Properties

Label 390.2.x.a.199.5
Level $390$
Weight $2$
Character 390.199
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 199.5
Root \(-1.44229 - 0.433312i\) of defining polynomial
Character \(\chi\) \(=\) 390.199
Dual form 390.2.x.a.49.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.230377 - 2.22417i) q^{5} +(-0.866025 + 0.500000i) q^{6} +(0.432713 + 0.749482i) q^{7} +1.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.230377 - 2.22417i) q^{5} +(-0.866025 + 0.500000i) q^{6} +(0.432713 + 0.749482i) q^{7} +1.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +(2.04138 + 0.912572i) q^{10} +(0.151430 + 0.0874279i) q^{11} -1.00000i q^{12} +(1.35486 + 3.34131i) q^{13} -0.865427 q^{14} +(0.912572 - 2.04138i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(7.08339 - 4.08960i) q^{17} -1.00000 q^{18} +(5.20843 - 3.00709i) q^{19} +(-1.81100 + 1.31160i) q^{20} +0.865427i q^{21} +(-0.151430 + 0.0874279i) q^{22} +(2.52211 + 1.45614i) q^{23} +(0.866025 + 0.500000i) q^{24} +(-4.89385 + 1.02479i) q^{25} +(-3.57109 - 0.497314i) q^{26} +1.00000i q^{27} +(0.432713 - 0.749482i) q^{28} +(3.24491 - 5.62035i) q^{29} +(1.31160 + 1.81100i) q^{30} +6.95057i q^{31} +(-0.500000 - 0.866025i) q^{32} +(0.0874279 + 0.151430i) q^{33} +8.17919i q^{34} +(1.56729 - 1.13509i) q^{35} +(0.500000 - 0.866025i) q^{36} +(-0.879573 + 1.52347i) q^{37} +6.01418i q^{38} +(-0.497314 + 3.57109i) q^{39} +(-0.230377 - 2.22417i) q^{40} +(-7.08339 - 4.08960i) q^{41} +(-0.749482 - 0.432713i) q^{42} +(-7.94476 + 4.58691i) q^{43} -0.174856i q^{44} +(1.81100 - 1.31160i) q^{45} +(-2.52211 + 1.45614i) q^{46} -11.9021 q^{47} +(-0.866025 + 0.500000i) q^{48} +(3.12552 - 5.41356i) q^{49} +(1.55943 - 4.75060i) q^{50} +8.17919 q^{51} +(2.21623 - 2.84400i) q^{52} +2.48735i q^{53} +(-0.866025 - 0.500000i) q^{54} +(0.159569 - 0.356946i) q^{55} +(0.432713 + 0.749482i) q^{56} +6.01418 q^{57} +(3.24491 + 5.62035i) q^{58} +(-6.09393 + 3.51833i) q^{59} +(-2.22417 + 0.230377i) q^{60} +(3.98695 + 6.90559i) q^{61} +(-6.01937 - 3.47529i) q^{62} +(-0.432713 + 0.749482i) q^{63} +1.00000 q^{64} +(7.11951 - 3.78319i) q^{65} -0.174856 q^{66} +(1.36766 - 2.36886i) q^{67} +(-7.08339 - 4.08960i) q^{68} +(1.45614 + 2.52211i) q^{69} +(0.199374 + 1.92486i) q^{70} +(12.2677 - 7.08275i) q^{71} +(0.500000 + 0.866025i) q^{72} -12.8706 q^{73} +(-0.879573 - 1.52347i) q^{74} +(-4.75060 - 1.55943i) q^{75} +(-5.20843 - 3.00709i) q^{76} +0.151325i q^{77} +(-2.84400 - 2.21623i) q^{78} +9.48961 q^{79} +(2.04138 + 0.912572i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(7.08339 - 4.08960i) q^{82} +0.139544 q^{83} +(0.749482 - 0.432713i) q^{84} +(-10.7278 - 14.8125i) q^{85} -9.17382i q^{86} +(5.62035 - 3.24491i) q^{87} +(0.151430 + 0.0874279i) q^{88} +(-11.3790 - 6.56966i) q^{89} +(0.230377 + 2.22417i) q^{90} +(-1.91799 + 2.46127i) q^{91} -2.91228i q^{92} +(-3.47529 + 6.01937i) q^{93} +(5.95105 - 10.3075i) q^{94} +(-7.88817 - 10.8917i) q^{95} -1.00000i q^{96} +(-4.32411 - 7.48957i) q^{97} +(3.12552 + 5.41356i) q^{98} +0.174856i 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 \( 12 q - 6 q^{2} - 6 q^{4} - 2 q^{5} - 2 q^{7} + 12 q^{8} + 6 q^{9} - 2 q^{10} + 6 q^{11} - 8 q^{13} + 4 q^{14} + 6 q^{15} - 6 q^{16} + 18 q^{17} - 12 q^{18} - 6 q^{19} + 4 q^{20} - 6 q^{22} + 6 q^{23} - 10 q^{25} - 2 q^{26} - 2 q^{28} + 14 q^{29} - 6 q^{30} - 6 q^{32} + 6 q^{33} + 26 q^{35} + 6 q^{36} - 12 q^{37} - 2 q^{39} - 2 q^{40} - 18 q^{41} - 12 q^{42} - 36 q^{43} - 4 q^{45} - 6 q^{46} + 16 q^{47} + 8 q^{49} - 10 q^{50} + 16 q^{51} + 10 q^{52} - 28 q^{55} - 2 q^{56} - 8 q^{57} + 14 q^{58} - 36 q^{59} + 10 q^{61} + 6 q^{62} + 2 q^{63} + 12 q^{64} + 6 q^{65} - 12 q^{66} + 4 q^{67} - 18 q^{68} + 16 q^{69} - 4 q^{70} - 12 q^{71} + 6 q^{72} + 28 q^{73} - 12 q^{74} - 8 q^{75} + 6 q^{76} - 2 q^{78} + 4 q^{79} - 2 q^{80} - 6 q^{81} + 18 q^{82} + 72 q^{83} + 12 q^{84} + 18 q^{85} + 6 q^{87} + 6 q^{88} + 18 q^{89} + 2 q^{90} + 2 q^{91} - 16 q^{93} - 8 q^{94} - 42 q^{95} - 48 q^{97} + 8 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

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
\(5\) −0.230377 2.22417i −0.103028 0.994678i
\(6\) −0.866025 + 0.500000i −0.353553 + 0.204124i
\(7\) 0.432713 + 0.749482i 0.163550 + 0.283277i 0.936140 0.351629i \(-0.114372\pi\)
−0.772589 + 0.634906i \(0.781039\pi\)
\(8\) 1.00000 0.353553
\(9\) 0.500000 + 0.866025i 0.166667 + 0.288675i
\(10\) 2.04138 + 0.912572i 0.645539 + 0.288581i
\(11\) 0.151430 + 0.0874279i 0.0456577 + 0.0263605i 0.522655 0.852544i \(-0.324942\pi\)
−0.476997 + 0.878905i \(0.658275\pi\)
\(12\) 1.00000i 0.288675i
\(13\) 1.35486 + 3.34131i 0.375770 + 0.926713i
\(14\) −0.865427 −0.231295
\(15\) 0.912572 2.04138i 0.235625 0.527081i
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 7.08339 4.08960i 1.71797 0.991873i 0.795370 0.606125i \(-0.207277\pi\)
0.922604 0.385748i \(-0.126057\pi\)
\(18\) −1.00000 −0.235702
\(19\) 5.20843 3.00709i 1.19490 0.689873i 0.235483 0.971879i \(-0.424333\pi\)
0.959413 + 0.282005i \(0.0909996\pi\)
\(20\) −1.81100 + 1.31160i −0.404951 + 0.293282i
\(21\) 0.865427i 0.188852i
\(22\) −0.151430 + 0.0874279i −0.0322849 + 0.0186397i
\(23\) 2.52211 + 1.45614i 0.525896 + 0.303626i 0.739344 0.673328i \(-0.235136\pi\)
−0.213448 + 0.976954i \(0.568469\pi\)
\(24\) 0.866025 + 0.500000i 0.176777 + 0.102062i
\(25\) −4.89385 + 1.02479i −0.978771 + 0.204959i
\(26\) −3.57109 0.497314i −0.700348 0.0975312i
\(27\) 1.00000i 0.192450i
\(28\) 0.432713 0.749482i 0.0817752 0.141639i
\(29\) 3.24491 5.62035i 0.602564 1.04367i −0.389867 0.920871i \(-0.627479\pi\)
0.992431 0.122801i \(-0.0391877\pi\)
\(30\) 1.31160 + 1.81100i 0.239464 + 0.330642i
\(31\) 6.95057i 1.24836i 0.781281 + 0.624180i \(0.214567\pi\)
−0.781281 + 0.624180i \(0.785433\pi\)
\(32\) −0.500000 0.866025i −0.0883883 0.153093i
\(33\) 0.0874279 + 0.151430i 0.0152192 + 0.0263605i
\(34\) 8.17919i 1.40272i
\(35\) 1.56729 1.13509i 0.264920 0.191865i
\(36\) 0.500000 0.866025i 0.0833333 0.144338i
\(37\) −0.879573 + 1.52347i −0.144601 + 0.250456i −0.929224 0.369517i \(-0.879523\pi\)
0.784623 + 0.619973i \(0.212856\pi\)
\(38\) 6.01418i 0.975628i
\(39\) −0.497314 + 3.57109i −0.0796339 + 0.571832i
\(40\) −0.230377 2.22417i −0.0364258 0.351672i
\(41\) −7.08339 4.08960i −1.10624 0.638688i −0.168387 0.985721i \(-0.553856\pi\)
−0.937853 + 0.347034i \(0.887189\pi\)
\(42\) −0.749482 0.432713i −0.115648 0.0667691i
\(43\) −7.94476 + 4.58691i −1.21156 + 0.699497i −0.963100 0.269144i \(-0.913259\pi\)
−0.248465 + 0.968641i \(0.579926\pi\)
\(44\) 0.174856i 0.0263605i
\(45\) 1.81100 1.31160i 0.269968 0.195521i
\(46\) −2.52211 + 1.45614i −0.371865 + 0.214696i
\(47\) −11.9021 −1.73610 −0.868050 0.496478i \(-0.834627\pi\)
−0.868050 + 0.496478i \(0.834627\pi\)
\(48\) −0.866025 + 0.500000i −0.125000 + 0.0721688i
\(49\) 3.12552 5.41356i 0.446503 0.773365i
\(50\) 1.55943 4.75060i 0.220537 0.671836i
\(51\) 8.17919 1.14532
\(52\) 2.21623 2.84400i 0.307336 0.394391i
\(53\) 2.48735i 0.341663i 0.985300 + 0.170832i \(0.0546454\pi\)
−0.985300 + 0.170832i \(0.945355\pi\)
\(54\) −0.866025 0.500000i −0.117851 0.0680414i
\(55\) 0.159569 0.356946i 0.0215162 0.0481306i
\(56\) 0.432713 + 0.749482i 0.0578238 + 0.100154i
\(57\) 6.01418 0.796597
\(58\) 3.24491 + 5.62035i 0.426077 + 0.737988i
\(59\) −6.09393 + 3.51833i −0.793363 + 0.458048i −0.841145 0.540810i \(-0.818118\pi\)
0.0477824 + 0.998858i \(0.484785\pi\)
\(60\) −2.22417 + 0.230377i −0.287139 + 0.0297415i
\(61\) 3.98695 + 6.90559i 0.510476 + 0.884171i 0.999926 + 0.0121394i \(0.00386418\pi\)
−0.489450 + 0.872031i \(0.662802\pi\)
\(62\) −6.01937 3.47529i −0.764461 0.441362i
\(63\) −0.432713 + 0.749482i −0.0545168 + 0.0944258i
\(64\) 1.00000 0.125000
\(65\) 7.11951 3.78319i 0.883067 0.469248i
\(66\) −0.174856 −0.0215233
\(67\) 1.36766 2.36886i 0.167086 0.289402i −0.770308 0.637672i \(-0.779897\pi\)
0.937394 + 0.348270i \(0.113231\pi\)
\(68\) −7.08339 4.08960i −0.858987 0.495936i
\(69\) 1.45614 + 2.52211i 0.175299 + 0.303626i
\(70\) 0.199374 + 1.92486i 0.0238298 + 0.230064i
\(71\) 12.2677 7.08275i 1.45591 0.840568i 0.457100 0.889415i \(-0.348888\pi\)
0.998806 + 0.0488476i \(0.0155549\pi\)
\(72\) 0.500000 + 0.866025i 0.0589256 + 0.102062i
\(73\) −12.8706 −1.50639 −0.753193 0.657800i \(-0.771487\pi\)
−0.753193 + 0.657800i \(0.771487\pi\)
\(74\) −0.879573 1.52347i −0.102248 0.177099i
\(75\) −4.75060 1.55943i −0.548552 0.180067i
\(76\) −5.20843 3.00709i −0.597448 0.344937i
\(77\) 0.151325i 0.0172451i
\(78\) −2.84400 2.21623i −0.322019 0.250939i
\(79\) 9.48961 1.06766 0.533832 0.845590i \(-0.320751\pi\)
0.533832 + 0.845590i \(0.320751\pi\)
\(80\) 2.04138 + 0.912572i 0.228233 + 0.102029i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 7.08339 4.08960i 0.782229 0.451620i
\(83\) 0.139544 0.0153169 0.00765845 0.999971i \(-0.497562\pi\)
0.00765845 + 0.999971i \(0.497562\pi\)
\(84\) 0.749482 0.432713i 0.0817752 0.0472129i
\(85\) −10.7278 14.8125i −1.16359 1.60664i
\(86\) 9.17382i 0.989238i
\(87\) 5.62035 3.24491i 0.602564 0.347891i
\(88\) 0.151430 + 0.0874279i 0.0161424 + 0.00931985i
\(89\) −11.3790 6.56966i −1.20617 0.696382i −0.244249 0.969713i \(-0.578541\pi\)
−0.961920 + 0.273330i \(0.911875\pi\)
\(90\) 0.230377 + 2.22417i 0.0242839 + 0.234448i
\(91\) −1.91799 + 2.46127i −0.201060 + 0.258011i
\(92\) 2.91228i 0.303626i
\(93\) −3.47529 + 6.01937i −0.360370 + 0.624180i
\(94\) 5.95105 10.3075i 0.613804 1.06314i
\(95\) −7.88817 10.8917i −0.809309 1.11746i
\(96\) 1.00000i 0.102062i
\(97\) −4.32411 7.48957i −0.439047 0.760451i 0.558570 0.829458i \(-0.311350\pi\)
−0.997616 + 0.0690066i \(0.978017\pi\)
\(98\) 3.12552 + 5.41356i 0.315725 + 0.546852i
\(99\) 0.174856i 0.0175737i
\(100\) 3.33442 + 3.72580i 0.333442 + 0.372580i
\(101\) −5.28276 + 9.15001i −0.525654 + 0.910460i 0.473899 + 0.880579i \(0.342846\pi\)
−0.999553 + 0.0298810i \(0.990487\pi\)
\(102\) −4.08960 + 7.08339i −0.404930 + 0.701360i
\(103\) 8.93568i 0.880459i 0.897885 + 0.440230i \(0.145103\pi\)
−0.897885 + 0.440230i \(0.854897\pi\)
\(104\) 1.35486 + 3.34131i 0.132855 + 0.327642i
\(105\) 1.92486 0.199374i 0.187847 0.0194569i
\(106\) −2.15410 1.24367i −0.209225 0.120796i
\(107\) −0.745455 0.430389i −0.0720658 0.0416072i 0.463534 0.886079i \(-0.346581\pi\)
−0.535600 + 0.844472i \(0.679914\pi\)
\(108\) 0.866025 0.500000i 0.0833333 0.0481125i
\(109\) 5.45336i 0.522337i −0.965293 0.261168i \(-0.915892\pi\)
0.965293 0.261168i \(-0.0841078\pi\)
\(110\) 0.229340 + 0.316664i 0.0218667 + 0.0301927i
\(111\) −1.52347 + 0.879573i −0.144601 + 0.0834854i
\(112\) −0.865427 −0.0817752
\(113\) −10.2036 + 5.89106i −0.959876 + 0.554184i −0.896135 0.443782i \(-0.853636\pi\)
−0.0637409 + 0.997966i \(0.520303\pi\)
\(114\) −3.00709 + 5.20843i −0.281640 + 0.487814i
\(115\) 2.65766 5.94505i 0.247829 0.554379i
\(116\) −6.48982 −0.602564
\(117\) −2.21623 + 2.84400i −0.204891 + 0.262928i
\(118\) 7.03667i 0.647778i
\(119\) 6.13015 + 3.53925i 0.561950 + 0.324442i
\(120\) 0.912572 2.04138i 0.0833061 0.186351i
\(121\) −5.48471 9.49980i −0.498610 0.863618i
\(122\) −7.97389 −0.721922
\(123\) −4.08960 7.08339i −0.368746 0.638688i
\(124\) 6.01937 3.47529i 0.540555 0.312090i
\(125\) 3.40675 + 10.6487i 0.304709 + 0.952446i
\(126\) −0.432713 0.749482i −0.0385492 0.0667691i
\(127\) 6.01228 + 3.47119i 0.533503 + 0.308018i 0.742442 0.669911i \(-0.233668\pi\)
−0.208939 + 0.977929i \(0.567001\pi\)
\(128\) −0.500000 + 0.866025i −0.0441942 + 0.0765466i
\(129\) −9.17382 −0.807710
\(130\) −0.283413 + 8.05727i −0.0248569 + 0.706670i
\(131\) 2.27133 0.198447 0.0992235 0.995065i \(-0.468364\pi\)
0.0992235 + 0.995065i \(0.468364\pi\)
\(132\) 0.0874279 0.151430i 0.00760962 0.0131803i
\(133\) 4.50751 + 2.60241i 0.390851 + 0.225658i
\(134\) 1.36766 + 2.36886i 0.118148 + 0.204638i
\(135\) 2.22417 0.230377i 0.191426 0.0198277i
\(136\) 7.08339 4.08960i 0.607395 0.350680i
\(137\) 3.68809 + 6.38795i 0.315094 + 0.545760i 0.979458 0.201650i \(-0.0646305\pi\)
−0.664363 + 0.747410i \(0.731297\pi\)
\(138\) −2.91228 −0.247910
\(139\) 0.410380 + 0.710798i 0.0348079 + 0.0602891i 0.882905 0.469552i \(-0.155585\pi\)
−0.848097 + 0.529842i \(0.822251\pi\)
\(140\) −1.76666 0.789764i −0.149310 0.0667473i
\(141\) −10.3075 5.95105i −0.868050 0.501169i
\(142\) 14.1655i 1.18874i
\(143\) −0.0869582 + 0.624426i −0.00727181 + 0.0522171i
\(144\) −1.00000 −0.0833333
\(145\) −13.2482 5.92243i −1.10020 0.491831i
\(146\) 6.43528 11.1462i 0.532588 0.922469i
\(147\) 5.41356 3.12552i 0.446503 0.257788i
\(148\) 1.75915 0.144601
\(149\) −8.90766 + 5.14284i −0.729744 + 0.421318i −0.818329 0.574751i \(-0.805099\pi\)
0.0885845 + 0.996069i \(0.471766\pi\)
\(150\) 3.72580 3.33442i 0.304211 0.272255i
\(151\) 11.7419i 0.955544i 0.878484 + 0.477772i \(0.158555\pi\)
−0.878484 + 0.477772i \(0.841445\pi\)
\(152\) 5.20843 3.00709i 0.422459 0.243907i
\(153\) 7.08339 + 4.08960i 0.572658 + 0.330624i
\(154\) −0.131051 0.0756625i −0.0105604 0.00609706i
\(155\) 15.4592 1.60125i 1.24172 0.128616i
\(156\) 3.34131 1.35486i 0.267519 0.108475i
\(157\) 6.76034i 0.539534i −0.962926 0.269767i \(-0.913053\pi\)
0.962926 0.269767i \(-0.0869467\pi\)
\(158\) −4.74480 + 8.21824i −0.377476 + 0.653808i
\(159\) −1.24367 + 2.15410i −0.0986297 + 0.170832i
\(160\) −1.81100 + 1.31160i −0.143172 + 0.103691i
\(161\) 2.52036i 0.198633i
\(162\) −0.500000 0.866025i −0.0392837 0.0680414i
\(163\) −0.713746 1.23624i −0.0559049 0.0968301i 0.836719 0.547633i \(-0.184471\pi\)
−0.892623 + 0.450803i \(0.851138\pi\)
\(164\) 8.17919i 0.638688i
\(165\) 0.316664 0.229340i 0.0246522 0.0178541i
\(166\) −0.0697718 + 0.120848i −0.00541534 + 0.00937964i
\(167\) 2.93528 5.08406i 0.227139 0.393416i −0.729820 0.683639i \(-0.760396\pi\)
0.956959 + 0.290223i \(0.0937295\pi\)
\(168\) 0.865427i 0.0667691i
\(169\) −9.32872 + 9.05401i −0.717594 + 0.696462i
\(170\) 18.1919 1.88430i 1.39526 0.144519i
\(171\) 5.20843 + 3.00709i 0.398298 + 0.229958i
\(172\) 7.94476 + 4.58691i 0.605782 + 0.349749i
\(173\) 11.8669 6.85138i 0.902226 0.520901i 0.0243045 0.999705i \(-0.492263\pi\)
0.877922 + 0.478804i \(0.158930\pi\)
\(174\) 6.48982i 0.491992i
\(175\) −2.88570 3.22441i −0.218138 0.243743i
\(176\) −0.151430 + 0.0874279i −0.0114144 + 0.00659013i
\(177\) −7.03667 −0.528908
\(178\) 11.3790 6.56966i 0.852890 0.492416i
\(179\) −7.09191 + 12.2835i −0.530074 + 0.918115i 0.469310 + 0.883033i \(0.344503\pi\)
−0.999384 + 0.0350821i \(0.988831\pi\)
\(180\) −2.04138 0.912572i −0.152155 0.0680191i
\(181\) 13.7728 1.02373 0.511863 0.859067i \(-0.328956\pi\)
0.511863 + 0.859067i \(0.328956\pi\)
\(182\) −1.17253 2.89166i −0.0869138 0.214344i
\(183\) 7.97389i 0.589447i
\(184\) 2.52211 + 1.45614i 0.185932 + 0.107348i
\(185\) 3.59108 + 1.60535i 0.264021 + 0.118027i
\(186\) −3.47529 6.01937i −0.254820 0.441362i
\(187\) 1.43018 0.104585
\(188\) 5.95105 + 10.3075i 0.434025 + 0.751753i
\(189\) −0.749482 + 0.432713i −0.0545168 + 0.0314753i
\(190\) 13.3765 1.38553i 0.970436 0.100517i
\(191\) 2.78821 + 4.82932i 0.201748 + 0.349437i 0.949092 0.315000i \(-0.102005\pi\)
−0.747344 + 0.664437i \(0.768671\pi\)
\(192\) 0.866025 + 0.500000i 0.0625000 + 0.0360844i
\(193\) −0.110405 + 0.191227i −0.00794712 + 0.0137648i −0.869972 0.493102i \(-0.835863\pi\)
0.862024 + 0.506867i \(0.169196\pi\)
\(194\) 8.64822 0.620906
\(195\) 8.05727 + 0.283413i 0.576993 + 0.0202956i
\(196\) −6.25104 −0.446503
\(197\) 0.861905 1.49286i 0.0614082 0.106362i −0.833687 0.552237i \(-0.813774\pi\)
0.895095 + 0.445875i \(0.147108\pi\)
\(198\) −0.151430 0.0874279i −0.0107616 0.00621323i
\(199\) −3.97927 6.89229i −0.282083 0.488581i 0.689815 0.723986i \(-0.257692\pi\)
−0.971898 + 0.235404i \(0.924359\pi\)
\(200\) −4.89385 + 1.02479i −0.346048 + 0.0724639i
\(201\) 2.36886 1.36766i 0.167086 0.0964673i
\(202\) −5.28276 9.15001i −0.371694 0.643793i
\(203\) 5.61646 0.394198
\(204\) −4.08960 7.08339i −0.286329 0.495936i
\(205\) −7.46410 + 16.6968i −0.521315 + 1.16615i
\(206\) −7.73853 4.46784i −0.539169 0.311289i
\(207\) 2.91228i 0.202417i
\(208\) −3.57109 0.497314i −0.247610 0.0344825i
\(209\) 1.05161 0.0727416
\(210\) −0.789764 + 1.76666i −0.0544989 + 0.121911i
\(211\) 2.10991 3.65448i 0.145252 0.251585i −0.784215 0.620490i \(-0.786934\pi\)
0.929467 + 0.368905i \(0.120267\pi\)
\(212\) 2.15410 1.24367i 0.147945 0.0854158i
\(213\) 14.1655 0.970604
\(214\) 0.745455 0.430389i 0.0509582 0.0294208i
\(215\) 12.0323 + 16.6138i 0.820599 + 1.13305i
\(216\) 1.00000i 0.0680414i
\(217\) −5.20933 + 3.00761i −0.353632 + 0.204170i
\(218\) 4.72274 + 2.72668i 0.319865 + 0.184674i
\(219\) −11.1462 6.43528i −0.753193 0.434856i
\(220\) −0.388909 + 0.0402827i −0.0262202 + 0.00271586i
\(221\) 23.2616 + 18.1270i 1.56474 + 1.21935i
\(222\) 1.75915i 0.118066i
\(223\) 3.47638 6.02126i 0.232795 0.403214i −0.725834 0.687870i \(-0.758546\pi\)
0.958630 + 0.284656i \(0.0918794\pi\)
\(224\) 0.432713 0.749482i 0.0289119 0.0500769i
\(225\) −3.33442 3.72580i −0.222295 0.248387i
\(226\) 11.7821i 0.783735i
\(227\) 1.44823 + 2.50840i 0.0961221 + 0.166488i 0.910076 0.414441i \(-0.136023\pi\)
−0.813954 + 0.580929i \(0.802689\pi\)
\(228\) −3.00709 5.20843i −0.199149 0.344937i
\(229\) 7.88800i 0.521254i −0.965440 0.260627i \(-0.916071\pi\)
0.965440 0.260627i \(-0.0839293\pi\)
\(230\) 3.81974 + 5.27413i 0.251866 + 0.347766i
\(231\) −0.0756625 + 0.131051i −0.00497823 + 0.00862254i
\(232\) 3.24491 5.62035i 0.213039 0.368994i
\(233\) 1.42749i 0.0935181i −0.998906 0.0467590i \(-0.985111\pi\)
0.998906 0.0467590i \(-0.0148893\pi\)
\(234\) −1.35486 3.34131i −0.0885699 0.218428i
\(235\) 2.74197 + 26.4723i 0.178866 + 1.72686i
\(236\) 6.09393 + 3.51833i 0.396681 + 0.229024i
\(237\) 8.21824 + 4.74480i 0.533832 + 0.308208i
\(238\) −6.13015 + 3.53925i −0.397359 + 0.229415i
\(239\) 10.9084i 0.705604i 0.935698 + 0.352802i \(0.114771\pi\)
−0.935698 + 0.352802i \(0.885229\pi\)
\(240\) 1.31160 + 1.81100i 0.0846632 + 0.116899i
\(241\) −25.4317 + 14.6830i −1.63820 + 0.945816i −0.656749 + 0.754109i \(0.728069\pi\)
−0.981452 + 0.191707i \(0.938598\pi\)
\(242\) 10.9694 0.705141
\(243\) −0.866025 + 0.500000i −0.0555556 + 0.0320750i
\(244\) 3.98695 6.90559i 0.255238 0.442085i
\(245\) −12.7607 5.70452i −0.815252 0.364448i
\(246\) 8.17919 0.521486
\(247\) 17.1043 + 13.3288i 1.08832 + 0.848091i
\(248\) 6.95057i 0.441362i
\(249\) 0.120848 + 0.0697718i 0.00765845 + 0.00442161i
\(250\) −10.9254 2.37400i −0.690982 0.150145i
\(251\) 8.94708 + 15.4968i 0.564735 + 0.978150i 0.997074 + 0.0764387i \(0.0243549\pi\)
−0.432339 + 0.901711i \(0.642312\pi\)
\(252\) 0.865427 0.0545168
\(253\) 0.254615 + 0.441005i 0.0160075 + 0.0277258i
\(254\) −6.01228 + 3.47119i −0.377244 + 0.217802i
\(255\) −1.88430 18.1919i −0.117999 1.13922i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −10.5472 6.08945i −0.657918 0.379849i 0.133565 0.991040i \(-0.457358\pi\)
−0.791483 + 0.611191i \(0.790691\pi\)
\(258\) 4.58691 7.94476i 0.285568 0.494619i
\(259\) −1.52241 −0.0945981
\(260\) −6.83610 4.27408i −0.423957 0.265067i
\(261\) 6.48982 0.401710
\(262\) −1.13567 + 1.96703i −0.0701616 + 0.121524i
\(263\) −18.3309 10.5834i −1.13033 0.652598i −0.186314 0.982490i \(-0.559654\pi\)
−0.944019 + 0.329892i \(0.892988\pi\)
\(264\) 0.0874279 + 0.151430i 0.00538082 + 0.00931985i
\(265\) 5.53228 0.573027i 0.339845 0.0352008i
\(266\) −4.50751 + 2.60241i −0.276373 + 0.159564i
\(267\) −6.56966 11.3790i −0.402056 0.696382i
\(268\) −2.73532 −0.167086
\(269\) −6.04371 10.4680i −0.368492 0.638246i 0.620838 0.783939i \(-0.286792\pi\)
−0.989330 + 0.145692i \(0.953459\pi\)
\(270\) −0.912572 + 2.04138i −0.0555374 + 0.124234i
\(271\) −12.7275 7.34824i −0.773142 0.446374i 0.0608525 0.998147i \(-0.480618\pi\)
−0.833994 + 0.551773i \(0.813951\pi\)
\(272\) 8.17919i 0.495936i
\(273\) −2.89166 + 1.17253i −0.175011 + 0.0709648i
\(274\) −7.37617 −0.445611
\(275\) −0.830670 0.272675i −0.0500913 0.0164429i
\(276\) 1.45614 2.52211i 0.0876493 0.151813i
\(277\) −17.0717 + 9.85638i −1.02574 + 0.592212i −0.915762 0.401722i \(-0.868412\pi\)
−0.109980 + 0.993934i \(0.535079\pi\)
\(278\) −0.820759 −0.0492259
\(279\) −6.01937 + 3.47529i −0.360370 + 0.208060i
\(280\) 1.56729 1.13509i 0.0936633 0.0678347i
\(281\) 9.93073i 0.592418i −0.955123 0.296209i \(-0.904278\pi\)
0.955123 0.296209i \(-0.0957225\pi\)
\(282\) 10.3075 5.95105i 0.613804 0.354380i
\(283\) 10.0790 + 5.81912i 0.599135 + 0.345911i 0.768701 0.639608i \(-0.220903\pi\)
−0.169566 + 0.985519i \(0.554237\pi\)
\(284\) −12.2677 7.08275i −0.727953 0.420284i
\(285\) −1.38553 13.3765i −0.0820716 0.792358i
\(286\) −0.497290 0.387521i −0.0294053 0.0229146i
\(287\) 7.07849i 0.417830i
\(288\) 0.500000 0.866025i 0.0294628 0.0510310i
\(289\) 24.9496 43.2139i 1.46762 2.54200i
\(290\) 11.7530 8.51202i 0.690163 0.499843i
\(291\) 8.64822i 0.506967i
\(292\) 6.43528 + 11.1462i 0.376596 + 0.652284i
\(293\) 6.57636 + 11.3906i 0.384195 + 0.665445i 0.991657 0.128903i \(-0.0411457\pi\)
−0.607462 + 0.794349i \(0.707812\pi\)
\(294\) 6.25104i 0.364568i
\(295\) 9.22927 + 12.7434i 0.537349 + 0.741949i
\(296\) −0.879573 + 1.52347i −0.0511241 + 0.0885496i
\(297\) −0.0874279 + 0.151430i −0.00507308 + 0.00878684i
\(298\) 10.2857i 0.595834i
\(299\) −1.44832 + 10.4000i −0.0837583 + 0.601448i
\(300\) 1.02479 + 4.89385i 0.0591665 + 0.282547i
\(301\) −6.87561 3.96963i −0.396304 0.228806i
\(302\) −10.1688 5.87096i −0.585149 0.337836i
\(303\) −9.15001 + 5.28276i −0.525654 + 0.303487i
\(304\) 6.01418i 0.344937i
\(305\) 14.4407 10.4585i 0.826872 0.598854i
\(306\) −7.08339 + 4.08960i −0.404930 + 0.233787i
\(307\) −14.8609 −0.848155 −0.424077 0.905626i \(-0.639402\pi\)
−0.424077 + 0.905626i \(0.639402\pi\)
\(308\) 0.131051 0.0756625i 0.00746734 0.00431127i
\(309\) −4.46784 + 7.73853i −0.254167 + 0.440230i
\(310\) −6.34290 + 14.1887i −0.360252 + 0.805865i
\(311\) 9.17666 0.520361 0.260180 0.965560i \(-0.416218\pi\)
0.260180 + 0.965560i \(0.416218\pi\)
\(312\) −0.497314 + 3.57109i −0.0281548 + 0.202173i
\(313\) 7.43905i 0.420480i −0.977650 0.210240i \(-0.932576\pi\)
0.977650 0.210240i \(-0.0674245\pi\)
\(314\) 5.85463 + 3.38017i 0.330396 + 0.190754i
\(315\) 1.76666 + 0.789764i 0.0995401 + 0.0444982i
\(316\) −4.74480 8.21824i −0.266916 0.462312i
\(317\) −25.7510 −1.44632 −0.723161 0.690679i \(-0.757312\pi\)
−0.723161 + 0.690679i \(0.757312\pi\)
\(318\) −1.24367 2.15410i −0.0697417 0.120796i
\(319\) 0.982750 0.567391i 0.0550235 0.0317678i
\(320\) −0.230377 2.22417i −0.0128785 0.124335i
\(321\) −0.430389 0.745455i −0.0240219 0.0416072i
\(322\) −2.18270 1.26018i −0.121637 0.0702272i
\(323\) 24.5955 42.6007i 1.36853 2.37037i
\(324\) 1.00000 0.0555556
\(325\) −10.0546 14.9634i −0.557731 0.830022i
\(326\) 1.42749 0.0790614
\(327\) 2.72668 4.72274i 0.150786 0.261168i
\(328\) −7.08339 4.08960i −0.391115 0.225810i
\(329\) −5.15020 8.92040i −0.283940 0.491798i
\(330\) 0.0402827 + 0.388909i 0.00221749 + 0.0214087i
\(331\) 5.63295 3.25219i 0.309615 0.178756i −0.337139 0.941455i \(-0.609459\pi\)
0.646754 + 0.762699i \(0.276126\pi\)
\(332\) −0.0697718 0.120848i −0.00382922 0.00663241i
\(333\) −1.75915 −0.0964006
\(334\) 2.93528 + 5.08406i 0.160612 + 0.278187i
\(335\) −5.58382 2.49618i −0.305076 0.136381i
\(336\) −0.749482 0.432713i −0.0408876 0.0236065i
\(337\) 18.6696i 1.01700i −0.861063 0.508498i \(-0.830201\pi\)
0.861063 0.508498i \(-0.169799\pi\)
\(338\) −3.17664 12.6059i −0.172786 0.685671i
\(339\) −11.7821 −0.639917
\(340\) −7.46410 + 16.6968i −0.404798 + 0.905511i
\(341\) −0.607674 + 1.05252i −0.0329074 + 0.0569973i
\(342\) −5.20843 + 3.00709i −0.281640 + 0.162605i
\(343\) 11.4678 0.619203
\(344\) −7.94476 + 4.58691i −0.428353 + 0.247310i
\(345\) 5.27413 3.81974i 0.283950 0.205648i
\(346\) 13.7028i 0.736665i
\(347\) −24.6009 + 14.2033i −1.32064 + 0.762474i −0.983831 0.179098i \(-0.942682\pi\)
−0.336813 + 0.941572i \(0.609349\pi\)
\(348\) −5.62035 3.24491i −0.301282 0.173945i
\(349\) 1.93797 + 1.11889i 0.103737 + 0.0598926i 0.550971 0.834524i \(-0.314258\pi\)
−0.447234 + 0.894417i \(0.647591\pi\)
\(350\) 4.23527 0.886885i 0.226385 0.0474060i
\(351\) −3.34131 + 1.35486i −0.178346 + 0.0723170i
\(352\) 0.174856i 0.00931985i
\(353\) 0.813287 1.40866i 0.0432869 0.0749751i −0.843570 0.537019i \(-0.819550\pi\)
0.886857 + 0.462044i \(0.152884\pi\)
\(354\) 3.51833 6.09393i 0.186997 0.323889i
\(355\) −18.5794 25.6537i −0.986093 1.36156i
\(356\) 13.1393i 0.696382i
\(357\) 3.53925 + 6.13015i 0.187317 + 0.324442i
\(358\) −7.09191 12.2835i −0.374819 0.649206i
\(359\) 34.4613i 1.81880i 0.415923 + 0.909400i \(0.363459\pi\)
−0.415923 + 0.909400i \(0.636541\pi\)
\(360\) 1.81100 1.31160i 0.0954480 0.0691272i
\(361\) 8.58515 14.8699i 0.451850 0.782627i
\(362\) −6.88641 + 11.9276i −0.361942 + 0.626901i
\(363\) 10.9694i 0.575746i
\(364\) 3.09052 + 0.430389i 0.161987 + 0.0225585i
\(365\) 2.96508 + 28.6263i 0.155199 + 1.49837i
\(366\) −6.90559 3.98695i −0.360961 0.208401i
\(367\) 12.6735 + 7.31703i 0.661550 + 0.381946i 0.792867 0.609394i \(-0.208587\pi\)
−0.131317 + 0.991340i \(0.541921\pi\)
\(368\) −2.52211 + 1.45614i −0.131474 + 0.0759065i
\(369\) 8.17919i 0.425792i
\(370\) −3.18581 + 2.30729i −0.165622 + 0.119950i
\(371\) −1.86422 + 1.07631i −0.0967855 + 0.0558791i
\(372\) 6.95057 0.360370
\(373\) −19.1166 + 11.0370i −0.989819 + 0.571472i −0.905220 0.424943i \(-0.860294\pi\)
−0.0845988 + 0.996415i \(0.526961\pi\)
\(374\) −0.715090 + 1.23857i −0.0369764 + 0.0640450i
\(375\) −2.37400 + 10.9254i −0.122593 + 0.564185i
\(376\) −11.9021 −0.613804
\(377\) 23.1757 + 3.22747i 1.19361 + 0.166223i
\(378\) 0.865427i 0.0445128i
\(379\) 12.0573 + 6.96127i 0.619341 + 0.357577i 0.776612 0.629979i \(-0.216936\pi\)
−0.157272 + 0.987555i \(0.550270\pi\)
\(380\) −5.48837 + 12.2772i −0.281547 + 0.629806i
\(381\) 3.47119 + 6.01228i 0.177834 + 0.308018i
\(382\) −5.57642 −0.285314
\(383\) −12.3044 21.3119i −0.628728 1.08899i −0.987807 0.155681i \(-0.950243\pi\)
0.359080 0.933307i \(-0.383091\pi\)
\(384\) −0.866025 + 0.500000i −0.0441942 + 0.0255155i
\(385\) 0.336572 0.0348618i 0.0171533 0.00177672i
\(386\) −0.110405 0.191227i −0.00561946 0.00973319i
\(387\) −7.94476 4.58691i −0.403855 0.233166i
\(388\) −4.32411 + 7.48957i −0.219523 + 0.380226i
\(389\) 5.60980 0.284428 0.142214 0.989836i \(-0.454578\pi\)
0.142214 + 0.989836i \(0.454578\pi\)
\(390\) −4.27408 + 6.83610i −0.216426 + 0.346159i
\(391\) 23.8201 1.20463
\(392\) 3.12552 5.41356i 0.157863 0.273426i
\(393\) 1.96703 + 1.13567i 0.0992235 + 0.0572867i
\(394\) 0.861905 + 1.49286i 0.0434222 + 0.0752094i
\(395\) −2.18619 21.1065i −0.109999 1.06198i
\(396\) 0.151430 0.0874279i 0.00760962 0.00439342i
\(397\) −1.18438 2.05141i −0.0594424 0.102957i 0.834773 0.550595i \(-0.185599\pi\)
−0.894215 + 0.447637i \(0.852266\pi\)
\(398\) 7.95853 0.398925
\(399\) 2.60241 + 4.50751i 0.130284 + 0.225658i
\(400\) 1.55943 4.75060i 0.0779714 0.237530i
\(401\) 14.2942 + 8.25276i 0.713818 + 0.412123i 0.812473 0.582998i \(-0.198121\pi\)
−0.0986548 + 0.995122i \(0.531454\pi\)
\(402\) 2.73532i 0.136425i
\(403\) −23.2240 + 9.41704i −1.15687 + 0.469096i
\(404\) 10.5655 0.525654
\(405\) 2.04138 + 0.912572i 0.101437 + 0.0453461i
\(406\) −2.80823 + 4.86400i −0.139370 + 0.241396i
\(407\) −0.266387 + 0.153798i −0.0132043 + 0.00762351i
\(408\) 8.17919 0.404930
\(409\) 28.8448 16.6535i 1.42628 0.823464i 0.429457 0.903087i \(-0.358705\pi\)
0.996825 + 0.0796230i \(0.0253717\pi\)
\(410\) −10.7278 14.8125i −0.529808 0.731537i
\(411\) 7.37617i 0.363840i
\(412\) 7.73853 4.46784i 0.381250 0.220115i
\(413\) −5.27385 3.04486i −0.259509 0.149828i
\(414\) −2.52211 1.45614i −0.123955 0.0715654i
\(415\) −0.0321476 0.310368i −0.00157806 0.0152354i
\(416\) 2.21623 2.84400i 0.108660 0.139438i
\(417\) 0.820759i 0.0401927i
\(418\) −0.525807 + 0.910724i −0.0257181 + 0.0445450i
\(419\) 15.1303 26.2065i 0.739164 1.28027i −0.213708 0.976898i \(-0.568554\pi\)
0.952872 0.303372i \(-0.0981126\pi\)
\(420\) −1.13509 1.56729i −0.0553868 0.0764758i
\(421\) 40.2235i 1.96038i 0.198070 + 0.980188i \(0.436533\pi\)
−0.198070 + 0.980188i \(0.563467\pi\)
\(422\) 2.10991 + 3.65448i 0.102709 + 0.177897i
\(423\) −5.95105 10.3075i −0.289350 0.501169i
\(424\) 2.48735i 0.120796i
\(425\) −30.4741 + 27.2729i −1.47821 + 1.32293i
\(426\) −7.08275 + 12.2677i −0.343160 + 0.594371i
\(427\) −3.45041 + 5.97629i −0.166977 + 0.289213i
\(428\) 0.860777i 0.0416072i
\(429\) −0.387521 + 0.497290i −0.0187097 + 0.0240094i
\(430\) −20.4041 + 2.11344i −0.983974 + 0.101919i
\(431\) −28.1980 16.2801i −1.35825 0.784185i −0.368860 0.929485i \(-0.620252\pi\)
−0.989388 + 0.145300i \(0.953585\pi\)
\(432\) −0.866025 0.500000i −0.0416667 0.0240563i
\(433\) 26.6153 15.3663i 1.27905 0.738460i 0.302376 0.953189i \(-0.402220\pi\)
0.976674 + 0.214729i \(0.0688869\pi\)
\(434\) 6.01521i 0.288739i
\(435\) −8.51202 11.7530i −0.408120 0.563515i
\(436\) −4.72274 + 2.72668i −0.226178 + 0.130584i
\(437\) 17.5150 0.837854
\(438\) 11.1462 6.43528i 0.532588 0.307490i
\(439\) 3.26422 5.65380i 0.155793 0.269841i −0.777555 0.628815i \(-0.783540\pi\)
0.933347 + 0.358974i \(0.116873\pi\)
\(440\) 0.159569 0.356946i 0.00760713 0.0170167i
\(441\) 6.25104 0.297668
\(442\) −27.3292 + 11.0816i −1.29992 + 0.527100i
\(443\) 30.3111i 1.44012i −0.693911 0.720061i \(-0.744114\pi\)
0.693911 0.720061i \(-0.255886\pi\)
\(444\) 1.52347 + 0.879573i 0.0723005 + 0.0417427i
\(445\) −11.9906 + 26.8223i −0.568407 + 1.27150i
\(446\) 3.47638 + 6.02126i 0.164611 + 0.285115i
\(447\) −10.2857 −0.486496
\(448\) 0.432713 + 0.749482i 0.0204438 + 0.0354097i
\(449\) 13.8034 7.96938i 0.651421 0.376098i −0.137579 0.990491i \(-0.543932\pi\)
0.789001 + 0.614392i \(0.210599\pi\)
\(450\) 4.89385 1.02479i 0.230698 0.0483093i
\(451\) −0.715090 1.23857i −0.0336723 0.0583221i
\(452\) 10.2036 + 5.89106i 0.479938 + 0.277092i
\(453\) −5.87096 + 10.1688i −0.275842 + 0.477772i
\(454\) −2.89645 −0.135937
\(455\) 5.91614 + 3.69890i 0.277353 + 0.173407i
\(456\) 6.01418 0.281640
\(457\) 9.90436 17.1548i 0.463306 0.802470i −0.535817 0.844334i \(-0.679996\pi\)
0.999123 + 0.0418642i \(0.0133297\pi\)
\(458\) 6.83121 + 3.94400i 0.319202 + 0.184291i
\(459\) 4.08960 + 7.08339i 0.190886 + 0.330624i
\(460\) −6.47740 + 0.670922i −0.302010 + 0.0312819i
\(461\) −11.5898 + 6.69139i −0.539792 + 0.311649i −0.744995 0.667070i \(-0.767548\pi\)
0.205202 + 0.978720i \(0.434215\pi\)
\(462\) −0.0756625 0.131051i −0.00352014 0.00609706i
\(463\) 42.3599 1.96863 0.984316 0.176412i \(-0.0564493\pi\)
0.984316 + 0.176412i \(0.0564493\pi\)
\(464\) 3.24491 + 5.62035i 0.150641 + 0.260918i
\(465\) 14.1887 + 6.34290i 0.657986 + 0.294145i
\(466\) 1.23624 + 0.713746i 0.0572679 + 0.0330636i
\(467\) 33.4593i 1.54831i 0.632996 + 0.774155i \(0.281825\pi\)
−0.632996 + 0.774155i \(0.718175\pi\)
\(468\) 3.57109 + 0.497314i 0.165074 + 0.0229883i
\(469\) 2.36722 0.109308
\(470\) −24.2966 10.8615i −1.12072 0.501005i
\(471\) 3.38017 5.85463i 0.155750 0.269767i
\(472\) −6.09393 + 3.51833i −0.280496 + 0.161944i
\(473\) −1.60410 −0.0737564
\(474\) −8.21824 + 4.74480i −0.377476 + 0.217936i
\(475\) −22.4076 + 20.0538i −1.02813 + 0.920132i
\(476\) 7.07849i 0.324442i
\(477\) −2.15410 + 1.24367i −0.0986297 + 0.0569439i
\(478\) −9.44692 5.45418i −0.432092 0.249469i
\(479\) −19.3387 11.1652i −0.883606 0.510150i −0.0117600 0.999931i \(-0.503743\pi\)
−0.871846 + 0.489781i \(0.837077\pi\)
\(480\) −2.22417 + 0.230377i −0.101519 + 0.0105152i
\(481\) −6.28207 0.874847i −0.286438 0.0398896i
\(482\) 29.3660i 1.33759i
\(483\) −1.26018 + 2.18270i −0.0573403 + 0.0993163i
\(484\) −5.48471 + 9.49980i −0.249305 + 0.431809i
\(485\) −15.6619 + 11.3430i −0.711170 + 0.515058i
\(486\) 1.00000i 0.0453609i
\(487\) −14.3750 24.8982i −0.651392 1.12824i −0.982785 0.184751i \(-0.940852\pi\)
0.331393 0.943493i \(-0.392481\pi\)
\(488\) 3.98695 + 6.90559i 0.180481 + 0.312602i
\(489\) 1.42749i 0.0645534i
\(490\) 11.3206 8.19884i 0.511413 0.370386i
\(491\) 8.02546 13.9005i 0.362184 0.627321i −0.626136 0.779714i \(-0.715364\pi\)
0.988320 + 0.152393i \(0.0486978\pi\)
\(492\) −4.08960 + 7.08339i −0.184373 + 0.319344i
\(493\) 53.0815i 2.39067i
\(494\) −20.0952 + 8.14836i −0.904127 + 0.366612i
\(495\) 0.388909 0.0402827i 0.0174802 0.00181057i
\(496\) −6.01937 3.47529i −0.270278 0.156045i
\(497\) 10.6168 + 6.12960i 0.476228 + 0.274950i
\(498\) −0.120848 + 0.0697718i −0.00541534 + 0.00312655i
\(499\) 33.2509i 1.48851i 0.667894 + 0.744256i \(0.267196\pi\)
−0.667894 + 0.744256i \(0.732804\pi\)
\(500\) 7.51864 8.27466i 0.336244 0.370054i
\(501\) 5.08406 2.93528i 0.227139 0.131139i
\(502\) −17.8942 −0.798656
\(503\) −21.7736 + 12.5710i −0.970838 + 0.560514i −0.899492 0.436938i \(-0.856063\pi\)
−0.0713466 + 0.997452i \(0.522730\pi\)
\(504\) −0.432713 + 0.749482i −0.0192746 + 0.0333846i
\(505\) 21.5682 + 9.64180i 0.959772 + 0.429055i
\(506\) −0.509229 −0.0226380
\(507\) −12.6059 + 3.17664i −0.559848 + 0.141080i
\(508\) 6.94238i 0.308018i
\(509\) 22.8809 + 13.2103i 1.01418 + 0.585536i 0.912412 0.409272i \(-0.134217\pi\)
0.101766 + 0.994808i \(0.467551\pi\)
\(510\) 16.6968 + 7.46410i 0.739347 + 0.330516i
\(511\) −5.56927 9.64625i −0.246370 0.426725i
\(512\) 1.00000 0.0441942
\(513\) 3.00709 + 5.20843i 0.132766 + 0.229958i
\(514\) 10.5472 6.08945i 0.465219 0.268594i
\(515\) 19.8745 2.05858i 0.875774 0.0907117i
\(516\) 4.58691 + 7.94476i 0.201927 + 0.349749i
\(517\) −1.80233 1.04058i −0.0792664 0.0457645i
\(518\) 0.761206 1.31845i 0.0334455 0.0579293i
\(519\) 13.7028 0.601484
\(520\) 7.11951 3.78319i 0.312211 0.165904i
\(521\) −22.4462 −0.983384 −0.491692 0.870769i \(-0.663621\pi\)
−0.491692 + 0.870769i \(0.663621\pi\)
\(522\) −3.24491 + 5.62035i −0.142026 + 0.245996i
\(523\) 25.1815 + 14.5385i 1.10111 + 0.635726i 0.936512 0.350635i \(-0.114034\pi\)
0.164598 + 0.986361i \(0.447367\pi\)
\(524\) −1.13567 1.96703i −0.0496118 0.0859301i
\(525\) −0.886885 4.23527i −0.0387068 0.184842i
\(526\) 18.3309 10.5834i 0.799266 0.461456i
\(527\) 28.4250 + 49.2336i 1.23821 + 2.14465i
\(528\) −0.174856 −0.00760962
\(529\) −7.25931 12.5735i −0.315622 0.546674i
\(530\) −2.26988 + 5.07761i −0.0985974 + 0.220557i
\(531\) −6.09393 3.51833i −0.264454 0.152683i
\(532\) 5.20483i 0.225658i
\(533\) 4.06762 29.2086i 0.176188 1.26517i
\(534\) 13.1393 0.568594
\(535\) −0.785521 + 1.75717i −0.0339610 + 0.0759690i
\(536\) 1.36766 2.36886i 0.0590739 0.102319i
\(537\) −12.2835 + 7.09191i −0.530074 + 0.306038i
\(538\) 12.0874 0.521126
\(539\) 0.946592 0.546515i 0.0407726 0.0235401i
\(540\) −1.31160 1.81100i −0.0564421 0.0779330i
\(541\) 8.17282i 0.351377i −0.984446 0.175688i \(-0.943785\pi\)
0.984446 0.175688i \(-0.0562151\pi\)
\(542\) 12.7275 7.34824i 0.546694 0.315634i
\(543\) 11.9276 + 6.88641i 0.511863 + 0.295524i
\(544\) −7.08339 4.08960i −0.303698 0.175340i
\(545\) −12.1292 + 1.25633i −0.519557 + 0.0538152i
\(546\) 0.430389 3.09052i 0.0184189 0.132262i
\(547\) 40.7393i 1.74188i 0.491385 + 0.870942i \(0.336491\pi\)
−0.491385 + 0.870942i \(0.663509\pi\)
\(548\) 3.68809 6.38795i 0.157547 0.272880i
\(549\) −3.98695 + 6.90559i −0.170159 + 0.294724i
\(550\) 0.651479 0.583044i 0.0277791 0.0248611i
\(551\) 39.0309i 1.66277i
\(552\) 1.45614 + 2.52211i 0.0619774 + 0.107348i
\(553\) 4.10628 + 7.11229i 0.174617 + 0.302445i
\(554\) 19.7128i 0.837515i
\(555\) 2.30729 + 3.18581i 0.0979390 + 0.135230i
\(556\) 0.410380 0.710798i 0.0174040 0.0301446i
\(557\) −0.458421 + 0.794008i −0.0194239 + 0.0336432i −0.875574 0.483084i \(-0.839517\pi\)
0.856150 + 0.516727i \(0.172850\pi\)
\(558\) 6.95057i 0.294241i
\(559\) −26.0903 20.3313i −1.10350 0.859922i
\(560\) 0.199374 + 1.92486i 0.00842511 + 0.0813400i
\(561\) 1.23857 + 0.715090i 0.0522925 + 0.0301911i
\(562\) 8.60027 + 4.96537i 0.362780 + 0.209451i
\(563\) −10.9632 + 6.32961i −0.462044 + 0.266761i −0.712903 0.701262i \(-0.752620\pi\)
0.250859 + 0.968024i \(0.419287\pi\)
\(564\) 11.9021i 0.501169i
\(565\) 15.4534 + 21.3374i 0.650129 + 0.897671i
\(566\) −10.0790 + 5.81912i −0.423652 + 0.244596i
\(567\) −0.865427 −0.0363445
\(568\) 12.2677 7.08275i 0.514741 0.297186i
\(569\) 12.2559 21.2279i 0.513795 0.889918i −0.486077 0.873916i \(-0.661573\pi\)
0.999872 0.0160026i \(-0.00509402\pi\)
\(570\) 12.2772 + 5.48837i 0.514235 + 0.229882i
\(571\) −11.1443 −0.466376 −0.233188 0.972432i \(-0.574916\pi\)
−0.233188 + 0.972432i \(0.574916\pi\)
\(572\) 0.584248 0.236905i 0.0244286 0.00990549i
\(573\) 5.57642i 0.232958i
\(574\) 6.13015 + 3.53925i 0.255868 + 0.147725i
\(575\) −13.8351 4.54149i −0.576962 0.189393i
\(576\) 0.500000 + 0.866025i 0.0208333 + 0.0360844i
\(577\) 23.8325 0.992161 0.496081 0.868276i \(-0.334772\pi\)
0.496081 + 0.868276i \(0.334772\pi\)
\(578\) 24.9496 + 43.2139i 1.03777 + 1.79746i
\(579\) −0.191227 + 0.110405i −0.00794712 + 0.00458827i
\(580\) 1.49510 + 14.4344i 0.0620808 + 0.599358i
\(581\) 0.0603824 + 0.104585i 0.00250508 + 0.00433893i
\(582\) 7.48957 + 4.32411i 0.310453 + 0.179240i
\(583\) −0.217463 + 0.376658i −0.00900642 + 0.0155996i
\(584\) −12.8706 −0.532588
\(585\) 6.83610 + 4.27408i 0.282638 + 0.176711i
\(586\) −13.1527 −0.543334
\(587\) 18.6811 32.3566i 0.771051 1.33550i −0.165937 0.986136i \(-0.553065\pi\)
0.936988 0.349362i \(-0.113602\pi\)
\(588\) −5.41356 3.12552i −0.223251 0.128894i
\(589\) 20.9010 + 36.2016i 0.861210 + 1.49166i
\(590\) −15.6507 + 1.62109i −0.644331 + 0.0667391i
\(591\) 1.49286 0.861905i 0.0614082 0.0354540i
\(592\) −0.879573 1.52347i −0.0361502 0.0626140i
\(593\) 6.46136 0.265336 0.132668 0.991161i \(-0.457646\pi\)
0.132668 + 0.991161i \(0.457646\pi\)
\(594\) −0.0874279 0.151430i −0.00358721 0.00621323i
\(595\) 6.45963 14.4499i 0.264819 0.592386i
\(596\) 8.90766 + 5.14284i 0.364872 + 0.210659i
\(597\) 7.95853i 0.325721i
\(598\) −8.28251 6.45428i −0.338697 0.263935i
\(599\) −38.5057 −1.57330 −0.786651 0.617398i \(-0.788187\pi\)
−0.786651 + 0.617398i \(0.788187\pi\)
\(600\) −4.75060 1.55943i −0.193942 0.0636634i
\(601\) −0.371169 + 0.642883i −0.0151403 + 0.0262237i −0.873496 0.486831i \(-0.838153\pi\)
0.858356 + 0.513055i \(0.171486\pi\)
\(602\) 6.87561 3.96963i 0.280229 0.161790i
\(603\) 2.73532 0.111391
\(604\) 10.1688 5.87096i 0.413763 0.238886i
\(605\) −19.8656 + 14.3875i −0.807652 + 0.584933i
\(606\) 10.5655i 0.429195i
\(607\) 25.5500 14.7513i 1.03704 0.598736i 0.118047 0.993008i \(-0.462337\pi\)
0.918994 + 0.394272i \(0.129003\pi\)
\(608\) −5.20843 3.00709i −0.211230 0.121954i
\(609\) 4.86400 + 2.80823i 0.197099 + 0.113795i
\(610\) 1.83700 + 17.7353i 0.0743780 + 0.718081i
\(611\) −16.1257 39.7686i −0.652374 1.60887i
\(612\) 8.17919i 0.330624i
\(613\) −6.86720 + 11.8943i −0.277364 + 0.480408i −0.970729 0.240178i \(-0.922794\pi\)
0.693365 + 0.720587i \(0.256127\pi\)
\(614\) 7.43044 12.8699i 0.299868 0.519387i
\(615\) −14.8125 + 10.7278i −0.597298 + 0.432587i
\(616\) 0.151325i 0.00609706i
\(617\) 21.4394 + 37.1342i 0.863119 + 1.49497i 0.868902 + 0.494983i \(0.164826\pi\)
−0.00578297 + 0.999983i \(0.501841\pi\)
\(618\) −4.46784 7.73853i −0.179723 0.311289i
\(619\) 30.0054i 1.20602i 0.797734 + 0.603010i \(0.206032\pi\)
−0.797734 + 0.603010i \(0.793968\pi\)
\(620\) −9.11635 12.5875i −0.366121 0.505525i
\(621\) −1.45614 + 2.52211i −0.0584329 + 0.101209i
\(622\) −4.58833 + 7.94722i −0.183975 + 0.318655i
\(623\) 11.3711i 0.455574i
\(624\) −2.84400 2.21623i −0.113851 0.0887202i
\(625\) 22.8996 10.0304i 0.915984 0.401215i
\(626\) 6.44240 + 3.71952i 0.257490 + 0.148662i
\(627\) 0.910724 + 0.525807i 0.0363708 + 0.0209987i
\(628\) −5.85463 + 3.38017i −0.233625 + 0.134884i
\(629\) 14.3884i 0.573703i
\(630\) −1.56729 + 1.13509i −0.0624422 + 0.0452231i
\(631\) 7.73137 4.46371i 0.307781 0.177697i −0.338152 0.941091i \(-0.609802\pi\)
0.645933 + 0.763394i \(0.276468\pi\)
\(632\) 9.48961 0.377476
\(633\) 3.65448 2.10991i 0.145252 0.0838616i
\(634\) 12.8755 22.3011i 0.511352 0.885688i
\(635\) 6.33542 14.1720i 0.251414 0.562399i
\(636\) 2.48735 0.0986297
\(637\) 22.3230 + 3.10873i 0.884470 + 0.123172i
\(638\) 1.13478i 0.0449265i
\(639\) 12.2677 + 7.08275i 0.485302 + 0.280189i
\(640\) 2.04138 + 0.912572i 0.0806924 + 0.0360726i
\(641\) −11.9079 20.6250i −0.470332 0.814639i 0.529092 0.848564i \(-0.322532\pi\)
−0.999424 + 0.0339254i \(0.989199\pi\)
\(642\) 0.860777 0.0339722
\(643\) −4.79374 8.30300i −0.189047 0.327439i 0.755886 0.654703i \(-0.227206\pi\)
−0.944933 + 0.327265i \(0.893873\pi\)
\(644\) 2.18270 1.26018i 0.0860104 0.0496581i
\(645\) 2.11344 + 20.4041i 0.0832165 + 0.803411i
\(646\) 24.5955 + 42.6007i 0.967699 + 1.67610i
\(647\) −39.2219 22.6448i −1.54197 0.890259i −0.998714 0.0506940i \(-0.983857\pi\)
−0.543259 0.839565i \(-0.682810\pi\)
\(648\) −0.500000 + 0.866025i −0.0196419 + 0.0340207i
\(649\) −1.23040 −0.0482975
\(650\) 17.9860 1.22585i 0.705470 0.0480819i
\(651\) −6.01521 −0.235755
\(652\) −0.713746 + 1.23624i −0.0279524 + 0.0484150i
\(653\) 8.00988 + 4.62451i 0.313451 + 0.180971i 0.648470 0.761241i \(-0.275409\pi\)
−0.335019 + 0.942211i \(0.608743\pi\)
\(654\) 2.72668 + 4.72274i 0.106622 + 0.184674i
\(655\) −0.523262 5.05182i −0.0204455 0.197391i
\(656\) 7.08339 4.08960i 0.276560 0.159672i
\(657\) −6.43528 11.1462i −0.251064 0.434856i
\(658\) 10.3004 0.401551
\(659\) −11.0666 19.1679i −0.431093 0.746676i 0.565874 0.824491i \(-0.308539\pi\)
−0.996968 + 0.0778159i \(0.975205\pi\)
\(660\) −0.356946 0.159569i −0.0138941 0.00621120i
\(661\) 8.75083 + 5.05229i 0.340368 + 0.196511i 0.660435 0.750884i \(-0.270372\pi\)
−0.320067 + 0.947395i \(0.603705\pi\)
\(662\) 6.50437i 0.252800i
\(663\) 11.0816 + 27.3292i 0.430375 + 1.06138i
\(664\) 0.139544 0.00541534
\(665\) 4.74978 10.6250i 0.184189 0.412020i
\(666\) 0.879573 1.52347i 0.0340828 0.0590331i
\(667\) 16.3680 9.45008i 0.633772 0.365909i
\(668\) −5.87057 −0.227139
\(669\) 6.02126 3.47638i 0.232795 0.134405i
\(670\) 4.95366 3.58764i 0.191377 0.138603i
\(671\) 1.39428i 0.0538256i
\(672\) 0.749482 0.432713i 0.0289119 0.0166923i
\(673\) 11.6594 + 6.73157i 0.449437 + 0.259483i 0.707593 0.706621i \(-0.249781\pi\)
−0.258155 + 0.966103i \(0.583115\pi\)
\(674\) 16.1683 + 9.33479i 0.622781 + 0.359562i
\(675\) −1.02479 4.89385i −0.0394444 0.188364i
\(676\) 12.5054 + 3.55190i 0.480975 + 0.136612i
\(677\) 7.86444i 0.302255i −0.988514 0.151127i \(-0.951710\pi\)
0.988514 0.151127i \(-0.0482904\pi\)
\(678\) 5.89106 10.2036i 0.226245 0.391868i
\(679\) 3.74220 6.48168i 0.143612 0.248744i
\(680\) −10.7278 14.8125i −0.411392 0.568033i
\(681\) 2.89645i 0.110992i
\(682\) −0.607674 1.05252i −0.0232690 0.0403032i
\(683\) 9.21246 + 15.9565i 0.352505 + 0.610557i 0.986688 0.162627i \(-0.0519966\pi\)
−0.634183 + 0.773183i \(0.718663\pi\)
\(684\) 6.01418i 0.229958i
\(685\) 13.3582 9.67456i 0.510392 0.369646i
\(686\) −5.73390 + 9.93141i −0.218921 + 0.379183i
\(687\) 3.94400 6.83121i 0.150473 0.260627i
\(688\) 9.17382i 0.349749i
\(689\) −8.31100 + 3.37000i −0.316624 + 0.128387i
\(690\) 0.670922 + 6.47740i 0.0255416 + 0.246590i
\(691\) −20.5618 11.8714i −0.782208 0.451608i 0.0550042 0.998486i \(-0.482483\pi\)
−0.837212 + 0.546878i \(0.815816\pi\)
\(692\) −11.8669 6.85138i −0.451113 0.260450i
\(693\) −0.131051 + 0.0756625i −0.00497823 + 0.00287418i
\(694\) 28.4066i 1.07830i
\(695\) 1.48639 1.07650i 0.0563821 0.0408342i
\(696\) 5.62035 3.24491i 0.213039 0.122998i
\(697\) −66.8992 −2.53399
\(698\) −1.93797 + 1.11889i −0.0733532 + 0.0423505i
\(699\) 0.713746 1.23624i 0.0269963 0.0467590i
\(700\) −1.34957 + 4.11130i −0.0510090 + 0.155392i
\(701\) −6.52189 −0.246328 −0.123164 0.992386i \(-0.539304\pi\)
−0.123164 + 0.992386i \(0.539304\pi\)
\(702\) 0.497314 3.57109i 0.0187699 0.134782i
\(703\) 10.5798i 0.399025i
\(704\) 0.151430 + 0.0874279i 0.00570722 + 0.00329506i
\(705\) −10.8615 + 24.2966i −0.409069 + 0.915064i
\(706\) 0.813287 + 1.40866i 0.0306085 + 0.0530154i
\(707\) −9.14369 −0.343884
\(708\) 3.51833 + 6.09393i 0.132227 + 0.229024i
\(709\) 27.5565 15.9098i 1.03491 0.597504i 0.116521 0.993188i \(-0.462826\pi\)
0.918387 + 0.395684i \(0.129493\pi\)
\(710\) 31.5065 3.26340i 1.18242 0.122473i
\(711\) 4.74480 + 8.21824i 0.177944 + 0.308208i
\(712\) −11.3790 6.56966i −0.426445 0.246208i
\(713\) −10.1210 + 17.5301i −0.379035 + 0.656507i
\(714\) −7.07849 −0.264906
\(715\) 1.40886 + 0.0495564i 0.0526884 + 0.00185330i
\(716\) 14.1838 0.530074
\(717\) −5.45418 + 9.44692i −0.203690 + 0.352802i
\(718\) −29.8444 17.2307i −1.11378 0.643043i
\(719\) 11.6970 + 20.2597i 0.436223 + 0.755560i 0.997395 0.0721392i \(-0.0229826\pi\)
−0.561172 + 0.827699i \(0.689649\pi\)
\(720\) 0.230377 + 2.22417i 0.00858564 + 0.0828899i
\(721\) −6.69713 + 3.86659i −0.249414 + 0.143999i
\(722\) 8.58515 + 14.8699i 0.319506 + 0.553401i
\(723\) −29.3660 −1.09213
\(724\) −6.88641 11.9276i −0.255931 0.443286i
\(725\) −10.1204 + 30.8305i −0.375862 + 1.14502i
\(726\) 9.49980 + 5.48471i 0.352571 + 0.203557i
\(727\) 36.0471i 1.33691i −0.743750 0.668457i \(-0.766955\pi\)
0.743750 0.668457i \(-0.233045\pi\)
\(728\) −1.91799 + 2.46127i −0.0710853 + 0.0912208i
\(729\) −1.00000 −0.0370370
\(730\) −26.2737 11.7453i −0.972432 0.434714i
\(731\) −37.5172 + 64.9817i −1.38762 + 2.40344i
\(732\) 6.90559 3.98695i 0.255238 0.147362i
\(733\) −17.0888 −0.631189 −0.315594 0.948894i \(-0.602204\pi\)
−0.315594 + 0.948894i \(0.602204\pi\)
\(734\) −12.6735 + 7.31703i −0.467787 + 0.270077i
\(735\) −8.19884 11.3206i −0.302419 0.417567i
\(736\) 2.91228i 0.107348i
\(737\) 0.414209 0.239143i 0.0152576 0.00880896i
\(738\) 7.08339 + 4.08960i 0.260743 + 0.150540i
\(739\) 33.4931 + 19.3373i 1.23206 + 0.711333i 0.967460 0.253024i \(-0.0814253\pi\)
0.264604 + 0.964357i \(0.414759\pi\)
\(740\) −0.405267 3.91264i −0.0148979 0.143831i
\(741\) 8.14836 + 20.0952i 0.299337 + 0.738217i
\(742\) 2.15262i 0.0790250i
\(743\) 0.225532 0.390632i 0.00827395 0.0143309i −0.861859 0.507148i \(-0.830700\pi\)
0.870133 + 0.492817i \(0.164033\pi\)
\(744\) −3.47529 + 6.01937i −0.127410 + 0.220681i
\(745\) 13.4907 + 18.6274i 0.494260 + 0.682453i
\(746\) 22.0739i 0.808184i
\(747\) 0.0697718 + 0.120848i 0.00255282 + 0.00442161i
\(748\) −0.715090 1.23857i −0.0261463 0.0452867i
\(749\) 0.744940i 0.0272195i
\(750\) −8.27466 7.51864i −0.302148 0.274542i
\(751\) −11.1206 + 19.2614i −0.405795 + 0.702858i −0.994414 0.105553i \(-0.966339\pi\)
0.588618 + 0.808411i \(0.299672\pi\)
\(752\) 5.95105 10.3075i 0.217012 0.375876i
\(753\) 17.8942i 0.652100i
\(754\) −14.3829 + 18.4570i −0.523796 + 0.672165i
\(755\) 26.1160 2.70507i 0.950459 0.0984475i
\(756\) 0.749482 + 0.432713i 0.0272584 + 0.0157376i
\(757\) 7.30326 + 4.21654i 0.265442 + 0.153253i 0.626814 0.779169i \(-0.284358\pi\)
−0.361373 + 0.932421i \(0.617692\pi\)
\(758\) −12.0573 + 6.96127i −0.437940 + 0.252845i
\(759\) 0.509229i 0.0184838i
\(760\) −7.88817 10.8917i −0.286134 0.395082i
\(761\) 18.3585 10.5993i 0.665496 0.384224i −0.128872 0.991661i \(-0.541136\pi\)
0.794368 + 0.607437i \(0.207802\pi\)
\(762\) −6.94238 −0.251496
\(763\) 4.08719 2.35974i 0.147966 0.0854283i
\(764\) 2.78821 4.82932i 0.100874 0.174719i
\(765\) 7.46410 16.6968i 0.269865 0.603674i
\(766\) 24.6089 0.889155
\(767\) −20.0123 15.5949i −0.722601 0.563099i
\(768\) 1.00000i 0.0360844i
\(769\) 3.34820 + 1.93308i 0.120739 + 0.0697088i 0.559153 0.829064i \(-0.311126\pi\)
−0.438414 + 0.898773i \(0.644460\pi\)
\(770\) −0.138095 + 0.308911i −0.00497660 + 0.0111324i
\(771\) −6.08945 10.5472i −0.219306 0.379849i
\(772\) 0.220810 0.00794712
\(773\) −16.6218 28.7898i −0.597845 1.03550i −0.993139 0.116944i \(-0.962690\pi\)
0.395293 0.918555i \(-0.370643\pi\)
\(774\) 7.94476 4.58691i 0.285568 0.164873i
\(775\) −7.12291 34.0151i −0.255862 1.22186i
\(776\) −4.32411 7.48957i −0.155226 0.268860i
\(777\) −1.31845 0.761206i −0.0472990 0.0273081i
\(778\) −2.80490 + 4.85823i −0.100561 + 0.174176i
\(779\) −49.1911 −1.76245
\(780\) −3.78319 7.11951i −0.135460 0.254919i
\(781\) 2.47692 0.0886312
\(782\) −11.9100 + 20.6288i −0.425902 + 0.737684i
\(783\) 5.62035 + 3.24491i 0.200855 + 0.115964i
\(784\) 3.12552 + 5.41356i 0.111626 + 0.193341i
\(785\) −15.0361 + 1.55743i −0.536663 + 0.0555870i
\(786\) −1.96703 + 1.13567i −0.0701616 + 0.0405078i
\(787\) 15.9873 + 27.6908i 0.569886 + 0.987071i 0.996577 + 0.0826737i \(0.0263459\pi\)
−0.426691 + 0.904398i \(0.640321\pi\)
\(788\) −1.72381 −0.0614082
\(789\) −10.5834 18.3309i −0.376778 0.652598i
\(790\) 19.3718 + 8.65995i 0.689219 + 0.308107i
\(791\) −8.83049 5.09828i −0.313976 0.181274i
\(792\) 0.174856i 0.00621323i
\(793\) −17.6720 + 22.6777i −0.627551 + 0.805310i
\(794\) 2.36876 0.0840643
\(795\) 5.07761 + 2.26988i 0.180084 + 0.0805044i
\(796\) −3.97927 + 6.89229i −0.141041 + 0.244291i
\(797\) 31.2464 18.0401i 1.10680 0.639014i 0.168805 0.985649i \(-0.446009\pi\)
0.938000 + 0.346635i \(0.112676\pi\)
\(798\) −5.20483 −0.184249
\(799\) −84.3072 + 48.6748i −2.98257 + 1.72199i
\(800\) 3.33442 + 3.72580i 0.117890 + 0.131727i
\(801\) 13.1393i 0.464255i
\(802\) −14.2942 + 8.25276i −0.504746 + 0.291415i
\(803\) −1.94898 1.12525i −0.0687782 0.0397091i
\(804\) −2.36886 1.36766i −0.0835432 0.0482337i
\(805\) 5.60572 0.580634i 0.197576 0.0204647i
\(806\) 3.45661 24.8211i 0.121754 0.874286i
\(807\) 12.0874i 0.425498i
\(808\) −5.28276 + 9.15001i −0.185847 + 0.321896i
\(809\) 12.4162 21.5054i 0.436529 0.756090i −0.560890 0.827890i \(-0.689541\pi\)
0.997419 + 0.0718003i \(0.0228744\pi\)
\(810\) −1.81100 + 1.31160i −0.0636320 + 0.0460848i
\(811\) 21.3899i 0.751102i −0.926802 0.375551i \(-0.877453\pi\)
0.926802 0.375551i \(-0.122547\pi\)
\(812\) −2.80823 4.86400i −0.0985496 0.170693i
\(813\) −7.34824 12.7275i −0.257714 0.446374i
\(814\) 0.307597i 0.0107813i
\(815\) −2.58518 + 1.87229i −0.0905551 + 0.0655836i
\(816\) −4.08960 + 7.08339i −0.143164 + 0.247968i
\(817\) −27.5865 + 47.7812i −0.965129 + 1.67165i
\(818\) 33.3071i 1.16455i
\(819\) −3.09052 0.430389i −0.107991 0.0150390i
\(820\) 18.1919 1.88430i 0.635289 0.0658025i
\(821\) 28.4938 + 16.4509i 0.994441 + 0.574141i 0.906599 0.421994i \(-0.138670\pi\)
0.0878420 + 0.996134i \(0.472003\pi\)
\(822\) −6.38795 3.68809i −0.222805 0.128637i
\(823\) −27.5779 + 15.9221i −0.961306 + 0.555010i −0.896575 0.442893i \(-0.853952\pi\)
−0.0647309 + 0.997903i \(0.520619\pi\)
\(824\) 8.93568i 0.311289i
\(825\) −0.583044 0.651479i −0.0202990 0.0226816i
\(826\) 5.27385 3.04486i 0.183501 0.105944i
\(827\) −1.91814 −0.0667004 −0.0333502 0.999444i \(-0.510618\pi\)
−0.0333502 + 0.999444i \(0.510618\pi\)
\(828\) 2.52211 1.45614i 0.0876493 0.0506044i
\(829\) −13.2223 + 22.9016i −0.459228 + 0.795407i −0.998920 0.0464558i \(-0.985207\pi\)
0.539692 + 0.841863i \(0.318541\pi\)
\(830\) 0.284861 + 0.127344i 0.00988766 + 0.00442016i
\(831\) −19.7128 −0.683828
\(832\) 1.35486 + 3.34131i 0.0469713 + 0.115839i
\(833\) 51.1284i 1.77149i
\(834\) −0.710798 0.410380i −0.0246129 0.0142103i
\(835\) −11.9840 5.35732i −0.414724 0.185398i
\(836\) −0.525807 0.910724i −0.0181854 0.0314981i
\(837\) −6.95057 −0.240247
\(838\) 15.1303 + 26.2065i 0.522668 + 0.905288i
\(839\) 25.9126 14.9607i 0.894604 0.516500i 0.0191582 0.999816i \(-0.493901\pi\)
0.875446 + 0.483317i \(0.160568\pi\)
\(840\) 1.92486 0.199374i 0.0664138 0.00687907i
\(841\) −6.55886 11.3603i −0.226168 0.391734i
\(842\) −34.8346 20.1118i −1.20048 0.693098i
\(843\) 4.96537 8.60027i 0.171016 0.296209i
\(844\) −4.21983 −0.145252
\(845\) 22.2868 + 18.6628i 0.766688 + 0.642020i
\(846\) 11.9021 0.409202
\(847\) 4.74662 8.22138i 0.163096 0.282490i
\(848\) −2.15410 1.24367i −0.0739723 0.0427079i
\(849\) 5.81912 + 10.0790i 0.199712 + 0.345911i
\(850\) −8.38199 40.0278i −0.287500 1.37294i
\(851\) −4.43676 + 2.56156i −0.152090 + 0.0878092i
\(852\) −7.08275 12.2677i −0.242651 0.420284i
\(853\) 9.19805 0.314935 0.157468 0.987524i \(-0.449667\pi\)
0.157468 + 0.987524i \(0.449667\pi\)
\(854\) −3.45041 5.97629i −0.118071 0.204504i
\(855\) 5.48837 12.2772i 0.187698 0.419871i
\(856\) −0.745455 0.430389i −0.0254791 0.0147104i
\(857\) 13.1946i 0.450720i −0.974276 0.225360i \(-0.927644\pi\)
0.974276 0.225360i \(-0.0723559\pi\)
\(858\) −0.236905 0.584248i −0.00808780 0.0199459i
\(859\) −52.7575 −1.80006 −0.900032 0.435824i \(-0.856457\pi\)
−0.900032 + 0.435824i \(0.856457\pi\)
\(860\) 8.37177 18.7272i 0.285475 0.638592i
\(861\) 3.53925 6.13015i 0.120617 0.208915i
\(862\) 28.1980 16.2801i 0.960426 0.554502i
\(863\) −18.6411 −0.634551 −0.317276 0.948333i \(-0.602768\pi\)
−0.317276 + 0.948333i \(0.602768\pi\)
\(864\) 0.866025 0.500000i 0.0294628 0.0170103i
\(865\) −17.9725 24.8157i −0.611083 0.843758i
\(866\) 30.7327i 1.04434i
\(867\) 43.2139 24.9496i 1.46762 0.847332i
\(868\) 5.20933 + 3.00761i 0.176816 + 0.102085i
\(869\) 1.43701 + 0.829657i 0.0487471 + 0.0281442i
\(870\) 14.4344 1.49510i 0.489374 0.0506888i
\(871\) 9.76808 + 1.36031i 0.330979 + 0.0460924i
\(872\) 5.45336i 0.184674i
\(873\) 4.32411 7.48957i 0.146349 0.253484i
\(874\) −8.75748 + 15.1684i −0.296226 + 0.513079i
\(875\) −6.50684 + 7.16111i −0.219971 + 0.242090i
\(876\) 12.8706i 0.434856i
\(877\) −22.7268 39.3640i −0.767429 1.32923i −0.938953 0.344047i \(-0.888202\pi\)
0.171523 0.985180i \(-0.445131\pi\)
\(878\) 3.26422 + 5.65380i 0.110162 + 0.190807i
\(879\) 13.1527i 0.443630i
\(880\) 0.229340 + 0.316664i 0.00773106 + 0.0106747i
\(881\) 10.0027 17.3252i 0.337000 0.583701i −0.646867 0.762603i \(-0.723921\pi\)
0.983867 + 0.178902i \(0.0572545\pi\)
\(882\) −3.12552 + 5.41356i −0.105242 + 0.182284i
\(883\) 29.0388i 0.977233i 0.872499 + 0.488617i \(0.162498\pi\)
−0.872499 + 0.488617i \(0.837502\pi\)
\(884\) 4.06762 29.2086i 0.136809 0.982392i
\(885\) 1.62109 + 15.6507i 0.0544922 + 0.526094i
\(886\) 26.2501 + 15.1555i 0.881891 + 0.509160i
\(887\) 2.48763 + 1.43623i 0.0835264 + 0.0482240i 0.541181 0.840906i \(-0.317977\pi\)
−0.457655 + 0.889130i \(0.651311\pi\)
\(888\) −1.52347 + 0.879573i −0.0511241 + 0.0295165i
\(889\) 6.00812i 0.201506i
\(890\) −17.2335 23.7953i −0.577667 0.797619i
\(891\) −0.151430 + 0.0874279i −0.00507308 + 0.00292895i
\(892\) −6.95276 −0.232795
\(893\) −61.9912 + 35.7906i −2.07446 + 1.19769i
\(894\) 5.14284 8.90766i 0.172002 0.297917i
\(895\) 28.9545 + 12.9438i 0.967842 + 0.432662i
\(896\) −0.865427 −0.0289119
\(897\) −6.45428 + 8.28251i −0.215502 + 0.276545i
\(898\) 15.9388i 0.531883i
\(899\) 39.0646 + 22.5540i 1.30288 + 0.752217i
\(900\) −1.55943 + 4.75060i −0.0519810 + 0.158353i
\(901\) 10.1722 + 17.6188i 0.338886 + 0.586968i
\(902\) 1.43018 0.0476198
\(903\) −3.96963 6.87561i −0.132101 0.228806i
\(904\) −10.2036 + 5.89106i −0.339367 + 0.195934i
\(905\) −3.17294 30.6331i −0.105472 1.01828i
\(906\) −5.87096 10.1688i −0.195050 0.337836i
\(907\) −28.9860 16.7351i −0.962464 0.555679i −0.0655336 0.997850i \(-0.520875\pi\)
−0.896931 + 0.442171i \(0.854208\pi\)
\(908\) 1.44823 2.50840i 0.0480611 0.0832442i
\(909\) −10.5655 −0.350436
\(910\) −6.16142 + 3.27408i −0.204249 + 0.108535i
\(911\) 20.7528 0.687570 0.343785 0.939048i \(-0.388291\pi\)
0.343785 + 0.939048i \(0.388291\pi\)
\(912\) −3.00709 + 5.20843i −0.0995746 + 0.172468i
\(913\) 0.0211310 + 0.0122000i 0.000699335 + 0.000403761i
\(914\) 9.90436 + 17.1548i 0.327607 + 0.567432i
\(915\) 17.7353 1.83700i 0.586310 0.0607294i
\(916\) −6.83121 + 3.94400i −0.225710 + 0.130313i
\(917\) 0.982835 + 1.70232i 0.0324561 + 0.0562156i
\(918\) −8.17919 −0.269954
\(919\) −13.7419 23.8017i −0.453304 0.785146i 0.545285 0.838251i \(-0.316421\pi\)
−0.998589 + 0.0531051i \(0.983088\pi\)
\(920\) 2.65766 5.94505i 0.0876206 0.196003i
\(921\) −12.8699 7.43044i −0.424077 0.244841i
\(922\) 13.3828i 0.440739i
\(923\) 40.2866 + 31.3940i 1.32605 + 1.03335i
\(924\) 0.151325 0.00497823
\(925\) 2.74326 8.35700i 0.0901979 0.274776i
\(926\) −21.1800 + 36.6848i −0.696017 + 1.20554i
\(927\) −7.73853 + 4.46784i −0.254167 + 0.146743i
\(928\) −6.48982 −0.213039
\(929\) 8.03305 4.63788i 0.263556 0.152164i −0.362400 0.932023i \(-0.618042\pi\)
0.625956 + 0.779859i \(0.284709\pi\)
\(930\) −12.5875 + 9.11635i −0.412759 + 0.298937i
\(931\) 37.5948i 1.23212i
\(932\) −1.23624 + 0.713746i −0.0404945 + 0.0233795i
\(933\) 7.94722 + 4.58833i 0.260180 + 0.150215i
\(934\) −28.9766 16.7296i −0.948143 0.547410i
\(935\) −0.329480 3.18096i −0.0107752 0.104029i
\(936\) −2.21623 + 2.84400i −0.0724398 + 0.0929590i
\(937\) 15.0600i 0.491989i −0.969271 0.245995i \(-0.920885\pi\)
0.969271 0.245995i \(-0.0791146\pi\)
\(938\) −1.18361 + 2.05007i −0.0386462 + 0.0669373i
\(939\) 3.71952 6.44240i 0.121382 0.210240i
\(940\) 21.5547 15.6107i 0.703036 0.509166i
\(941\) 19.4194i 0.633055i −0.948583 0.316528i \(-0.897483\pi\)
0.948583 0.316528i \(-0.102517\pi\)
\(942\) 3.38017 + 5.85463i 0.110132 + 0.190754i
\(943\) −11.9100 20.6288i −0.387844 0.671766i
\(944\) 7.03667i 0.229024i
\(945\) 1.13509 + 1.56729i 0.0369245 + 0.0509838i
\(946\) 0.802048 1.38919i 0.0260768 0.0451664i
\(947\) −2.72224 + 4.71506i −0.0884610 + 0.153219i −0.906861 0.421430i \(-0.861528\pi\)
0.818400 + 0.574649i \(0.194862\pi\)
\(948\) 9.48961i 0.308208i
\(949\) −17.4378 43.0046i −0.566055 1.39599i
\(950\) −6.16329 29.4325i −0.199964 0.954916i
\(951\) −22.3011 12.8755i −0.723161 0.417517i
\(952\) 6.13015 + 3.53925i 0.198679 + 0.114708i
\(953\) 20.2248 11.6768i 0.655146 0.378249i −0.135279 0.990808i \(-0.543193\pi\)
0.790425 + 0.612559i \(0.209860\pi\)
\(954\) 2.48735i 0.0805308i
\(955\) 10.0989 7.31401i 0.326792 0.236676i
\(956\) 9.44692 5.45418i 0.305535 0.176401i
\(957\) 1.13478 0.0366823
\(958\) 19.3387 11.1652i 0.624803 0.360730i
\(959\) −3.19177 + 5.52831i −0.103068 + 0.178518i
\(960\) 0.912572 2.04138i 0.0294531 0.0658851i
\(961\) −17.3104 −0.558401
\(962\) 3.89867 5.00301i 0.125698 0.161303i
\(963\) 0.860777i 0.0277382i
\(964\) 25.4317 + 14.6830i 0.819101 + 0.472908i
\(965\) 0.450756 + 0.201505i 0.0145103 + 0.00648667i
\(966\) −1.26018 2.18270i −0.0405457 0.0702272i
\(967\) 32.2070 1.03571 0.517854 0.855469i \(-0.326731\pi\)
0.517854 + 0.855469i \(0.326731\pi\)
\(968\) −5.48471 9.49980i −0.176285 0.305335i
\(969\) 42.6007 24.5955i 1.36853 0.790123i
\(970\) −1.99235 19.2351i −0.0639705 0.617602i
\(971\) −15.4181 26.7049i −0.494789 0.857000i 0.505193 0.863007i \(-0.331421\pi\)
−0.999982 + 0.00600636i \(0.998088\pi\)
\(972\) 0.866025 + 0.500000i 0.0277778 + 0.0160375i
\(973\) −0.355154 + 0.615144i −0.0113857 + 0.0197206i
\(974\) 28.7499 0.921207
\(975\) −1.22585 17.9860i −0.0392587 0.576014i
\(976\) −7.97389 −0.255238
\(977\) 10.6533 18.4521i 0.340829 0.590334i −0.643758 0.765230i \(-0.722625\pi\)
0.984587 + 0.174896i \(0.0559588\pi\)
\(978\) 1.23624 + 0.713746i 0.0395307 + 0.0228231i
\(979\) −1.14874 1.98968i −0.0367140 0.0635905i
\(980\) 1.44009 + 13.9034i 0.0460021 + 0.444127i
\(981\) 4.72274 2.72668i 0.150786 0.0870561i
\(982\) 8.02546 + 13.9005i 0.256103 + 0.443583i
\(983\) 6.15826 0.196418 0.0982090 0.995166i \(-0.468689\pi\)
0.0982090 + 0.995166i \(0.468689\pi\)
\(984\) −4.08960 7.08339i −0.130372 0.225810i
\(985\) −3.51894 1.57310i −0.112123 0.0501232i
\(986\) 45.9699 + 26.5407i 1.46398 + 0.845229i
\(987\) 10.3004i 0.327865i
\(988\) 2.99093 21.4772i 0.0951542 0.683279i
\(989\) −26.7167 −0.849542
\(990\) −0.159569 + 0.356946i −0.00507142 + 0.0113445i
\(991\) −2.46451 + 4.26866i −0.0782877 + 0.135598i −0.902511 0.430666i \(-0.858279\pi\)
0.824224 + 0.566265i \(0.191612\pi\)
\(992\) 6.01937 3.47529i 0.191115 0.110340i
\(993\) 6.50437 0.206410
\(994\) −10.6168 + 6.12960i −0.336744 + 0.194419i
\(995\) −14.4129 + 10.4384i −0.456919 + 0.330919i
\(996\) 0.139544i 0.00442161i
\(997\) −20.2628 + 11.6988i −0.641730 + 0.370503i −0.785281 0.619140i \(-0.787481\pi\)
0.143550 + 0.989643i \(0.454148\pi\)
\(998\) −28.7961 16.6254i −0.911524 0.526269i
\(999\) −1.52347 0.879573i −0.0482003 0.0278285i
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.a.199.5 yes 12
3.2 odd 2 1170.2.bj.d.199.3 12
5.2 odd 4 1950.2.bc.j.901.2 12
5.3 odd 4 1950.2.bc.i.901.5 12
5.4 even 2 390.2.x.b.199.2 yes 12
13.10 even 6 390.2.x.b.49.2 yes 12
15.14 odd 2 1170.2.bj.c.199.4 12
39.23 odd 6 1170.2.bj.c.829.4 12
65.23 odd 12 1950.2.bc.i.751.5 12
65.49 even 6 inner 390.2.x.a.49.5 12
65.62 odd 12 1950.2.bc.j.751.2 12
195.179 odd 6 1170.2.bj.d.829.3 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
390.2.x.a.49.5 12 65.49 even 6 inner
390.2.x.a.199.5 yes 12 1.1 even 1 trivial
390.2.x.b.49.2 yes 12 13.10 even 6
390.2.x.b.199.2 yes 12 5.4 even 2
1170.2.bj.c.199.4 12 15.14 odd 2
1170.2.bj.c.829.4 12 39.23 odd 6
1170.2.bj.d.199.3 12 3.2 odd 2
1170.2.bj.d.829.3 12 195.179 odd 6
1950.2.bc.i.751.5 12 65.23 odd 12
1950.2.bc.i.901.5 12 5.3 odd 4
1950.2.bc.j.751.2 12 65.62 odd 12
1950.2.bc.j.901.2 12 5.2 odd 4