 0.0997519 + 0.172775i
\(115\) 1.27344 + 4.69196i 0.118749 + 0.437527i
\(116\) −4.76693 −0.442598
\(117\) 3.56583 0.533691i 0.329661 0.0493397i
\(118\) 1.94143i 0.178723i
\(119\) 4.94754 2.85646i 0.453540 0.261851i
\(120\) −0.585699 2.15800i −0.0534668 0.196997i
\(121\) 7.77188 13.4613i 0.706535 1.22375i
\(122\) −3.07591 −0.278480
\(123\) −2.36800 + 4.10150i −0.213516 + 0.369820i
\(124\) 5.11861 + 2.95523i 0.459665 + 0.265388i
\(125\) −7.82884 + 7.98180i −0.700233 + 0.713914i
\(126\) 0.603137 1.04466i 0.0537317 0.0930660i
\(127\) 1.04089 0.600957i 0.0923639 0.0533263i −0.453107 0.891456i \(-0.649684\pi\)
0.545471 + 0.838130i \(0.316351\pi\)
\(128\) 0.500000 + 0.866025i 0.0441942 + 0.0765466i
\(129\) −1.97389 −0.173791
\(130\) 6.49734 + 4.77331i 0.569855 + 0.418647i
\(131\) −6.65149 −0.581143 −0.290572 0.956853i \(-0.593845\pi\)
−0.290572 + 0.956853i \(0.593845\pi\)
\(132\) −2.57603 4.46182i −0.224215 0.388351i
\(133\) −2.22526 + 1.28475i −0.192954 + 0.111402i
\(134\) 7.02765 12.1723i 0.607097 1.05152i
\(135\) 2.16173 + 0.571769i 0.186052 + 0.0492100i
\(136\) −4.10150 2.36800i −0.351701 0.203055i
\(137\) 7.35746 12.7435i 0.628590 1.08875i −0.359245 0.933243i \(-0.616966\pi\)
0.987835 0.155507i \(-0.0497010\pi\)
\(138\) 2.17422 0.185082
\(139\) −7.82540 + 13.5540i −0.663742 + 1.14963i 0.315883 + 0.948798i \(0.397699\pi\)
−0.979625 + 0.200837i \(0.935634\pi\)
\(140\) 2.60314 0.706513i 0.220005 0.0597113i
\(141\) −0.738110 + 0.426148i −0.0621600 + 0.0358881i
\(142\) 0.344918i 0.0289448i
\(143\) 17.2849 + 6.80447i 1.44544 + 0.569018i
\(144\) −1.00000 −0.0833333
\(145\) 10.2870 2.79198i 0.854290 0.231862i
\(146\) −7.86142 13.6164i −0.650615 1.12690i
\(147\) −4.80203 2.77245i −0.396065 0.228668i
\(148\) 4.40068 0.361734
\(149\) −19.7555 11.4058i −1.61843 0.934401i −0.987327 0.158702i \(-0.949269\pi\)
−0.631103 0.775699i \(-0.717398\pi\)
\(150\) 2.52788 + 4.31391i 0.206400 + 0.352230i
\(151\) 19.8995i 1.61940i 0.586845 + 0.809699i \(0.300370\pi\)
−0.586845 + 0.809699i \(0.699630\pi\)
\(152\) 1.84474 + 1.06506i 0.149628 + 0.0863877i
\(153\) 4.10150 2.36800i 0.331587 0.191442i
\(154\) 5.38217 3.10740i 0.433708 0.250401i
\(155\) −12.7768 3.37942i −1.02626 0.271442i
\(156\) 2.82126 2.24511i 0.225881 0.179752i
\(157\) 4.74392i 0.378606i −0.981919 0.189303i \(-0.939377\pi\)
0.981919 0.189303i \(-0.0606228\pi\)
\(158\) −6.79315 11.7661i −0.540434 0.936060i
\(159\) −2.24021 3.88016i −0.177660 0.307716i
\(160\) −1.58623 1.57603i −0.125402 0.124596i
\(161\) 2.62270i 0.206698i
\(162\) 0.500000 0.866025i 0.0392837 0.0680414i
\(163\) −1.93329 + 3.34855i −0.151427 + 0.262279i −0.931752 0.363095i \(-0.881720\pi\)
0.780325 + 0.625374i \(0.215053\pi\)
\(164\) 4.73601i 0.369820i
\(165\) 8.17235 + 8.11982i 0.636217 + 0.632127i
\(166\) −5.10226 8.83737i −0.396012 0.685913i
\(167\) 11.3614 + 19.6785i 0.879173 + 1.52277i 0.852250 + 0.523134i \(0.175237\pi\)
0.0269225 + 0.999638i \(0.491429\pi\)
\(168\) 1.20627i 0.0930660i
\(169\) −2.91899 + 12.6681i −0.224538 + 0.974465i
\(170\) 10.2380 + 2.70790i 0.785217 + 0.207687i
\(171\) −1.84474 + 1.06506i −0.141071 + 0.0814471i
\(172\) −1.70944 + 0.986944i −0.130343 + 0.0752538i
\(173\) 4.06859 + 2.34900i 0.309329 + 0.178591i 0.646626 0.762807i \(-0.276179\pi\)
−0.337297 + 0.941398i \(0.609513\pi\)
\(174\) 4.76693i 0.361380i
\(175\) −5.20376 + 3.04931i −0.393367 + 0.230506i
\(176\) −4.46182 2.57603i −0.336322 0.194176i
\(177\) −1.94143 −0.145927
\(178\) 14.1941 + 8.19497i 1.06389 + 0.614239i
\(179\) −4.34913 7.53292i −0.325069 0.563037i 0.656457 0.754363i \(-0.272054\pi\)
−0.981526 + 0.191327i \(0.938721\pi\)
\(180\) 2.15800 0.585699i 0.160848 0.0436554i
\(181\) 9.75480 0.725069 0.362534 0.931970i \(-0.381912\pi\)
0.362534 + 0.931970i \(0.381912\pi\)
\(182\) 2.70821 + 3.40321i 0.200746 + 0.252263i
\(183\) 3.07591i 0.227378i
\(184\) 1.88293 1.08711i 0.138811 0.0801427i
\(185\) −9.49666 + 2.57747i −0.698208 + 0.189500i
\(186\) −2.95523 + 5.11861i −0.216688 + 0.375315i
\(187\) 24.4002 1.78432
\(188\) −0.426148 + 0.738110i −0.0310800 + 0.0538322i
\(189\) 1.04466 + 0.603137i 0.0759881 + 0.0438718i
\(190\) −4.60474 1.21794i −0.334063 0.0883583i
\(191\) −5.77729 + 10.0066i −0.418030 + 0.724049i −0.995741 0.0921920i \(-0.970613\pi\)
0.577711 + 0.816241i \(0.303946\pi\)
\(192\) −0.866025 + 0.500000i −0.0625000 + 0.0360844i
\(193\) −5.23154 9.06130i −0.376575 0.652247i 0.613987 0.789316i \(-0.289565\pi\)
−0.990561 + 0.137070i \(0.956232\pi\)
\(194\) −8.48278 −0.609028
\(195\) −4.77331 + 6.49734i −0.341824 + 0.465285i
\(196\) −5.54490 −0.396065
\(197\) 8.79472 + 15.2329i 0.626598 + 1.08530i 0.988230 + 0.152978i \(0.0488865\pi\)
−0.361632 + 0.932321i \(0.617780\pi\)
\(198\) 4.46182 2.57603i 0.317088 0.183071i
\(199\) 12.7858 22.1457i 0.906362 1.56986i 0.0872828 0.996184i \(-0.472182\pi\)
0.819079 0.573681i \(-0.194485\pi\)
\(200\) 4.34616 + 2.47202i 0.307320 + 0.174798i
\(201\) 12.1723 + 7.02765i 0.858564 + 0.495692i
\(202\) −6.79121 + 11.7627i −0.477828 + 0.827623i
\(203\) 5.75022 0.403586
\(204\) 2.36800 4.10150i 0.165793 0.287163i
\(205\) −2.77388 10.2203i −0.193736 0.713817i
\(206\) −1.86798 + 1.07848i −0.130148 + 0.0751412i
\(207\) 2.17422i 0.151119i
\(208\) 1.32073 3.35495i 0.0915760 0.232624i
\(209\) −10.9745 −0.759122
\(210\) 0.706513 + 2.60314i 0.0487541 + 0.179634i
\(211\) −6.45984 11.1888i −0.444714 0.770267i 0.553318 0.832970i \(-0.313361\pi\)
−0.998032 + 0.0627029i \(0.980028\pi\)
\(212\) −3.88016 2.24021i −0.266490 0.153858i
\(213\) 0.344918 0.0236334
\(214\) −7.00959 4.04699i −0.479165 0.276646i
\(215\) 3.11091 3.13104i 0.212162 0.213535i
\(216\) 1.00000i 0.0680414i
\(217\) −6.17445 3.56482i −0.419149 0.241996i
\(218\) −14.6219 + 8.44195i −0.990319 + 0.571761i
\(219\) 13.6164 7.86142i 0.920109 0.531225i
\(220\) 11.1374 + 2.94579i 0.750882 + 0.198605i
\(221\) 2.52757 + 16.8878i 0.170022 + 1.13600i
\(222\) 4.40068i 0.295354i
\(223\) 3.57679 + 6.19518i 0.239519 + 0.414860i 0.960576 0.278016i \(-0.0896768\pi\)
−0.721057 + 0.692876i \(0.756343\pi\)
\(224\) −0.603137 1.04466i −0.0402988 0.0697995i
\(225\) −4.31391 + 2.52788i −0.287594 + 0.168525i
\(226\) 4.95102i 0.329337i
\(227\) −12.9192 + 22.3768i −0.857480 + 1.48520i 0.0168460 + 0.999858i \(0.494638\pi\)
−0.874325 + 0.485340i \(0.838696\pi\)
\(228\) −1.06506 + 1.84474i −0.0705353 + 0.122171i
\(229\) 8.95153i 0.591533i 0.955260 + 0.295767i \(0.0955751\pi\)
−0.955260 + 0.295767i \(0.904425\pi\)
\(230\) −3.42664 + 3.44881i −0.225946 + 0.227408i
\(231\) 3.10740 + 5.38217i 0.204452 + 0.354121i
\(232\) −2.38346 4.12828i −0.156482 0.271035i
\(233\) 3.86657i 0.253308i 0.991947 + 0.126654i \(0.0404237\pi\)
−0.991947 + 0.126654i \(0.959576\pi\)
\(234\) 2.24511 + 2.82126i 0.146767 + 0.184431i
\(235\) 0.487316 1.84243i 0.0317890 0.120187i
\(236\) −1.68133 + 0.970715i −0.109445 + 0.0631882i
\(237\) 11.7661 6.79315i 0.764290 0.441263i
\(238\) 4.94754 + 2.85646i 0.320701 + 0.185157i
\(239\) 15.4177i 0.997286i −0.866807 0.498643i \(-0.833832\pi\)
0.866807 0.498643i \(-0.166168\pi\)
\(240\) 1.57603 1.58623i 0.101732 0.102391i
\(241\) 9.76603 + 5.63842i 0.629085 + 0.363203i 0.780398 0.625283i \(-0.215017\pi\)
−0.151312 + 0.988486i \(0.548350\pi\)
\(242\) 15.5438 0.999191
\(243\) 0.866025 + 0.500000i 0.0555556 + 0.0320750i
\(244\) −1.53795 2.66381i −0.0984574 0.170533i
\(245\) 11.9659 3.24764i 0.764473 0.207484i
\(246\) −4.73601 −0.301957
\(247\) −1.13682 7.59565i −0.0723344 0.483299i
\(248\) 5.91046i 0.375315i
\(249\) 8.83737 5.10226i 0.560046 0.323342i
\(250\) −10.8269 2.78907i −0.684751 0.176397i
\(251\) 6.15329 10.6578i 0.388392 0.672715i −0.603841 0.797104i \(-0.706364\pi\)
0.992233 + 0.124390i \(0.0396973\pi\)
\(252\) 1.20627 0.0759881
\(253\) −5.60085 + 9.70096i −0.352123 + 0.609894i
\(254\) 1.04089 + 0.600957i 0.0653112 + 0.0377074i
\(255\) −2.70790 + 10.2380i −0.169575 + 0.641127i
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 24.3239 14.0434i 1.51728 0.876004i 0.517490 0.855689i \(-0.326866\pi\)
0.999794 0.0203154i \(-0.00646704\pi\)
\(258\) −0.986944 1.70944i −0.0614444 0.106425i
\(259\) −5.30842 −0.329849
\(260\) −0.885137 + 8.01352i −0.0548939 + 0.496978i
\(261\) 4.76693 0.295065
\(262\) −3.32575 5.76036i −0.205465 0.355876i
\(263\) 6.56756 3.79178i 0.404973 0.233811i −0.283654 0.958927i \(-0.591547\pi\)
0.688628 + 0.725115i \(0.258213\pi\)
\(264\) 2.57603 4.46182i 0.158544 0.274606i
\(265\) 9.68546 + 2.56176i 0.594973 + 0.157368i
\(266\) −2.22526 1.28475i −0.136439 0.0787732i
\(267\) −8.19497 + 14.1941i −0.501524 + 0.868665i
\(268\) 14.0553 0.858564
\(269\) −12.2355 + 21.1924i −0.746010 + 1.29213i 0.203712 + 0.979031i \(0.434699\pi\)
−0.949722 + 0.313096i \(0.898634\pi\)
\(270\) 0.585699 + 2.15800i 0.0356445 + 0.131332i
\(271\) 10.0199 5.78497i 0.608664 0.351412i −0.163779 0.986497i \(-0.552368\pi\)
0.772442 + 0.635085i \(0.219035\pi\)
\(272\) 4.73601i 0.287163i
\(273\) −3.40321 + 2.70821i −0.205972 + 0.163909i
\(274\) 14.7149 0.888961
\(275\) −25.7598 + 0.166140i −1.55337 + 0.0100186i
\(276\) 1.08711 + 1.88293i 0.0654363 + 0.113339i
\(277\) −11.2111 6.47271i −0.673608 0.388908i 0.123835 0.992303i \(-0.460481\pi\)
−0.797442 + 0.603395i \(0.793814\pi\)
\(278\) −15.6508 −0.938673
\(279\) −5.11861 2.95523i −0.306443 0.176925i
\(280\) 1.91343 + 1.90113i 0.114349 + 0.113614i
\(281\) 2.57187i 0.153425i −0.997053 0.0767124i \(-0.975558\pi\)
0.997053 0.0767124i \(-0.0244423\pi\)
\(282\) −0.738110 0.426148i −0.0439538 0.0253767i
\(283\) −4.80517 + 2.77427i −0.285638 + 0.164913i −0.635973 0.771711i \(-0.719401\pi\)
0.350335 + 0.936624i \(0.386068\pi\)
\(284\) 0.298707 0.172459i 0.0177250 0.0102335i
\(285\) 1.21794 4.60474i 0.0721443 0.272761i
\(286\) 2.74961 + 18.3714i 0.162588 + 1.08632i
\(287\) 5.71292i 0.337223i
\(288\) −0.500000 0.866025i −0.0294628 0.0510310i
\(289\) 2.71489 + 4.70233i 0.159700 + 0.276608i
\(290\) 7.56144 + 7.51283i 0.444023 + 0.441168i
\(291\) 8.48278i 0.497270i
\(292\) 7.86142 13.6164i 0.460055 0.796838i
\(293\) 12.0658 20.8986i 0.704891 1.22091i −0.261840 0.965111i \(-0.584329\pi\)
0.966731 0.255795i \(-0.0823374\pi\)
\(294\) 5.54490i 0.323385i
\(295\) 3.05976 3.07955i 0.178146 0.179299i
\(296\) 2.20034 + 3.81110i 0.127892 + 0.221516i
\(297\) 2.57603 + 4.46182i 0.149477 + 0.258901i
\(298\) 22.8116i 1.32144i
\(299\) −7.29439 2.87155i −0.421845 0.166066i
\(300\) −2.47202 + 4.34616i −0.142722 + 0.250926i
\(301\) 2.06205 1.19052i 0.118855 0.0686207i
\(302\) −17.2335 + 9.94975i −0.991675 + 0.572544i
\(303\) −11.7627 6.79121i −0.675751 0.390145i
\(304\) 2.13012i 0.122171i
\(305\) 4.87910 + 4.84773i 0.279376 + 0.277580i
\(306\) 4.10150 + 2.36800i 0.234467 + 0.135370i
\(307\) 30.3243 1.73070 0.865348 0.501171i \(-0.167097\pi\)
0.865348 + 0.501171i \(0.167097\pi\)
\(308\) 5.38217 + 3.10740i 0.306678 + 0.177061i
\(309\) −1.07848 1.86798i −0.0613525 0.106266i
\(310\) −3.46175 12.7548i −0.196614 0.724422i
\(311\) 8.76406 0.496964 0.248482 0.968636i \(-0.420068\pi\)
0.248482 + 0.968636i \(0.420068\pi\)
\(312\) 3.35495 + 1.32073i 0.189937 + 0.0747715i
\(313\) 29.0155i 1.64005i −0.572326 0.820026i \(-0.693959\pi\)
0.572326 0.820026i \(-0.306041\pi\)
\(314\) 4.10836 2.37196i 0.231848 0.133857i
\(315\) −2.60314 + 0.706513i −0.146670 + 0.0398075i
\(316\) 6.79315 11.7661i 0.382145 0.661894i
\(317\) −25.9970 −1.46014 −0.730068 0.683375i \(-0.760511\pi\)
−0.730068 + 0.683375i \(0.760511\pi\)
\(318\) 2.24021 3.88016i 0.125625 0.217588i
\(319\) 21.2692 + 12.2798i 1.19084 + 0.687534i
\(320\) 0.571769 2.16173i 0.0319629 0.120844i
\(321\) 4.04699 7.00959i 0.225881 0.391237i
\(322\) −2.27133 + 1.31135i −0.126576 + 0.0730787i
\(323\) −5.04413 8.73669i −0.280663 0.486122i
\(324\) 1.00000 0.0555556
\(325\) −2.78339 17.8116i −0.154395 0.988009i
\(326\) −3.86657 −0.214150
\(327\) −8.44195 14.6219i −0.466841 0.808592i
\(328\) −4.10150 + 2.36800i −0.226468 + 0.130751i
\(329\) 0.514051 0.890362i 0.0283405 0.0490873i
\(330\) −2.94579 + 11.1374i −0.162160 + 0.613092i
\(331\) −9.56025 5.51961i −0.525479 0.303385i 0.213694 0.976901i \(-0.431450\pi\)
−0.739173 + 0.673515i \(0.764784\pi\)
\(332\) 5.10226 8.83737i 0.280023 0.485014i
\(333\) −4.40068 −0.241156
\(334\) −11.3614 + 19.6785i −0.621669 + 1.07676i
\(335\) −30.3313 + 8.23218i −1.65718 + 0.449772i
\(336\) 1.04466 0.603137i 0.0569911 0.0329038i
\(337\) 17.7108i 0.964769i 0.875960 + 0.482384i \(0.160229\pi\)
−0.875960 + 0.482384i \(0.839771\pi\)
\(338\) −12.4303 + 3.80611i −0.676122 + 0.207025i
\(339\) 4.95102 0.268902
\(340\) 2.77388 + 10.2203i 0.150435 + 0.554274i
\(341\) −15.2255 26.3714i −0.824509 1.42809i
\(342\) −1.84474 1.06506i −0.0997519 0.0575918i
\(343\) 15.1326 0.817083
\(344\) −1.70944 0.986944i −0.0921667 0.0532124i
\(345\) −3.44881 3.42664i −0.185678 0.184484i
\(346\) 4.69800i 0.252566i
\(347\) −30.0526 17.3509i −1.61331 0.931443i −0.988597 0.150587i \(-0.951884\pi\)
−0.624710 0.780857i \(-0.714783\pi\)
\(348\) 4.12828 2.38346i 0.221299 0.127767i
\(349\) −30.4563 + 17.5840i −1.63029 + 0.941249i −0.646288 + 0.763093i \(0.723680\pi\)
−0.984002 + 0.178156i \(0.942987\pi\)
\(350\) −5.24266 2.98193i −0.280232 0.159391i
\(351\) −2.82126 + 2.24511i −0.150588 + 0.119835i
\(352\) 5.15206i 0.274606i
\(353\) 5.54542 + 9.60495i 0.295153 + 0.511220i 0.975020 0.222115i \(-0.0712961\pi\)
−0.679868 + 0.733335i \(0.737963\pi\)
\(354\) −0.970715 1.68133i −0.0515929 0.0893616i
\(355\) −0.543601 + 0.547118i −0.0288513 + 0.0290380i
\(356\) 16.3899i 0.868665i
\(357\) −2.85646 + 4.94754i −0.151180 + 0.261851i
\(358\) 4.34913 7.53292i 0.229859 0.398127i
\(359\) 26.1575i 1.38054i −0.723552 0.690270i \(-0.757492\pi\)
0.723552 0.690270i \(-0.242508\pi\)
\(360\) 1.58623 + 1.57603i 0.0836016 + 0.0830642i
\(361\) −7.23130 12.5250i −0.380595 0.659209i
\(362\) 4.87740 + 8.44791i 0.256351 + 0.444012i
\(363\) 15.5438i 0.815836i
\(364\) −1.59316 + 4.04699i −0.0835042 + 0.212120i
\(365\) −8.98983 + 33.9885i −0.470549 + 1.77904i
\(366\) 2.66381 1.53795i 0.139240 0.0803901i
\(367\) −13.4988 + 7.79352i −0.704630 + 0.406818i −0.809070 0.587713i \(-0.800028\pi\)
0.104440 + 0.994531i \(0.466695\pi\)
\(368\) 1.88293 + 1.08711i 0.0981544 + 0.0566695i
\(369\) 4.73601i 0.246547i
\(370\) −6.98049 6.93561i −0.362898 0.360565i
\(371\) 4.68053 + 2.70231i 0.243001 + 0.140297i
\(372\) −5.91046 −0.306443
\(373\) −0.860358 0.496728i −0.0445476 0.0257196i 0.477561 0.878599i \(-0.341521\pi\)
−0.522108 + 0.852879i \(0.674854\pi\)
\(374\) 12.2001 + 21.1312i 0.630853 + 1.09267i
\(375\) 2.78907 10.8269i 0.144027 0.559097i
\(376\) −0.852296 −0.0439538
\(377\) −6.29581 + 15.9928i −0.324251 + 0.823671i
\(378\) 1.20627i 0.0620440i
\(379\) 23.7856 13.7326i 1.22178 0.705398i 0.256486 0.966548i \(-0.417435\pi\)
0.965298 + 0.261150i \(0.0841018\pi\)
\(380\) −1.24761 4.59679i −0.0640009 0.235810i
\(381\) −0.600957 + 1.04089i −0.0307880 + 0.0533263i
\(382\) −11.5546 −0.591184
\(383\) 16.2851 28.2067i 0.832132 1.44130i −0.0642122 0.997936i \(-0.520453\pi\)
0.896344 0.443359i \(-0.146213\pi\)
\(384\) −0.866025 0.500000i −0.0441942 0.0255155i
\(385\) −13.4347 3.55343i −0.684697 0.181100i
\(386\) 5.23154 9.06130i 0.266279 0.461208i
\(387\) 1.70944 0.986944i 0.0868956 0.0501692i
\(388\) −4.24139 7.34631i −0.215324 0.372952i
\(389\) −16.9110 −0.857421 −0.428710 0.903442i \(-0.641032\pi\)
−0.428710 + 0.903442i \(0.641032\pi\)
\(390\) −8.01352 0.885137i −0.405780 0.0448207i
\(391\) −10.2971 −0.520747
\(392\) −2.77245 4.80203i −0.140030 0.242539i
\(393\) 5.76036 3.32575i 0.290572 0.167762i
\(394\) −8.79472 + 15.2329i −0.443072 + 0.767423i
\(395\) −7.76823 + 29.3699i −0.390862 + 1.47776i
\(396\) 4.46182 + 2.57603i 0.224215 + 0.129450i
\(397\) −16.1198 + 27.9204i −0.809031 + 1.40128i 0.104504 + 0.994524i \(0.466674\pi\)
−0.913536 + 0.406759i \(0.866659\pi\)
\(398\) 25.5716 1.28179
\(399\) 1.28475 2.22526i 0.0643181 0.111402i
\(400\) 0.0322474 + 4.99990i 0.00161237 + 0.249995i
\(401\) 28.0082 16.1705i 1.39866 0.807518i 0.404410 0.914578i \(-0.367477\pi\)
0.994253 + 0.107060i \(0.0341437\pi\)
\(402\) 14.0553i 0.701015i
\(403\) 16.6749 13.2696i 0.830638 0.661007i
\(404\) −13.5824 −0.675751
\(405\) −2.15800 + 0.585699i −0.107232 + 0.0291036i
\(406\) 2.87511 + 4.97984i 0.142689 + 0.247145i
\(407\) −19.6350 11.3363i −0.973272 0.561919i
\(408\) 4.73601 0.234467
\(409\) 1.00971 + 0.582957i 0.0499270 + 0.0288254i 0.524756 0.851253i \(-0.324157\pi\)
−0.474829 + 0.880078i \(0.657490\pi\)
\(410\) 7.46410 7.51240i 0.368626 0.371011i
\(411\) 14.7149i 0.725833i
\(412\) −1.86798 1.07848i −0.0920288 0.0531328i
\(413\) 2.02814 1.17095i 0.0997984 0.0576186i
\(414\) −1.88293 + 1.08711i −0.0925408 + 0.0534285i
\(415\) −5.83462 + 22.0594i −0.286410 + 1.08285i
\(416\) 3.56583 0.533691i 0.174829 0.0261663i
\(417\) 15.6508i 0.766423i
\(418\) −5.48725 9.50420i −0.268390 0.464866i
\(419\) 5.91396 + 10.2433i 0.288916 + 0.500417i 0.973551 0.228469i \(-0.0733719\pi\)
−0.684635 + 0.728886i \(0.740039\pi\)
\(420\) −1.90113 + 1.91343i −0.0927654 + 0.0933657i
\(421\) 23.9102i 1.16531i 0.812719 + 0.582655i \(0.197986\pi\)
−0.812719 + 0.582655i \(0.802014\pi\)
\(422\) 6.45984 11.1888i 0.314460 0.544661i
\(423\) 0.426148 0.738110i 0.0207200 0.0358881i
\(424\) 4.48042i 0.217588i
\(425\) −11.9720 20.4307i −0.580729 0.991036i
\(426\) 0.172459 + 0.298707i 0.00835566 + 0.0144724i
\(427\) 1.85519 + 3.21329i 0.0897791 + 0.155502i
\(428\) 8.09397i 0.391237i
\(429\) −18.3714 + 2.74961i −0.886980 + 0.132752i
\(430\) 4.26701 + 1.12861i 0.205774 + 0.0544263i
\(431\) −22.8082 + 13.1683i −1.09863 + 0.634294i −0.935861 0.352370i \(-0.885376\pi\)
−0.162769 + 0.986664i \(0.552043\pi\)
\(432\) 0.866025 0.500000i 0.0416667 0.0240563i
\(433\) −11.2232 6.47972i −0.539353 0.311396i 0.205464 0.978665i \(-0.434130\pi\)
−0.744817 + 0.667269i \(0.767463\pi\)
\(434\) 7.12964i 0.342234i
\(435\) −7.51283 + 7.56144i −0.360213 + 0.362543i
\(436\) −14.6219 8.44195i −0.700261 0.404296i
\(437\) 4.63134 0.221547
\(438\) 13.6164 + 7.86142i 0.650615 + 0.375633i
\(439\) 11.6234 + 20.1324i 0.554756 + 0.960865i 0.997922 + 0.0644259i \(0.0205216\pi\)
−0.443167 + 0.896439i \(0.646145\pi\)
\(440\) 3.01756 + 11.1181i 0.143856 + 0.530037i
\(441\) 5.54490 0.264043
\(442\) −13.3615 + 10.6328i −0.635542 + 0.505753i
\(443\) 23.3728i 1.11047i −0.831692 0.555237i \(-0.812627\pi\)
0.831692 0.555237i \(-0.187373\pi\)
\(444\) −3.81110 + 2.20034i −0.180867 + 0.104423i
\(445\) −9.59957 35.3695i −0.455063 1.67667i
\(446\) −3.57679 + 6.19518i −0.169366 + 0.293350i
\(447\) 22.8116 1.07895
\(448\) 0.603137 1.04466i 0.0284955 0.0493557i
\(449\) 1.20931 + 0.698196i 0.0570709 + 0.0329499i 0.528264 0.849080i \(-0.322843\pi\)
−0.471193 + 0.882030i \(0.656176\pi\)
\(450\) −4.34616 2.47202i −0.204880 0.116532i
\(451\) 12.2001 21.1312i 0.574481 0.995030i
\(452\) 4.28771 2.47551i 0.201677 0.116438i
\(453\) −9.94975 17.2335i −0.467480 0.809699i
\(454\) −25.8385 −1.21266
\(455\) 1.06772 9.66650i 0.0500554 0.453173i
\(456\) −2.13012 −0.0997519
\(457\) −3.60093 6.23699i −0.168444 0.291754i 0.769429 0.638733i \(-0.220541\pi\)
−0.937873 + 0.346979i \(0.887208\pi\)
\(458\) −7.75225 + 4.47576i −0.362239 + 0.209139i
\(459\) −2.36800 + 4.10150i −0.110529 + 0.191442i
\(460\) −4.70007 1.24315i −0.219142 0.0579622i
\(461\) −4.10920 2.37245i −0.191384 0.110496i 0.401246 0.915970i \(-0.368577\pi\)
−0.592630 + 0.805474i \(0.701911\pi\)
\(462\) −3.10740 + 5.38217i −0.144569 + 0.250401i
\(463\) −15.7510 −0.732012 −0.366006 0.930612i \(-0.619275\pi\)
−0.366006 + 0.930612i \(0.619275\pi\)
\(464\) 2.38346 4.12828i 0.110650 0.191651i
\(465\) 12.7548 3.46175i 0.591488 0.160535i
\(466\) −3.34855 + 1.93329i −0.155119 + 0.0895578i
\(467\) 17.9789i 0.831962i 0.909373 + 0.415981i \(0.136562\pi\)
−0.909373 + 0.415981i \(0.863438\pi\)
\(468\) −1.32073 + 3.35495i −0.0610506 + 0.155083i
\(469\) −16.9545 −0.782888
\(470\) 1.83925 0.499189i 0.0848384 0.0230259i
\(471\) 2.37196 + 4.10836i 0.109294 + 0.189303i
\(472\) −1.68133 0.970715i −0.0773894 0.0446808i
\(473\) 10.1696 0.467598
\(474\) 11.7661 + 6.79315i 0.540434 + 0.312020i
\(475\) 5.38467 + 9.18914i 0.247066 + 0.421627i
\(476\) 5.71292i 0.261851i
\(477\) 3.88016 + 2.24021i 0.177660 + 0.102572i
\(478\) 13.3521 7.70884i 0.610711 0.352594i
\(479\) 2.83964 1.63947i 0.129747 0.0749093i −0.433722 0.901047i \(-0.642800\pi\)
0.563468 + 0.826138i \(0.309467\pi\)
\(480\) 2.16173 + 0.571769i 0.0986691 + 0.0260976i
\(481\) 5.81210 14.7640i 0.265009 0.673183i
\(482\) 11.2768i 0.513646i
\(483\) −1.31135 2.27133i −0.0596685 0.103349i
\(484\) 7.77188 + 13.4613i 0.353267 + 0.611877i
\(485\) 13.4556 + 13.3691i 0.610989 + 0.607061i
\(486\) 1.00000i 0.0453609i
\(487\) 4.98852 8.64037i 0.226052 0.391533i −0.730583 0.682824i \(-0.760752\pi\)
0.956634 + 0.291291i \(0.0940849\pi\)
\(488\) 1.53795 2.66381i 0.0696199 0.120585i
\(489\) 3.86657i 0.174852i
\(490\) 8.79549 + 8.73894i 0.397340 + 0.394785i
\(491\) 10.0376 + 17.3857i 0.452992 + 0.784605i 0.998570 0.0534548i \(-0.0170233\pi\)
−0.545578 + 0.838060i \(0.683690\pi\)
\(492\) −2.36800 4.10150i −0.106758 0.184910i
\(493\) 22.5762i 1.01678i
\(494\) 6.00961 4.78234i 0.270385 0.215168i
\(495\) −11.1374 2.94579i −0.500588 0.132403i
\(496\) −5.11861 + 2.95523i −0.229832 + 0.132694i
\(497\) −0.360323 + 0.208033i −0.0161627 + 0.00933153i
\(498\) 8.83737 + 5.10226i 0.396012 + 0.228638i
\(499\) 23.9474i 1.07203i −0.844208 0.536016i \(-0.819929\pi\)
0.844208 0.536016i \(-0.180071\pi\)
\(500\) −2.99802 10.7709i −0.134076 0.481688i
\(501\) −19.6785 11.3614i −0.879173 0.507591i
\(502\) 12.3066 0.549269
\(503\) −10.5377 6.08395i −0.469853 0.271270i 0.246325 0.969187i \(-0.420777\pi\)
−0.716178 + 0.697917i \(0.754110\pi\)
\(504\) 0.603137 + 1.04466i 0.0268659 + 0.0465330i
\(505\) 29.3109 7.95522i 1.30432 0.354002i
\(506\) −11.2017 −0.497977
\(507\) −3.80611 12.4303i −0.169035 0.552051i
\(508\) 1.20191i 0.0533263i
\(509\) 34.9666 20.1880i 1.54987 0.894817i 0.551717 0.834031i \(-0.313973\pi\)
0.998151 0.0607857i \(-0.0193606\pi\)
\(510\) −10.2203 + 2.77388i −0.452563 + 0.122829i
\(511\) −9.48302 + 16.4251i −0.419504 + 0.726602i
\(512\) −1.00000 −0.0441942
\(513\) 1.06506 1.84474i 0.0470235 0.0814471i
\(514\) 24.3239 + 14.0434i 1.07288 + 0.619429i
\(515\) 4.66276 + 1.23328i 0.205466 + 0.0543449i
\(516\) 0.986944 1.70944i 0.0434478 0.0752538i
\(517\) 3.80279 2.19554i 0.167246 0.0965598i
\(518\) −2.65421 4.59723i −0.116619 0.201991i
\(519\) −4.69800 −0.206219
\(520\) −7.38248 + 3.24021i −0.323743 + 0.142093i
\(521\) −0.259356 −0.0113626 −0.00568129 0.999984i \(-0.501808\pi\)
−0.00568129 + 0.999984i \(0.501808\pi\)
\(522\) 2.38346 + 4.12828i 0.104321 + 0.180690i
\(523\) 33.4527 19.3139i 1.46278 0.844539i 0.463645 0.886021i \(-0.346541\pi\)
0.999139 + 0.0414825i \(0.0132081\pi\)
\(524\) 3.32575 5.76036i 0.145286 0.251642i
\(525\) 2.98193 5.24266i 0.130142 0.228808i
\(526\) 6.56756 + 3.79178i 0.286359 + 0.165330i
\(527\) 13.9960 24.2418i 0.609676 1.05599i
\(528\) 5.15206 0.224215
\(529\) −9.13639 + 15.8247i −0.397234 + 0.688030i
\(530\) 2.62418 + 9.66874i 0.113987 + 0.419983i
\(531\) 1.68133 0.970715i 0.0729634 0.0421255i
\(532\) 2.56951i 0.111402i
\(533\) 15.8891 + 6.25498i 0.688232 + 0.270933i
\(534\) −16.3899 −0.709262
\(535\) 4.74063 + 17.4668i 0.204955 + 0.755155i
\(536\) 7.02765 + 12.1723i 0.303548 + 0.525761i
\(537\) 7.53292 + 4.34913i 0.325069 + 0.187679i
\(538\) −24.4709 −1.05502
\(539\) 24.7403 + 14.2838i 1.06564 + 0.615249i
\(540\) −1.57603 + 1.58623i −0.0678216 + 0.0682604i
\(541\) 19.4443i 0.835975i −0.908453 0.417988i \(-0.862736\pi\)
0.908453 0.417988i \(-0.137264\pi\)
\(542\) 10.0199 + 5.78497i 0.430390 + 0.248486i
\(543\) −8.44791 + 4.87740i −0.362534 + 0.209309i
\(544\) 4.10150 2.36800i 0.175851 0.101527i
\(545\) 36.4984 + 9.65369i 1.56342 + 0.413518i
\(546\) −4.04699 1.59316i −0.173195 0.0681809i
\(547\) 25.2121i 1.07799i 0.842308 + 0.538997i \(0.181197\pi\)
−0.842308 + 0.538997i \(0.818803\pi\)
\(548\) 7.35746 + 12.7435i 0.314295 + 0.544375i
\(549\) 1.53795 + 2.66381i 0.0656383 + 0.113689i
\(550\) −13.0238 22.2256i −0.555336 0.947701i
\(551\) 10.1541i 0.432580i
\(552\) −1.08711 + 1.88293i −0.0462704 + 0.0801427i
\(553\) −8.19440 + 14.1931i −0.348462 + 0.603553i
\(554\) 12.9454i 0.549998i
\(555\) 6.93561 6.98049i 0.294400 0.296305i
\(556\) −7.82540 13.5540i −0.331871 0.574817i
\(557\) −5.63445 9.75916i −0.238739 0.413509i 0.721613 0.692296i \(-0.243401\pi\)
−0.960353 + 0.278787i \(0.910067\pi\)
\(558\) 5.91046i 0.250210i
\(559\) 1.05345 + 7.03856i 0.0445560 + 0.297699i
\(560\) −0.689710 + 2.60764i −0.0291456 + 0.110193i
\(561\) −21.1312 + 12.2001i −0.892160 + 0.515089i
\(562\) 2.22730 1.28593i 0.0939531 0.0542439i
\(563\) 14.2495 + 8.22694i 0.600544 + 0.346724i 0.769256 0.638941i \(-0.220627\pi\)
−0.168712 + 0.985665i \(0.553961\pi\)
\(564\) 0.852296i 0.0358881i
\(565\) −7.80296 + 7.85345i −0.328273 + 0.330397i
\(566\) −4.80517 2.77427i −0.201976 0.116611i
\(567\) −1.20627 −0.0506587
\(568\) 0.298707 + 0.172459i 0.0125335 + 0.00723621i
\(569\) 15.2444 + 26.4040i 0.639077 + 1.10691i 0.985636 + 0.168886i \(0.0540170\pi\)
−0.346558 + 0.938028i \(0.612650\pi\)
\(570\) 4.59679 1.24761i 0.192538 0.0522565i
\(571\) 13.0909 0.547836 0.273918 0.961753i \(-0.411680\pi\)
0.273918 + 0.961753i \(0.411680\pi\)
\(572\) −14.5353 + 11.5669i −0.607751 + 0.483638i
\(573\) 11.5546i 0.482699i
\(574\) 4.94754 2.85646i 0.206506 0.119226i
\(575\) 10.8709 0.0701128i 0.453346 0.00292390i
\(576\) 0.500000 0.866025i 0.0208333 0.0360844i
\(577\) −13.1315 −0.546670 −0.273335 0.961919i \(-0.588127\pi\)
−0.273335 + 0.961919i \(0.588127\pi\)
\(578\) −2.71489 + 4.70233i −0.112925 + 0.195591i
\(579\) 9.06130 + 5.23154i 0.376575 + 0.217416i
\(580\) −2.72558 + 10.3048i −0.113174 + 0.427884i
\(581\) −6.15472 + 10.6603i −0.255341 + 0.442263i
\(582\) 7.34631 4.24139i 0.304514 0.175811i
\(583\) 11.5417 + 19.9908i 0.478009 + 0.827935i
\(584\) 15.7228 0.650615
\(585\) 0.885137 8.01352i 0.0365959 0.331318i
\(586\) 24.1316 0.996866
\(587\) 3.03785 + 5.26171i 0.125386 + 0.217174i 0.921884 0.387467i \(-0.126650\pi\)
−0.796498 + 0.604641i \(0.793317\pi\)
\(588\) 4.80203 2.77245i 0.198032 0.114334i
\(589\) −6.29499 + 10.9032i −0.259381 + 0.449260i
\(590\) 4.19685 + 1.11005i 0.172782 + 0.0457000i
\(591\) −15.2329 8.79472i −0.626598 0.361767i
\(592\) −2.20034 + 3.81110i −0.0904334 + 0.156635i
\(593\) 18.3609 0.753990 0.376995 0.926215i \(-0.376957\pi\)
0.376995 + 0.926215i \(0.376957\pi\)
\(594\) −2.57603 + 4.46182i −0.105696 + 0.183071i
\(595\) −3.34605 12.3285i −0.137175 0.505418i
\(596\) 19.7555 11.4058i 0.809215 0.467200i
\(597\) 25.5716i 1.04658i
\(598\) −1.16036 7.75290i −0.0474507 0.317040i
\(599\) 22.1098 0.903382 0.451691 0.892174i \(-0.350821\pi\)
0.451691 + 0.892174i \(0.350821\pi\)
\(600\) −4.99990 + 0.0322474i −0.204120 + 0.00131649i
\(601\) −5.90349 10.2251i −0.240808 0.417092i 0.720136 0.693832i \(-0.244079\pi\)
−0.960945 + 0.276740i \(0.910746\pi\)
\(602\) 2.06205 + 1.19052i 0.0840428 + 0.0485222i
\(603\) −14.0553 −0.572376
\(604\) −17.2335 9.94975i −0.701220 0.404850i
\(605\) −24.6560 24.4975i −1.00241 0.995963i
\(606\) 13.5824i 0.551748i
\(607\) 22.3119 + 12.8818i 0.905612 + 0.522856i 0.879017 0.476791i \(-0.158200\pi\)
0.0265955 + 0.999646i \(0.491533\pi\)
\(608\) −1.84474 + 1.06506i −0.0748139 + 0.0431938i
\(609\) −4.97984 + 2.87511i −0.201793 + 0.116505i
\(610\) −1.75871 + 6.64928i −0.0712080 + 0.269222i
\(611\) 1.91349 + 2.40455i 0.0774117 + 0.0972775i
\(612\) 4.73601i 0.191442i
\(613\) 6.54178 + 11.3307i 0.264220 + 0.457642i 0.967359 0.253410i \(-0.0815522\pi\)
−0.703139 + 0.711052i \(0.748219\pi\)
\(614\) 15.1621 + 26.2616i 0.611894 + 1.05983i
\(615\) 7.51240 + 7.46410i 0.302929 + 0.300982i
\(616\) 6.21480i 0.250401i
\(617\) −2.20914 + 3.82634i −0.0889366 + 0.154043i −0.907062 0.420997i \(-0.861680\pi\)
0.818125 + 0.575040i \(0.195014\pi\)
\(618\) 1.07848 1.86798i 0.0433828 0.0751412i
\(619\) 1.12760i 0.0453220i 0.999743 + 0.0226610i \(0.00721383\pi\)
−0.999743 + 0.0226610i \(0.992786\pi\)
\(620\) 9.31508 9.37535i 0.374103 0.376523i
\(621\) −1.08711 1.88293i −0.0436242 0.0755593i
\(622\) 4.38203 + 7.58990i 0.175703 + 0.304327i
\(623\) 19.7708i 0.792099i
\(624\) 0.533691 + 3.56583i 0.0213647 + 0.142748i
\(625\) 12.7782 + 21.4876i 0.511129 + 0.859504i
\(626\) 25.1282 14.5077i 1.00432 0.579846i
\(627\) 9.50420 5.48725i 0.379561 0.219140i
\(628\) 4.10836 + 2.37196i 0.163941 + 0.0946515i
\(629\) 20.8417i 0.831011i
\(630\) −1.91343 1.90113i −0.0762328 0.0757427i
\(631\) −14.3916 8.30898i −0.572920 0.330775i 0.185395 0.982664i \(-0.440644\pi\)
−0.758315 + 0.651889i \(0.773977\pi\)
\(632\) 13.5863 0.540434
\(633\) 11.1888 + 6.45984i 0.444714 + 0.256756i
\(634\) −12.9985 22.5140i −0.516236 0.894147i
\(635\) −0.703960 2.59373i −0.0279358 0.102929i
\(636\) 4.48042 0.177660
\(637\) −7.32331 + 18.6029i −0.290160 + 0.737072i
\(638\) 24.5595i 0.972320i
\(639\) −0.298707 + 0.172459i −0.0118167 + 0.00682236i
\(640\) 2.15800 0.585699i 0.0853024 0.0231518i
\(641\) 5.05184 8.75005i 0.199536 0.345606i −0.748842 0.662748i \(-0.769390\pi\)
0.948378 + 0.317142i \(0.102723\pi\)
\(642\) 8.09397 0.319444
\(643\) −17.5208 + 30.3469i −0.690951 + 1.19676i 0.280575 + 0.959832i \(0.409475\pi\)
−0.971526 + 0.236931i \(0.923858\pi\)
\(644\) −2.27133 1.31135i −0.0895028 0.0516745i
\(645\) −1.12861 + 4.26701i −0.0444389 + 0.168014i
\(646\) 5.04413 8.73669i 0.198459 0.343740i
\(647\) −17.2864 + 9.98031i −0.679598 + 0.392366i −0.799704 0.600395i \(-0.795010\pi\)
0.120105 + 0.992761i \(0.461677\pi\)
\(648\) 0.500000 + 0.866025i 0.0196419 + 0.0340207i
\(649\) 10.0024 0.392628
\(650\) 14.0336 11.3163i 0.550443 0.443861i
\(651\) 7.12964 0.279433
\(652\) −1.93329 3.34855i −0.0757133 0.131139i
\(653\) 4.51410 2.60621i 0.176650 0.101989i −0.409068 0.912504i \(-0.634146\pi\)
0.585718 + 0.810515i \(0.300813\pi\)
\(654\) 8.44195 14.6219i 0.330106 0.571761i
\(655\) −3.80312 + 14.3787i −0.148600 + 0.561824i
\(656\) −4.10150 2.36800i −0.160137 0.0924551i
\(657\) −7.86142 + 13.6164i −0.306703 + 0.531225i
\(658\) 1.02810 0.0400796
\(659\) 3.66183 6.34248i 0.142645 0.247068i −0.785847 0.618421i \(-0.787773\pi\)
0.928492 + 0.371353i \(0.121106\pi\)
\(660\) −11.1181 + 3.01756i −0.432773 + 0.117458i
\(661\) −31.7189 + 18.3129i −1.23372 + 0.712289i −0.967803 0.251707i \(-0.919008\pi\)
−0.265917 + 0.963996i \(0.585675\pi\)
\(662\) 11.0392i 0.429052i
\(663\) −10.6328 13.3615i −0.412946 0.518918i
\(664\) 10.2045 0.396012
\(665\) 1.50496 + 5.54499i 0.0583597 + 0.215025i
\(666\) −2.20034 3.81110i −0.0852614 0.147677i
\(667\) −8.97578 5.18217i −0.347543 0.200654i
\(668\) −22.7228 −0.879173
\(669\) −6.19518 3.57679i −0.239519 0.138287i
\(670\) −22.2949 22.1516i −0.861329 0.855791i
\(671\) 15.8473i 0.611777i
\(672\) 1.04466 + 0.603137i 0.0402988 + 0.0232665i
\(673\) 29.4292 16.9909i 1.13441 0.654952i 0.189370 0.981906i \(-0.439355\pi\)
0.945041 + 0.326953i \(0.106022\pi\)
\(674\) −15.3380 + 8.85540i −0.590798 + 0.341097i
\(675\) 2.47202 4.34616i 0.0951481 0.167284i
\(676\) −9.51136 8.86194i −0.365822 0.340844i
\(677\) 41.7902i 1.60613i −0.595894 0.803063i \(-0.703202\pi\)
0.595894 0.803063i \(-0.296798\pi\)
\(678\) 2.47551 + 4.28771i 0.0950713 + 0.164668i
\(679\) 5.11628 + 8.86166i 0.196345 + 0.340079i
\(680\) −7.46410 + 7.51240i −0.286235 + 0.288087i
\(681\) 25.8385i 0.990132i
\(682\) 15.2255 26.3714i 0.583016 1.00981i
\(683\) 24.2071 41.9280i 0.926260 1.60433i 0.136737 0.990607i \(-0.456338\pi\)
0.789523 0.613721i \(-0.210328\pi\)
\(684\) 2.13012i 0.0814471i
\(685\) −23.3412 23.1912i −0.891823 0.886089i
\(686\) 7.56629 + 13.1052i 0.288882 + 0.500359i
\(687\) −4.47576 7.75225i −0.170761 0.295767i
\(688\) 1.97389i 0.0752538i
\(689\) −12.6404 + 10.0590i −0.481562 + 0.383218i
\(690\) 1.24315 4.70007i 0.0473259 0.178929i
\(691\) −23.8905 + 13.7932i −0.908837 + 0.524717i −0.880057 0.474868i \(-0.842496\pi\)
−0.0287804 + 0.999586i \(0.509162\pi\)
\(692\) −4.06859 + 2.34900i −0.154664 + 0.0892955i
\(693\) −5.38217 3.10740i −0.204452 0.118040i
\(694\) 34.7017i 1.31726i
\(695\) 24.8258 + 24.6662i 0.941695 + 0.935641i
\(696\) 4.12828 + 2.38346i 0.156482 + 0.0903449i
\(697\) 22.4298 0.849589
\(698\) −30.4563 17.5840i −1.15279 0.665563i
\(699\) −1.93329 3.34855i −0.0731236 0.126654i
\(700\) −0.0388991 6.03124i −0.00147025 0.227960i
\(701\) −19.7883 −0.747392 −0.373696 0.927551i \(-0.621910\pi\)
−0.373696 + 0.927551i \(0.621910\pi\)
\(702\) −3.35495 1.32073i −0.126624 0.0498476i
\(703\) 9.37396i 0.353546i
\(704\) 4.46182 2.57603i 0.168161 0.0970879i
\(705\) 0.499189 + 1.83925i 0.0188005 + 0.0692703i
\(706\) −5.54542 + 9.60495i −0.208705 + 0.361487i
\(707\) 16.3841 0.616189
\(708\) 0.970715 1.68133i 0.0364817 0.0631882i
\(709\) −6.09389 3.51831i −0.228861 0.132133i 0.381186 0.924499i \(-0.375516\pi\)
−0.610046 + 0.792366i \(0.708849\pi\)
\(710\) −0.745619 0.197213i −0.0279826 0.00740128i
\(711\) −6.79315 + 11.7661i −0.254763 + 0.441263i
\(712\) −14.1941 + 8.19497i −0.531946 + 0.307119i
\(713\) 6.42532 + 11.1290i 0.240630 + 0.416783i
\(714\) −5.71292 −0.213801
\(715\) 24.5924 33.4747i 0.919704 1.25188i
\(716\) 8.69827 0.325069
\(717\) 7.70884 + 13.3521i 0.287892 + 0.498643i
\(718\) 22.6531 13.0788i 0.845405 0.488095i
\(719\) −5.52118 + 9.56296i −0.205905 + 0.356638i −0.950421 0.310967i \(-0.899347\pi\)
0.744516 + 0.667605i \(0.232681\pi\)
\(720\) −0.571769 + 2.16173i −0.0213086 + 0.0805630i
\(721\) 2.25330 + 1.30094i 0.0839171 + 0.0484496i
\(722\) 7.23130 12.5250i 0.269121 0.466131i
\(723\) −11.2768 −0.419390
\(724\) −4.87740 + 8.44791i −0.181267 + 0.313964i
\(725\) −0.153721 23.8341i −0.00570905 0.885178i
\(726\) −13.4613 + 7.77188i −0.499595 + 0.288442i
\(727\) 14.1056i 0.523147i 0.965184 + 0.261573i \(0.0842414\pi\)
−0.965184 + 0.261573i \(0.915759\pi\)
\(728\) −4.30137 + 0.643777i −0.159419 + 0.0238600i
\(729\) −1.00000 −0.0370370
\(730\) −33.9298 + 9.20885i −1.25580 + 0.340835i
\(731\) 4.67418 + 8.09591i 0.172881 + 0.299438i
\(732\) 2.66381 + 1.53795i 0.0984574 + 0.0568444i
\(733\) −11.3855 −0.420535 −0.210267 0.977644i \(-0.567433\pi\)
−0.210267 + 0.977644i \(0.567433\pi\)
\(734\) −13.4988 7.79352i −0.498249 0.287664i
\(735\) −8.73894 + 8.79549i −0.322341 + 0.324426i
\(736\) 2.17422i 0.0801427i
\(737\) −62.7122 36.2069i −2.31003 1.33370i
\(738\) 4.10150 2.36800i 0.150978 0.0871675i
\(739\) −7.93251 + 4.57983i −0.291802 + 0.168472i −0.638754 0.769411i \(-0.720550\pi\)
0.346952 + 0.937883i \(0.387217\pi\)
\(740\) 2.51617 9.51308i 0.0924963 0.349708i
\(741\) 4.78234 + 6.00961i 0.175684 + 0.220769i
\(742\) 5.40461i 0.198410i
\(743\) 19.9566 + 34.5658i 0.732135 + 1.26809i 0.955969 + 0.293468i \(0.0948093\pi\)
−0.223834 + 0.974627i \(0.571857\pi\)
\(744\) −2.95523 5.11861i −0.108344 0.187657i
\(745\) −35.9519 + 36.1845i −1.31717 + 1.32570i
\(746\) 0.993455i 0.0363730i
\(747\) −5.10226 + 8.83737i −0.186682 + 0.323342i
\(748\) −12.2001 + 21.1312i −0.446080 + 0.772634i
\(749\) 9.76355i 0.356752i
\(750\) 10.7709 2.99802i 0.393297 0.109472i
\(751\) 8.79993 + 15.2419i 0.321114 + 0.556186i 0.980718 0.195427i \(-0.0626094\pi\)
−0.659604 + 0.751613i \(0.729276\pi\)
\(752\) −0.426148 0.738110i −0.0155400 0.0269161i
\(753\) 12.3066i 0.448476i
\(754\) −16.9981 + 2.54407i −0.619033 + 0.0926494i
\(755\) 43.0174 + 11.3779i 1.56556 + 0.414085i
\(756\) −1.04466 + 0.603137i −0.0379941 + 0.0219359i
\(757\) 19.1099 11.0331i 0.694560 0.401004i −0.110758 0.993847i \(-0.535328\pi\)
0.805318 + 0.592843i \(0.201995\pi\)
\(758\) 23.7856 + 13.7326i 0.863932 + 0.498791i
\(759\) 11.2017i 0.406596i
\(760\) 3.35713 3.37886i 0.121776 0.122564i
\(761\) −17.4454 10.0721i −0.632394 0.365113i 0.149285 0.988794i \(-0.452303\pi\)
−0.781678 + 0.623682i \(0.785636\pi\)
\(762\) −1.20191 −0.0435408
\(763\) 17.6380 + 10.1833i 0.638538 + 0.368660i
\(764\) −5.77729 10.0066i −0.209015 0.362025i
\(765\) −2.77388 10.2203i −0.100290 0.369516i
\(766\) 32.5703 1.17681
\(767\) 1.03612 + 6.92282i 0.0374123 + 0.249969i
\(768\) 1.00000i 0.0360844i
\(769\) 26.9356 15.5513i 0.971323 0.560794i 0.0716840 0.997427i \(-0.477163\pi\)
0.899639 + 0.436634i \(0.143829\pi\)
\(770\) −3.64000 13.4115i −0.131177 0.483318i
\(771\) −14.0434 + 24.3239i −0.505761 + 0.876004i
\(772\) 10.4631 0.376575
\(773\) 0.416119 0.720739i 0.0149668 0.0259232i −0.858445 0.512906i \(-0.828569\pi\)
0.873412 + 0.486982i \(0.161902\pi\)
\(774\) 1.70944 + 0.986944i 0.0614444 + 0.0354750i
\(775\) −14.6108 + 25.6878i −0.524835 + 0.922734i
\(776\) 4.24139 7.34631i 0.152257 0.263717i
\(777\) 4.59723 2.65421i 0.164925 0.0952193i
\(778\) −8.45549 14.6453i −0.303144 0.525061i
\(779\) −10.0883 −0.361449
\(780\) −3.24021 7.38248i −0.116018 0.264335i
\(781\) −1.77704 −0.0635874
\(782\) −5.14856 8.91756i −0.184112 0.318891i
\(783\) −4.12828 + 2.38346i −0.147533 + 0.0851780i
\(784\) 2.77245 4.80203i 0.0990161 0.171501i
\(785\) −10.2551 2.71243i −0.366019 0.0968106i
\(786\) 5.76036 + 3.32575i 0.205465 + 0.118625i
\(787\) 12.4115 21.4974i 0.442422 0.766298i −0.555446 0.831552i \(-0.687453\pi\)
0.997869 + 0.0652545i \(0.0207859\pi\)
\(788\) −17.5894 −0.626598
\(789\) −3.79178 + 6.56756i −0.134991 + 0.233811i
\(790\) −29.3192 + 7.95749i −1.04313 + 0.283115i
\(791\) −5.17215 + 2.98614i −0.183900 + 0.106175i
\(792\) 5.15206i 0.183071i
\(793\) −10.9682 + 1.64158i −0.389491 + 0.0582944i
\(794\) −32.2397 −1.14414
\(795\) −9.66874 + 2.62418i −0.342915 + 0.0930700i
\(796\) 12.7858 + 22.1457i 0.453181 + 0.784932i
\(797\) 20.5483 + 11.8636i 0.727858 + 0.420229i 0.817638 0.575733i \(-0.195283\pi\)
−0.0897802 + 0.995962i \(0.528616\pi\)
\(798\) 2.56951 0.0909595
\(799\) 3.49569 + 2.01824i 0.123669 + 0.0714002i
\(800\) −4.31391 + 2.52788i −0.152520 + 0.0893739i
\(801\) 16.3899i 0.579110i
\(802\) 28.0082 + 16.1705i 0.989003 + 0.571001i
\(803\) −70.1524 + 40.5025i −2.47562 + 1.42930i
\(804\) −12.1723 + 7.02765i −0.429282 + 0.247846i
\(805\) 5.66958 + 1.49958i 0.199826 + 0.0528532i
\(806\) 19.8293 + 7.80611i 0.698457 + 0.274959i
\(807\) 24.4709i 0.861418i
\(808\) −6.79121 11.7627i −0.238914 0.413811i
\(809\) 18.7196 + 32.4233i 0.658145 + 1.13994i 0.981095 + 0.193525i \(0.0619921\pi\)
−0.322950 + 0.946416i \(0.604675\pi\)
\(810\) −1.58623 1.57603i −0.0557344 0.0553761i
\(811\) 40.2205i 1.41233i 0.708046 + 0.706166i \(0.249577\pi\)
−0.708046 + 0.706166i \(0.750423\pi\)
\(812\) −2.87511 + 4.97984i −0.100897 + 0.174758i
\(813\) −5.78497 + 10.0199i −0.202888 + 0.351412i
\(814\) 22.6726i 0.794673i
\(815\) 6.13327 + 6.09384i 0.214839 + 0.213458i
\(816\) 2.36800 + 4.10150i 0.0828967 + 0.143581i
\(817\) −2.10231 3.64130i −0.0735504 0.127393i
\(818\) 1.16591i 0.0407652i
\(819\) 1.59316 4.04699i 0.0556695 0.141413i
\(820\) 10.2380 + 2.70790i 0.357526 + 0.0945641i
\(821\) −24.5442 + 14.1706i −0.856598 + 0.494557i −0.862872 0.505423i \(-0.831336\pi\)
0.00627372 + 0.999980i \(0.498003\pi\)
\(822\) −12.7435 + 7.35746i −0.444480 + 0.256621i
\(823\) −41.0437 23.6966i −1.43069 0.826011i −0.433520 0.901144i \(-0.642729\pi\)
−0.997174 + 0.0751325i \(0.976062\pi\)
\(824\) 2.15696i 0.0751412i
\(825\) 22.2256 13.0238i 0.773795 0.453430i
\(826\) 2.02814 + 1.17095i 0.0705681 + 0.0407425i
\(827\) −2.70177 −0.0939496 −0.0469748 0.998896i \(-0.514958\pi\)
−0.0469748 + 0.998896i \(0.514958\pi\)
\(828\) −1.88293 1.08711i −0.0654363 0.0377796i
\(829\) −10.4285 18.0627i −0.362197 0.627343i 0.626125 0.779722i \(-0.284640\pi\)
−0.988322 + 0.152379i \(0.951307\pi\)
\(830\) −22.0213 + 5.97677i −0.764371 + 0.207457i
\(831\) 12.9454 0.449072
\(832\) 2.24511 + 2.82126i 0.0778351 + 0.0978095i
\(833\) 26.2607i 0.909880i
\(834\) 13.5540 7.82540i 0.469336 0.270972i
\(835\) 49.0358 13.3087i 1.69695 0.460568i
\(836\) 5.48725 9.50420i 0.189781 0.328710i
\(837\) 5.91046 0.204296
\(838\) −5.91396 + 10.2433i −0.204294 + 0.353848i
\(839\) 5.34438 + 3.08558i 0.184508 + 0.106526i 0.589409 0.807835i \(-0.299361\pi\)
−0.404901 + 0.914361i \(0.632694\pi\)
\(840\) −2.60764 0.689710i −0.0899721 0.0237973i
\(841\) 3.13821 5.43553i 0.108214 0.187432i
\(842\) −20.7068 + 11.9551i −0.713604 + 0.412000i
\(843\) 1.28593 + 2.22730i 0.0442899 + 0.0767124i
\(844\) 12.9197 0.444714
\(845\) 25.7159 + 13.5533i 0.884655 + 0.466247i
\(846\) 0.852296 0.0293025
\(847\) −9.37502 16.2380i −0.322129 0.557944i
\(848\) 3.88016 2.24021i 0.133245 0.0769291i
\(849\) 2.77427 4.80517i 0.0952125 0.164913i
\(850\) 11.7075 20.5835i 0.401564 0.706007i
\(851\) 8.28616 + 4.78402i 0.284046 + 0.163994i
\(852\) −0.172459 + 0.298707i −0.00590834 + 0.0102335i
\(853\) −52.4997 −1.79756 −0.898778 0.438405i \(-0.855544\pi\)
−0.898778 + 0.438405i \(0.855544\pi\)
\(854\) −1.85519 + 3.21329i −0.0634834 + 0.109956i
\(855\) 1.24761 + 4.59679i 0.0426673 + 0.157207i
\(856\) 7.00959 4.04699i 0.239583 0.138323i
\(857\) 23.9128i 0.816846i −0.912793 0.408423i \(-0.866079\pi\)
0.912793 0.408423i \(-0.133921\pi\)
\(858\) −11.5669 14.5353i −0.394889 0.496227i
\(859\) −35.2521 −1.20279 −0.601393 0.798953i \(-0.705387\pi\)
−0.601393 + 0.798953i \(0.705387\pi\)
\(860\) 1.15610 + 4.25965i 0.0394228 + 0.145253i
\(861\) 2.85646 + 4.94754i 0.0973480 + 0.168612i
\(862\) −22.8082 13.1683i −0.776849 0.448514i
\(863\) −7.68909 −0.261740 −0.130870 0.991400i \(-0.541777\pi\)
−0.130870 + 0.991400i \(0.541777\pi\)
\(864\) 0.866025 + 0.500000i 0.0294628 + 0.0170103i
\(865\) 7.40419 7.45210i 0.251750 0.253379i
\(866\) 12.9594i 0.440380i
\(867\) −4.70233 2.71489i −0.159700 0.0922026i
\(868\) 6.17445 3.56482i 0.209574 0.120998i
\(869\) −60.6196 + 34.9988i −2.05638 + 1.18725i
\(870\) −10.3048 2.72558i −0.349366 0.0924058i
\(871\) 18.5632 47.1548i 0.628991 1.59778i
\(872\) 16.8839i 0.571761i
\(873\) 4.24139 + 7.34631i 0.143549 + 0.248635i
\(874\) 2.31567 + 4.01086i 0.0783287 + 0.135669i
\(875\) 3.61644 + 12.9926i 0.122258 + 0.439231i
\(876\) 15.7228i 0.531225i
\(877\) 8.42697 14.5959i 0.284559 0.492870i −0.687943 0.725764i \(-0.741486\pi\)
0.972502 + 0.232894i \(0.0748196\pi\)
\(878\) −11.6234 + 20.1324i −0.392272 + 0.679434i
\(879\) 24.1316i 0.813938i
\(880\) −8.11982 + 8.17235i −0.273719 + 0.275490i
\(881\) −24.0475 41.6516i −0.810182 1.40328i −0.912736 0.408550i \(-0.866035\pi\)
0.102554 0.994727i \(-0.467299\pi\)
\(882\) 2.77245 + 4.80203i 0.0933533 + 0.161693i
\(883\) 38.3641i 1.29105i −0.763737 0.645527i \(-0.776638\pi\)
0.763737 0.645527i \(-0.223362\pi\)
\(884\) −15.8891 6.25498i −0.534407 0.210378i
\(885\) −1.11005 + 4.19685i −0.0373139 + 0.141076i
\(886\) 20.2414 11.6864i 0.680024 0.392612i
\(887\) −16.2697 + 9.39331i −0.546283 + 0.315396i −0.747621 0.664125i \(-0.768804\pi\)
0.201339 + 0.979522i \(0.435471\pi\)
\(888\) −3.81110 2.20034i −0.127892 0.0738385i
\(889\) 1.44984i 0.0486260i
\(890\) 25.8311 25.9982i 0.865859 0.871462i
\(891\) −4.46182 2.57603i −0.149477 0.0863003i
\(892\) −7.15357 −0.239519
\(893\) −1.57226 0.907745i −0.0526137 0.0303765i
\(894\) 11.4058 + 19.7555i 0.381468 + 0.660721i
\(895\) −18.7708 + 5.09457i −0.627440 + 0.170293i
\(896\) 1.20627 0.0402988
\(897\) 7.75290 1.16036i 0.258862 0.0387433i
\(898\) 1.39639i 0.0465982i
\(899\) 24.4000 14.0874i 0.813787 0.469840i
\(900\) −0.0322474 4.99990i −0.00107491 0.166663i
\(901\) −10.6097 + 18.3765i −0.353459 + 0.612209i
\(902\) 24.4002 0.812439
\(903\) −1.19052 + 2.06205i −0.0396182 + 0.0686207i
\(904\) 4.28771 + 2.47551i 0.142607 + 0.0823342i
\(905\) 5.57749 21.0873i 0.185402 0.700964i
\(906\) 9.94975 17.2335i 0.330558 0.572544i
\(907\) 18.2967 10.5636i 0.607532 0.350759i −0.164467 0.986383i \(-0.552590\pi\)
0.771999 + 0.635624i \(0.219257\pi\)
\(908\) −12.9192 22.3768i −0.428740 0.742599i
\(909\) 13.5824 0.450501
\(910\) 8.90530 3.90858i 0.295208 0.129568i
\(911\) 19.2766 0.638664 0.319332 0.947643i \(-0.396542\pi\)
0.319332 + 0.947643i \(0.396542\pi\)
\(912\) −1.06506 1.84474i −0.0352676 0.0610853i
\(913\) −45.5307 + 26.2872i −1.50685 + 0.869978i
\(914\) 3.60093 6.23699i 0.119108 0.206301i
\(915\) −6.64928 1.75871i −0.219819 0.0581411i
\(916\) −7.75225 4.47576i −0.256142 0.147883i
\(917\) −4.01176 + 6.94857i −0.132480 + 0.229462i
\(918\) −4.73601 −0.156312
\(919\) 17.8995 31.0028i 0.590450 1.02269i −0.403722 0.914882i \(-0.632284\pi\)
0.994172 0.107807i \(-0.0343830\pi\)
\(920\) −1.27344 4.69196i −0.0419840 0.154689i
\(921\) −26.2616 + 15.1621i −0.865348 + 0.499609i
\(922\) 4.74489i 0.156265i
\(923\) −0.184079 1.22992i −0.00605905 0.0404833i
\(924\) −6.21480 −0.204452
\(925\) 0.141910 + 22.0029i 0.00466598 + 0.723452i
\(926\) −7.87551 13.6408i −0.258805 0.448264i
\(927\) 1.86798 + 1.07848i 0.0613525 + 0.0354219i
\(928\) 4.76693 0.156482
\(929\) −13.4933 7.79033i −0.442699 0.255593i 0.262043 0.965056i \(-0.415604\pi\)
−0.704742 + 0.709464i \(0.748937\pi\)
\(930\) 9.37535 + 9.31508i 0.307430 + 0.305454i
\(931\) 11.8113i 0.387100i
\(932\) −3.34855 1.93329i −0.109685 0.0633269i
\(933\) −7.58990 + 4.38203i −0.248482 + 0.143461i
\(934\) −15.5701 + 8.98943i −0.509471 + 0.294143i
\(935\) 13.9513 52.7467i 0.456256 1.72500i
\(936\) −3.56583 + 0.533691i −0.116553 + 0.0174442i
\(937\) 27.4692i 0.897381i −0.893687 0.448690i \(-0.851891\pi\)
0.893687 0.448690i \(-0.148109\pi\)
\(938\) −8.47727 14.6831i −0.276793 0.479419i
\(939\) 14.5077 + 25.1282i 0.473442 + 0.820026i
\(940\) 1.35194 + 1.34324i 0.0440953 + 0.0438118i
\(941\) 5.01957i 0.163633i 0.996647 + 0.0818167i \(0.0260722\pi\)
−0.996647 + 0.0818167i \(0.973928\pi\)
\(942\) −2.37196 + 4.10836i −0.0772826 + 0.133857i
\(943\) −5.14856 + 8.91756i −0.167660 + 0.290396i
\(944\) 1.94143i 0.0631882i
\(945\) 1.90113 1.91343i 0.0618436 0.0622438i
\(946\) 5.08480 + 8.80713i 0.165321 + 0.286344i
\(947\) 20.0915 + 34.7995i 0.652886 + 1.13083i 0.982419 + 0.186688i \(0.0597752\pi\)
−0.329534 + 0.944144i \(0.606891\pi\)
\(948\) 13.5863i 0.441263i
\(949\) −35.2994 44.3582i −1.14587 1.43993i
\(950\) −5.26570 + 9.25783i −0.170842 + 0.300364i
\(951\) 22.5140 12.9985i 0.730068 0.421505i
\(952\) −4.94754 + 2.85646i −0.160351 + 0.0925785i
\(953\) −9.42493 5.44149i −0.305304 0.176267i 0.339519 0.940599i \(-0.389736\pi\)
−0.644823 + 0.764332i \(0.723069\pi\)
\(954\) 4.48042i 0.145059i
\(955\) 18.3282 + 18.2104i 0.593087 + 0.589274i
\(956\) 13.3521 + 7.70884i 0.431838 + 0.249322i
\(957\) −24.5595 −0.793896
\(958\) 2.83964 + 1.63947i 0.0917447 + 0.0529688i
\(959\) −8.87511 15.3721i −0.286592 0.496392i
\(960\) 0.585699 + 2.15800i 0.0189034 + 0.0696491i
\(961\) −3.93359 −0.126890
\(962\) 15.6921 2.34860i 0.505933 0.0757220i
\(963\) 8.09397i 0.260825i
\(964\) −9.76603 + 5.63842i −0.314543 + 0.181601i
\(965\) −22.5793 + 6.12822i −0.726854 + 0.197274i
\(966\) 1.31135 2.27133i 0.0421920 0.0730787i
\(967\) −2.14376 −0.0689387 −0.0344693 0.999406i \(-0.510974\pi\)
−0.0344693 + 0.999406i \(0.510974\pi\)
\(968\) −7.77188 + 13.4613i −0.249798 + 0.432662i
\(969\) 8.73669 + 5.04413i 0.280663 + 0.162041i
\(970\) −4.85019 + 18.3375i −0.155730 + 0.588781i
\(971\) −4.57889 + 7.93087i −0.146944 + 0.254514i −0.930096 0.367316i \(-0.880277\pi\)
0.783153 + 0.621829i \(0.213610\pi\)
\(972\) −0.866025 + 0.500000i −0.0277778 + 0.0160375i
\(973\) 9.43958 + 16.3498i 0.302619 + 0.524151i
\(974\) 9.97704 0.319685
\(975\) 11.3163 + 14.0336i 0.362411 + 0.449435i
\(976\) 3.07591 0.0984574
\(977\) −7.16508 12.4103i −0.229231 0.397040i 0.728349 0.685206i \(-0.240288\pi\)
−0.957581 + 0.288166i \(0.906955\pi\)
\(978\) 3.34855 1.93329i 0.107075 0.0618197i
\(979\) 42.2210 73.1289i 1.34939 2.33721i
\(980\) −3.17040 + 11.9866i −0.101275 + 0.382898i
\(981\) 14.6219 + 8.44195i 0.466841 + 0.269531i
\(982\) −10.0376 + 17.3857i −0.320314 + 0.554800i
\(983\) 21.6099 0.689250 0.344625 0.938740i \(-0.388006\pi\)
0.344625 + 0.938740i \(0.388006\pi\)
\(984\) 2.36800 4.10150i 0.0754892 0.130751i
\(985\) 37.9580 10.3021i 1.20944 0.328253i
\(986\) −19.5516 + 11.2881i −0.622649 + 0.359486i
\(987\) 1.02810i 0.0327248i
\(988\) 7.14644 + 2.81330i 0.227358 + 0.0895031i
\(989\) −4.29166 −0.136467
\(990\) −3.01756 11.1181i −0.0959043 0.353358i
\(991\) −11.9222 20.6499i −0.378722 0.655966i 0.612154 0.790738i \(-0.290303\pi\)
−0.990877 + 0.134772i \(0.956970\pi\)
\(992\) −5.11861 2.95523i −0.162516 0.0938287i
\(993\) 11.0392 0.350319
\(994\) −0.360323 0.208033i −0.0114287 0.00659839i
\(995\) −40.5624 40.3017i −1.28592 1.27765i
\(996\) 10.2045i 0.323342i
\(997\) 25.5772 + 14.7670i 0.810037 + 0.467675i 0.846969 0.531642i \(-0.178425\pi\)
−0.0369315 + 0.999318i \(0.511758\pi\)
\(998\) 20.7390 11.9737i 0.656482 0.379020i
\(999\) 3.81110 2.20034i 0.120578 0.0696157i
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 390.2.x.b.49.3 yes 12
3.2 odd 2 1170.2.bj.c.829.3 12
5.2 odd 4 1950.2.bc.j.751.3 12
5.3 odd 4 1950.2.bc.i.751.4 12
5.4 even 2 390.2.x.a.49.4 12
13.4 even 6 390.2.x.a.199.4 yes 12
15.14 odd 2 1170.2.bj.d.829.4 12
39.17 odd 6 1170.2.bj.d.199.4 12
65.4 even 6 inner 390.2.x.b.199.3 yes 12
65.17 odd 12 1950.2.bc.j.901.3 12
65.43 odd 12 1950.2.bc.i.901.4 12
195.134 odd 6 1170.2.bj.c.199.3 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
390.2.x.a.49.4 12 5.4 even 2
390.2.x.a.199.4 yes 12 13.4 even 6
390.2.x.b.49.3 yes 12 1.1 even 1 trivial
390.2.x.b.199.3 yes 12 65.4 even 6 inner
1170.2.bj.c.199.3 12 195.134 odd 6
1170.2.bj.c.829.3 12 3.2 odd 2
1170.2.bj.d.199.4 12 39.17 odd 6
1170.2.bj.d.829.4 12 15.14 odd 2
1950.2.bc.i.751.4 12 5.3 odd 4
1950.2.bc.i.901.4 12 65.43 odd 12
1950.2.bc.j.751.3 12 5.2 odd 4
1950.2.bc.j.901.3 12 65.17 odd 12