Properties

Label 560.2.r.a.237.7
Level $560$
Weight $2$
Character 560.237
Analytic conductor $4.472$
Analytic rank $0$
Dimension $184$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [560,2,Mod(237,560)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(560, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([0, 3, 1, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("560.237");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 560.r (of order \(4\), 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: \(4.47162251319\)
Analytic rank: \(0\)
Dimension: \(184\)
Relative dimension: \(92\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 237.7
Character \(\chi\) \(=\) 560.237
Dual form 560.2.r.a.293.8

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.34754 - 0.429109i) q^{2} -2.77875i q^{3} +(1.63173 + 1.15648i) q^{4} +(1.52419 - 1.63611i) q^{5} +(-1.19239 + 3.74447i) q^{6} +(-0.904951 - 2.48617i) q^{7} +(-1.70257 - 2.25860i) q^{8} -4.72144 q^{9} +O(q^{10})\) \(q+(-1.34754 - 0.429109i) q^{2} -2.77875i q^{3} +(1.63173 + 1.15648i) q^{4} +(1.52419 - 1.63611i) q^{5} +(-1.19239 + 3.74447i) q^{6} +(-0.904951 - 2.48617i) q^{7} +(-1.70257 - 2.25860i) q^{8} -4.72144 q^{9} +(-2.75598 + 1.55067i) q^{10} +(-4.66171 + 4.66171i) q^{11} +(3.21357 - 4.53417i) q^{12} +0.783504i q^{13} +(0.152619 + 3.73854i) q^{14} +(-4.54632 - 4.23534i) q^{15} +(1.32509 + 3.77414i) q^{16} +(-1.44597 + 1.44597i) q^{17} +(6.36233 + 2.02601i) q^{18} +(-2.51677 - 2.51677i) q^{19} +(4.37920 - 0.906982i) q^{20} +(-6.90845 + 2.51463i) q^{21} +(8.28223 - 4.28147i) q^{22} +(0.0180574 + 0.0180574i) q^{23} +(-6.27607 + 4.73100i) q^{24} +(-0.353681 - 4.98748i) q^{25} +(0.336208 - 1.05580i) q^{26} +4.78344i q^{27} +(1.39858 - 5.10333i) q^{28} +(3.87232 - 3.87232i) q^{29} +(4.30893 + 7.65816i) q^{30} -4.17072i q^{31} +(-0.166100 - 5.65442i) q^{32} +(12.9537 + 12.9537i) q^{33} +(2.56898 - 1.32802i) q^{34} +(-5.44696 - 2.30881i) q^{35} +(-7.70412 - 5.46026i) q^{36} -3.09358 q^{37} +(2.31148 + 4.47141i) q^{38} +2.17716 q^{39} +(-6.29034 - 0.656957i) q^{40} +7.88509 q^{41} +(10.3885 - 0.424090i) q^{42} -6.47404i q^{43} +(-12.9979 + 2.21547i) q^{44} +(-7.19637 + 7.72477i) q^{45} +(-0.0165845 - 0.0320816i) q^{46} +(-6.82602 + 6.82602i) q^{47} +(10.4874 - 3.68210i) q^{48} +(-5.36213 + 4.49973i) q^{49} +(-1.66357 + 6.87259i) q^{50} +(4.01798 + 4.01798i) q^{51} +(-0.906109 + 1.27847i) q^{52} +5.71593i q^{53} +(2.05262 - 6.44588i) q^{54} +(0.521711 + 14.7324i) q^{55} +(-4.07453 + 6.27680i) q^{56} +(-6.99345 + 6.99345i) q^{57} +(-6.87976 + 3.55646i) q^{58} +(-0.940705 + 0.940705i) q^{59} +(-2.52028 - 12.1687i) q^{60} +(6.52391 - 6.52391i) q^{61} +(-1.78969 + 5.62021i) q^{62} +(4.27267 + 11.7383i) q^{63} +(-2.20253 + 7.69083i) q^{64} +(1.28189 + 1.19421i) q^{65} +(-11.8971 - 23.0142i) q^{66} -13.9337i q^{67} +(-4.03167 + 0.687193i) q^{68} +(0.0501768 - 0.0501768i) q^{69} +(6.34927 + 5.44855i) q^{70} +5.56763i q^{71} +(8.03856 + 10.6638i) q^{72} +(2.43585 - 2.43585i) q^{73} +(4.16873 + 1.32748i) q^{74} +(-13.8589 + 0.982791i) q^{75} +(-1.19609 - 7.01728i) q^{76} +(15.8085 + 7.37121i) q^{77} +(-2.93381 - 0.934238i) q^{78} -1.48168i q^{79} +(8.19459 + 3.58452i) q^{80} -0.872342 q^{81} +(-10.6255 - 3.38356i) q^{82} -15.0957i q^{83} +(-14.1809 - 3.88631i) q^{84} +(0.161824 + 4.56968i) q^{85} +(-2.77807 + 8.72403i) q^{86} +(-10.7602 - 10.7602i) q^{87} +(18.4658 + 2.59206i) q^{88} +6.44566i q^{89} +(13.0122 - 7.32141i) q^{90} +(1.94793 - 0.709033i) q^{91} +(0.00858172 + 0.0503478i) q^{92} -11.5894 q^{93} +(12.1275 - 6.26924i) q^{94} +(-7.95372 + 0.281661i) q^{95} +(-15.7122 + 0.461550i) q^{96} +(1.61133 - 1.61133i) q^{97} +(9.15656 - 3.76264i) q^{98} +(22.0100 - 22.0100i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 184 q - 4 q^{2} + 8 q^{8} - 168 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 184 q - 4 q^{2} + 8 q^{8} - 168 q^{9} - 8 q^{11} - 8 q^{15} - 8 q^{16} - 4 q^{21} - 12 q^{22} - 32 q^{28} - 44 q^{30} - 24 q^{32} + 20 q^{35} - 40 q^{36} - 8 q^{37} + 48 q^{39} - 32 q^{42} + 24 q^{44} - 8 q^{46} - 4 q^{50} - 8 q^{51} - 4 q^{56} + 24 q^{57} - 4 q^{58} + 64 q^{60} - 32 q^{63} - 8 q^{65} + 12 q^{70} - 64 q^{72} + 40 q^{74} - 28 q^{78} + 104 q^{81} - 48 q^{84} + 16 q^{85} + 8 q^{86} + 96 q^{88} - 20 q^{91} - 56 q^{92} + 16 q^{93} - 56 q^{95} - 80 q^{98} + 24 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/560\mathbb{Z}\right)^\times\).

\(n\) \(241\) \(337\) \(351\) \(421\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{4}\right)\) \(1\) \(e\left(\frac{3}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.34754 0.429109i −0.952855 0.303426i
\(3\) 2.77875i 1.60431i −0.597115 0.802155i \(-0.703687\pi\)
0.597115 0.802155i \(-0.296313\pi\)
\(4\) 1.63173 + 1.15648i 0.815866 + 0.578242i
\(5\) 1.52419 1.63611i 0.681639 0.731689i
\(6\) −1.19239 + 3.74447i −0.486789 + 1.52868i
\(7\) −0.904951 2.48617i −0.342039 0.939686i
\(8\) −1.70257 2.25860i −0.601948 0.798535i
\(9\) −4.72144 −1.57381
\(10\) −2.75598 + 1.55067i −0.871516 + 0.490366i
\(11\) −4.66171 + 4.66171i −1.40556 + 1.40556i −0.624673 + 0.780886i \(0.714768\pi\)
−0.780886 + 0.624673i \(0.785232\pi\)
\(12\) 3.21357 4.53417i 0.927679 1.30890i
\(13\) 0.783504i 0.217305i 0.994080 + 0.108652i \(0.0346536\pi\)
−0.994080 + 0.108652i \(0.965346\pi\)
\(14\) 0.152619 + 3.73854i 0.0407891 + 0.999168i
\(15\) −4.54632 4.23534i −1.17386 1.09356i
\(16\) 1.32509 + 3.77414i 0.331273 + 0.943535i
\(17\) −1.44597 + 1.44597i −0.350698 + 0.350698i −0.860369 0.509671i \(-0.829767\pi\)
0.509671 + 0.860369i \(0.329767\pi\)
\(18\) 6.36233 + 2.02601i 1.49962 + 0.477535i
\(19\) −2.51677 2.51677i −0.577386 0.577386i 0.356797 0.934182i \(-0.383869\pi\)
−0.934182 + 0.356797i \(0.883869\pi\)
\(20\) 4.37920 0.906982i 0.979219 0.202807i
\(21\) −6.90845 + 2.51463i −1.50755 + 0.548737i
\(22\) 8.28223 4.28147i 1.76578 0.912811i
\(23\) 0.0180574 + 0.0180574i 0.00376522 + 0.00376522i 0.708987 0.705222i \(-0.249153\pi\)
−0.705222 + 0.708987i \(0.749153\pi\)
\(24\) −6.27607 + 4.73100i −1.28110 + 0.965712i
\(25\) −0.353681 4.98748i −0.0707363 0.997495i
\(26\) 0.336208 1.05580i 0.0659359 0.207060i
\(27\) 4.78344i 0.920573i
\(28\) 1.39858 5.10333i 0.264307 0.964439i
\(29\) 3.87232 3.87232i 0.719072 0.719072i −0.249343 0.968415i \(-0.580215\pi\)
0.968415 + 0.249343i \(0.0802147\pi\)
\(30\) 4.30893 + 7.65816i 0.786700 + 1.39818i
\(31\) 4.17072i 0.749083i −0.927210 0.374541i \(-0.877800\pi\)
0.927210 0.374541i \(-0.122200\pi\)
\(32\) −0.166100 5.65442i −0.0293626 0.999569i
\(33\) 12.9537 + 12.9537i 2.25495 + 2.25495i
\(34\) 2.56898 1.32802i 0.440576 0.227754i
\(35\) −5.44696 2.30881i −0.920705 0.390260i
\(36\) −7.70412 5.46026i −1.28402 0.910044i
\(37\) −3.09358 −0.508582 −0.254291 0.967128i \(-0.581842\pi\)
−0.254291 + 0.967128i \(0.581842\pi\)
\(38\) 2.31148 + 4.47141i 0.374971 + 0.725358i
\(39\) 2.17716 0.348625
\(40\) −6.29034 0.656957i −0.994590 0.103874i
\(41\) 7.88509 1.23144 0.615722 0.787963i \(-0.288864\pi\)
0.615722 + 0.787963i \(0.288864\pi\)
\(42\) 10.3885 0.424090i 1.60298 0.0654385i
\(43\) 6.47404i 0.987282i −0.869666 0.493641i \(-0.835666\pi\)
0.869666 0.493641i \(-0.164334\pi\)
\(44\) −12.9979 + 2.21547i −1.95950 + 0.333995i
\(45\) −7.19637 + 7.72477i −1.07277 + 1.15154i
\(46\) −0.0165845 0.0320816i −0.00244524 0.00473017i
\(47\) −6.82602 + 6.82602i −0.995678 + 0.995678i −0.999991 0.00431268i \(-0.998627\pi\)
0.00431268 + 0.999991i \(0.498627\pi\)
\(48\) 10.4874 3.68210i 1.51372 0.531465i
\(49\) −5.36213 + 4.49973i −0.766018 + 0.642819i
\(50\) −1.66357 + 6.87259i −0.235264 + 0.971931i
\(51\) 4.01798 + 4.01798i 0.562629 + 0.562629i
\(52\) −0.906109 + 1.27847i −0.125655 + 0.177292i
\(53\) 5.71593i 0.785143i 0.919721 + 0.392572i \(0.128414\pi\)
−0.919721 + 0.392572i \(0.871586\pi\)
\(54\) 2.05262 6.44588i 0.279326 0.877173i
\(55\) 0.521711 + 14.7324i 0.0703475 + 1.98652i
\(56\) −4.07453 + 6.27680i −0.544482 + 0.838773i
\(57\) −6.99345 + 6.99345i −0.926306 + 0.926306i
\(58\) −6.87976 + 3.55646i −0.903356 + 0.466986i
\(59\) −0.940705 + 0.940705i −0.122469 + 0.122469i −0.765685 0.643216i \(-0.777600\pi\)
0.643216 + 0.765685i \(0.277600\pi\)
\(60\) −2.52028 12.1687i −0.325366 1.57097i
\(61\) 6.52391 6.52391i 0.835301 0.835301i −0.152936 0.988236i \(-0.548873\pi\)
0.988236 + 0.152936i \(0.0488727\pi\)
\(62\) −1.78969 + 5.62021i −0.227291 + 0.713767i
\(63\) 4.27267 + 11.7383i 0.538306 + 1.47889i
\(64\) −2.20253 + 7.69083i −0.275317 + 0.961354i
\(65\) 1.28189 + 1.19421i 0.159000 + 0.148124i
\(66\) −11.8971 23.0142i −1.46443 2.83286i
\(67\) 13.9337i 1.70228i −0.524942 0.851138i \(-0.675913\pi\)
0.524942 0.851138i \(-0.324087\pi\)
\(68\) −4.03167 + 0.687193i −0.488911 + 0.0833344i
\(69\) 0.0501768 0.0501768i 0.00604058 0.00604058i
\(70\) 6.34927 + 5.44855i 0.758883 + 0.651227i
\(71\) 5.56763i 0.660757i 0.943849 + 0.330378i \(0.107176\pi\)
−0.943849 + 0.330378i \(0.892824\pi\)
\(72\) 8.03856 + 10.6638i 0.947354 + 1.25674i
\(73\) 2.43585 2.43585i 0.285095 0.285095i −0.550042 0.835137i \(-0.685388\pi\)
0.835137 + 0.550042i \(0.185388\pi\)
\(74\) 4.16873 + 1.32748i 0.484605 + 0.154317i
\(75\) −13.8589 + 0.982791i −1.60029 + 0.113483i
\(76\) −1.19609 7.01728i −0.137201 0.804937i
\(77\) 15.8085 + 7.37121i 1.80154 + 0.840027i
\(78\) −2.93381 0.934238i −0.332189 0.105782i
\(79\) 1.48168i 0.166702i −0.996520 0.0833509i \(-0.973438\pi\)
0.996520 0.0833509i \(-0.0265622\pi\)
\(80\) 8.19459 + 3.58452i 0.916182 + 0.400761i
\(81\) −0.872342 −0.0969269
\(82\) −10.6255 3.38356i −1.17339 0.373652i
\(83\) 15.0957i 1.65697i −0.560015 0.828483i \(-0.689205\pi\)
0.560015 0.828483i \(-0.310795\pi\)
\(84\) −14.1809 3.88631i −1.54726 0.424031i
\(85\) 0.161824 + 4.56968i 0.0175523 + 0.495652i
\(86\) −2.77807 + 8.72403i −0.299567 + 0.940737i
\(87\) −10.7602 10.7602i −1.15361 1.15361i
\(88\) 18.4658 + 2.59206i 1.96846 + 0.276315i
\(89\) 6.44566i 0.683239i 0.939838 + 0.341619i \(0.110975\pi\)
−0.939838 + 0.341619i \(0.889025\pi\)
\(90\) 13.0122 7.32141i 1.37160 0.771745i
\(91\) 1.94793 0.709033i 0.204198 0.0743268i
\(92\) 0.00858172 + 0.0503478i 0.000894707 + 0.00524912i
\(93\) −11.5894 −1.20176
\(94\) 12.1275 6.26924i 1.25085 0.646622i
\(95\) −7.95372 + 0.281661i −0.816035 + 0.0288978i
\(96\) −15.7122 + 0.461550i −1.60362 + 0.0471068i
\(97\) 1.61133 1.61133i 0.163606 0.163606i −0.620556 0.784162i \(-0.713093\pi\)
0.784162 + 0.620556i \(0.213093\pi\)
\(98\) 9.15656 3.76264i 0.924952 0.380084i
\(99\) 22.0100 22.0100i 2.21209 2.21209i
\(100\) 5.19082 8.54725i 0.519082 0.854725i
\(101\) −9.19768 9.19768i −0.915203 0.915203i 0.0814726 0.996676i \(-0.474038\pi\)
−0.996676 + 0.0814726i \(0.974038\pi\)
\(102\) −3.69024 7.13854i −0.365388 0.706820i
\(103\) 1.54128 1.54128i 0.151867 0.151867i −0.627084 0.778951i \(-0.715752\pi\)
0.778951 + 0.627084i \(0.215752\pi\)
\(104\) 1.76962 1.33397i 0.173526 0.130806i
\(105\) −6.41560 + 15.1357i −0.626098 + 1.47710i
\(106\) 2.45276 7.70245i 0.238233 0.748128i
\(107\) −0.0942659 −0.00911303 −0.00455651 0.999990i \(-0.501450\pi\)
−0.00455651 + 0.999990i \(0.501450\pi\)
\(108\) −5.53197 + 7.80529i −0.532314 + 0.751064i
\(109\) −7.15529 + 7.15529i −0.685352 + 0.685352i −0.961201 0.275849i \(-0.911041\pi\)
0.275849 + 0.961201i \(0.411041\pi\)
\(110\) 5.61878 20.0764i 0.535729 1.91421i
\(111\) 8.59629i 0.815924i
\(112\) 8.18402 6.70982i 0.773318 0.634019i
\(113\) 7.90573 7.90573i 0.743709 0.743709i −0.229581 0.973290i \(-0.573736\pi\)
0.973290 + 0.229581i \(0.0737356\pi\)
\(114\) 12.4249 6.42301i 1.16370 0.601570i
\(115\) 0.0570666 0.00202087i 0.00532149 0.000188447i
\(116\) 10.7969 1.84031i 1.00246 0.170869i
\(117\) 3.69926i 0.341997i
\(118\) 1.67130 0.863973i 0.153856 0.0795352i
\(119\) 4.90345 + 2.28640i 0.449499 + 0.209594i
\(120\) −1.82552 + 17.4793i −0.166646 + 1.59563i
\(121\) 32.4631i 2.95119i
\(122\) −11.5907 + 5.99176i −1.04937 + 0.542469i
\(123\) 21.9107i 1.97562i
\(124\) 4.82336 6.80549i 0.433151 0.611151i
\(125\) −8.69911 7.02321i −0.778072 0.628175i
\(126\) −0.720581 17.6513i −0.0641945 1.57250i
\(127\) 9.22721 + 9.22721i 0.818783 + 0.818783i 0.985932 0.167149i \(-0.0534560\pi\)
−0.167149 + 0.985932i \(0.553456\pi\)
\(128\) 6.26821 9.41858i 0.554036 0.832493i
\(129\) −17.9897 −1.58391
\(130\) −1.21496 2.15932i −0.106559 0.189385i
\(131\) −4.52680 + 4.52680i −0.395508 + 0.395508i −0.876645 0.481137i \(-0.840224\pi\)
0.481137 + 0.876645i \(0.340224\pi\)
\(132\) 6.15623 + 36.1178i 0.535831 + 3.14365i
\(133\) −3.97957 + 8.53467i −0.345072 + 0.740049i
\(134\) −5.97909 + 18.7763i −0.516514 + 1.62202i
\(135\) 7.82621 + 7.29088i 0.673573 + 0.627499i
\(136\) 5.72771 + 0.804003i 0.491147 + 0.0689427i
\(137\) −9.22566 + 9.22566i −0.788201 + 0.788201i −0.981199 0.192998i \(-0.938179\pi\)
0.192998 + 0.981199i \(0.438179\pi\)
\(138\) −0.0891467 + 0.0460840i −0.00758867 + 0.00392293i
\(139\) 13.1431 13.1431i 1.11478 1.11478i 0.122286 0.992495i \(-0.460978\pi\)
0.992495 0.122286i \(-0.0390224\pi\)
\(140\) −6.21788 10.0667i −0.525507 0.850790i
\(141\) 18.9678 + 18.9678i 1.59738 + 1.59738i
\(142\) 2.38912 7.50261i 0.200491 0.629605i
\(143\) −3.65247 3.65247i −0.305435 0.305435i
\(144\) −6.25634 17.8194i −0.521362 1.48495i
\(145\) −0.433367 12.2377i −0.0359892 1.01628i
\(146\) −4.32765 + 2.23716i −0.358159 + 0.185149i
\(147\) 12.5036 + 14.9000i 1.03128 + 1.22893i
\(148\) −5.04790 3.57768i −0.414935 0.294083i
\(149\) −0.918245 0.918245i −0.0752256 0.0752256i 0.668493 0.743719i \(-0.266940\pi\)
−0.743719 + 0.668493i \(0.766940\pi\)
\(150\) 19.0972 + 4.62264i 1.55928 + 0.377437i
\(151\) 17.8556i 1.45307i 0.687129 + 0.726535i \(0.258870\pi\)
−0.687129 + 0.726535i \(0.741130\pi\)
\(152\) −1.39940 + 9.96932i −0.113506 + 0.808619i
\(153\) 6.82704 6.82704i 0.551934 0.551934i
\(154\) −18.1395 16.7166i −1.46172 1.34706i
\(155\) −6.82373 6.35697i −0.548095 0.510604i
\(156\) 3.55254 + 2.51785i 0.284431 + 0.201589i
\(157\) −7.44900 −0.594495 −0.297248 0.954800i \(-0.596069\pi\)
−0.297248 + 0.954800i \(0.596069\pi\)
\(158\) −0.635801 + 1.99662i −0.0505816 + 0.158843i
\(159\) 15.8831 1.25961
\(160\) −9.50439 8.34665i −0.751388 0.659861i
\(161\) 0.0285527 0.0612348i 0.00225027 0.00482598i
\(162\) 1.17552 + 0.374330i 0.0923573 + 0.0294101i
\(163\) 20.5825 1.61214 0.806072 0.591817i \(-0.201589\pi\)
0.806072 + 0.591817i \(0.201589\pi\)
\(164\) 12.8664 + 9.11898i 1.00469 + 0.712072i
\(165\) 40.9376 1.44970i 3.18699 0.112859i
\(166\) −6.47769 + 20.3420i −0.502766 + 1.57885i
\(167\) −2.63616 2.63616i −0.203992 0.203992i 0.597716 0.801708i \(-0.296075\pi\)
−0.801708 + 0.597716i \(0.796075\pi\)
\(168\) 17.4416 + 11.3221i 1.34565 + 0.873518i
\(169\) 12.3861 0.952779
\(170\) 1.74283 6.22727i 0.133669 0.477610i
\(171\) 11.8827 + 11.8827i 0.908696 + 0.908696i
\(172\) 7.48712 10.5639i 0.570888 0.805489i
\(173\) 19.5245i 1.48442i −0.670168 0.742210i \(-0.733778\pi\)
0.670168 0.742210i \(-0.266222\pi\)
\(174\) 9.88251 + 19.1171i 0.749191 + 1.44926i
\(175\) −12.0797 + 5.39274i −0.913137 + 0.407652i
\(176\) −23.7712 11.4168i −1.79182 0.860570i
\(177\) 2.61398 + 2.61398i 0.196479 + 0.196479i
\(178\) 2.76589 8.68579i 0.207312 0.651028i
\(179\) −1.12393 + 1.12393i −0.0840063 + 0.0840063i −0.747861 0.663855i \(-0.768919\pi\)
0.663855 + 0.747861i \(0.268919\pi\)
\(180\) −20.6761 + 4.28226i −1.54111 + 0.319181i
\(181\) 11.3745 + 11.3745i 0.845458 + 0.845458i 0.989562 0.144105i \(-0.0460303\pi\)
−0.144105 + 0.989562i \(0.546030\pi\)
\(182\) −2.92916 + 0.119578i −0.217124 + 0.00886368i
\(183\) −18.1283 18.1283i −1.34008 1.34008i
\(184\) 0.0100405 0.0715282i 0.000740193 0.00527313i
\(185\) −4.71521 + 5.06143i −0.346669 + 0.372124i
\(186\) 15.6171 + 4.97310i 1.14510 + 0.364645i
\(187\) 13.4814i 0.985855i
\(188\) −19.0324 + 3.24405i −1.38808 + 0.236597i
\(189\) 11.8925 4.32878i 0.865050 0.314872i
\(190\) 10.8388 + 3.03346i 0.786331 + 0.220071i
\(191\) 10.7109 0.775015 0.387508 0.921867i \(-0.373336\pi\)
0.387508 + 0.921867i \(0.373336\pi\)
\(192\) 21.3709 + 6.12028i 1.54231 + 0.441693i
\(193\) −11.0964 + 11.0964i −0.798735 + 0.798735i −0.982896 0.184161i \(-0.941043\pi\)
0.184161 + 0.982896i \(0.441043\pi\)
\(194\) −2.86277 + 1.47990i −0.205535 + 0.106250i
\(195\) 3.31841 3.56206i 0.237636 0.255085i
\(196\) −13.9534 + 1.14115i −0.996672 + 0.0815104i
\(197\) −11.3106 −0.805848 −0.402924 0.915234i \(-0.632006\pi\)
−0.402924 + 0.915234i \(0.632006\pi\)
\(198\) −39.1040 + 20.2147i −2.77900 + 1.43659i
\(199\) 18.7822i 1.33143i −0.746204 0.665717i \(-0.768126\pi\)
0.746204 0.665717i \(-0.231874\pi\)
\(200\) −10.6625 + 9.29033i −0.753955 + 0.656926i
\(201\) −38.7183 −2.73098
\(202\) 8.44744 + 16.3410i 0.594360 + 1.14975i
\(203\) −13.1315 6.12300i −0.921653 0.429751i
\(204\) 1.90954 + 11.2030i 0.133694 + 0.784365i
\(205\) 12.0184 12.9008i 0.839401 0.901034i
\(206\) −2.73832 + 1.41556i −0.190788 + 0.0986271i
\(207\) −0.0852567 0.0852567i −0.00592575 0.00592575i
\(208\) −2.95705 + 1.03822i −0.205035 + 0.0719873i
\(209\) 23.4649 1.62310
\(210\) 15.1402 17.6430i 1.04477 1.21748i
\(211\) −13.7992 13.7992i −0.949974 0.949974i 0.0488333 0.998807i \(-0.484450\pi\)
−0.998807 + 0.0488333i \(0.984450\pi\)
\(212\) −6.61038 + 9.32686i −0.454003 + 0.640571i
\(213\) 15.4711 1.06006
\(214\) 0.127027 + 0.0404503i 0.00868339 + 0.00276513i
\(215\) −10.5922 9.86768i −0.722383 0.672970i
\(216\) 10.8039 8.14412i 0.735110 0.554138i
\(217\) −10.3691 + 3.77429i −0.703902 + 0.256216i
\(218\) 12.7124 6.57164i 0.860995 0.445088i
\(219\) −6.76861 6.76861i −0.457380 0.457380i
\(220\) −16.1865 + 24.6427i −1.09129 + 1.66141i
\(221\) −1.13292 1.13292i −0.0762085 0.0762085i
\(222\) 3.68874 11.5838i 0.247572 0.777457i
\(223\) 3.20053 + 3.20053i 0.214323 + 0.214323i 0.806101 0.591778i \(-0.201574\pi\)
−0.591778 + 0.806101i \(0.701574\pi\)
\(224\) −13.9075 + 5.52992i −0.929237 + 0.369484i
\(225\) 1.66988 + 23.5481i 0.111326 + 1.56987i
\(226\) −14.0457 + 7.26087i −0.934307 + 0.482986i
\(227\) −2.63857 −0.175128 −0.0875640 0.996159i \(-0.527908\pi\)
−0.0875640 + 0.996159i \(0.527908\pi\)
\(228\) −19.4993 + 3.32362i −1.29137 + 0.220112i
\(229\) −7.19691 + 7.19691i −0.475585 + 0.475585i −0.903717 0.428131i \(-0.859172\pi\)
0.428131 + 0.903717i \(0.359172\pi\)
\(230\) −0.0777668 0.0217646i −0.00512779 0.00143511i
\(231\) 20.4827 43.9277i 1.34766 2.89023i
\(232\) −15.3389 2.15313i −1.00705 0.141360i
\(233\) −1.94321 1.94321i −0.127304 0.127304i 0.640584 0.767888i \(-0.278692\pi\)
−0.767888 + 0.640584i \(0.778692\pi\)
\(234\) −1.58739 + 4.98491i −0.103771 + 0.325874i
\(235\) 0.763928 + 21.5723i 0.0498332 + 1.40722i
\(236\) −2.62289 + 0.447068i −0.170735 + 0.0291016i
\(237\) −4.11721 −0.267441
\(238\) −5.62649 5.18513i −0.364711 0.336102i
\(239\) 13.6867i 0.885319i 0.896690 + 0.442659i \(0.145965\pi\)
−0.896690 + 0.442659i \(0.854035\pi\)
\(240\) 9.96047 22.7707i 0.642946 1.46984i
\(241\) 22.2479i 1.43312i −0.697528 0.716558i \(-0.745717\pi\)
0.697528 0.716558i \(-0.254283\pi\)
\(242\) −13.9302 + 43.7454i −0.895469 + 2.81206i
\(243\) 16.7743i 1.07607i
\(244\) 18.1901 3.10047i 1.16450 0.198487i
\(245\) −0.810869 + 15.6315i −0.0518045 + 0.998657i
\(246\) −9.40207 + 29.5255i −0.599454 + 1.88248i
\(247\) 1.97190 1.97190i 0.125469 0.125469i
\(248\) −9.41997 + 7.10092i −0.598169 + 0.450909i
\(249\) −41.9471 −2.65829
\(250\) 8.70869 + 13.1969i 0.550786 + 0.834647i
\(251\) 2.07947 + 2.07947i 0.131255 + 0.131255i 0.769682 0.638427i \(-0.220415\pi\)
−0.638427 + 0.769682i \(0.720415\pi\)
\(252\) −6.60332 + 24.0950i −0.415970 + 1.51785i
\(253\) −0.168356 −0.0105845
\(254\) −8.47457 16.3935i −0.531742 1.02862i
\(255\) 12.6980 0.449668i 0.795179 0.0281593i
\(256\) −12.4883 + 10.0022i −0.780516 + 0.625136i
\(257\) 7.66629 7.66629i 0.478210 0.478210i −0.426349 0.904559i \(-0.640200\pi\)
0.904559 + 0.426349i \(0.140200\pi\)
\(258\) 24.2419 + 7.71955i 1.50923 + 0.480598i
\(259\) 2.79954 + 7.69119i 0.173955 + 0.477907i
\(260\) 0.710624 + 3.43112i 0.0440710 + 0.212789i
\(261\) −18.2829 + 18.2829i −1.13168 + 1.13168i
\(262\) 8.04253 4.15755i 0.496869 0.256855i
\(263\) −4.91019 4.91019i −0.302775 0.302775i 0.539323 0.842099i \(-0.318680\pi\)
−0.842099 + 0.539323i \(0.818680\pi\)
\(264\) 7.20268 51.3118i 0.443294 3.15803i
\(265\) 9.35186 + 8.71217i 0.574480 + 0.535184i
\(266\) 9.02493 9.79314i 0.553354 0.600456i
\(267\) 17.9109 1.09613
\(268\) 16.1141 22.7361i 0.984327 1.38883i
\(269\) −3.64657 3.64657i −0.222335 0.222335i 0.587146 0.809481i \(-0.300252\pi\)
−0.809481 + 0.587146i \(0.800252\pi\)
\(270\) −7.41756 13.1830i −0.451418 0.802295i
\(271\) 24.3040i 1.47636i −0.674604 0.738180i \(-0.735685\pi\)
0.674604 0.738180i \(-0.264315\pi\)
\(272\) −7.37332 3.54124i −0.447073 0.214719i
\(273\) −1.97022 5.41280i −0.119243 0.327597i
\(274\) 16.3908 8.47314i 0.990202 0.511881i
\(275\) 24.8989 + 21.6014i 1.50146 + 1.30261i
\(276\) 0.139904 0.0238464i 0.00842122 0.00143539i
\(277\) 22.2309 1.33573 0.667864 0.744283i \(-0.267209\pi\)
0.667864 + 0.744283i \(0.267209\pi\)
\(278\) −23.3506 + 12.0710i −1.40048 + 0.723971i
\(279\) 19.6918i 1.17892i
\(280\) 4.05914 + 16.2334i 0.242580 + 0.970131i
\(281\) 4.57915i 0.273169i −0.990628 0.136585i \(-0.956387\pi\)
0.990628 0.136585i \(-0.0436126\pi\)
\(282\) −17.4206 33.6991i −1.03738 2.00675i
\(283\) 16.0989 0.956981 0.478491 0.878093i \(-0.341184\pi\)
0.478491 + 0.878093i \(0.341184\pi\)
\(284\) −6.43888 + 9.08488i −0.382077 + 0.539089i
\(285\) 0.782665 + 22.1014i 0.0463611 + 1.30917i
\(286\) 3.35454 + 6.48916i 0.198358 + 0.383712i
\(287\) −7.13562 19.6037i −0.421203 1.15717i
\(288\) 0.784232 + 26.6970i 0.0462113 + 1.57313i
\(289\) 12.8184i 0.754021i
\(290\) −4.66732 + 16.6767i −0.274074 + 0.979292i
\(291\) −4.47748 4.47748i −0.262474 0.262474i
\(292\) 6.79167 1.15763i 0.397453 0.0677453i
\(293\) 10.9758 0.641211 0.320606 0.947213i \(-0.396114\pi\)
0.320606 + 0.947213i \(0.396114\pi\)
\(294\) −10.4554 25.4438i −0.609772 1.48391i
\(295\) 0.105278 + 2.97291i 0.00612952 + 0.173089i
\(296\) 5.26703 + 6.98716i 0.306140 + 0.406121i
\(297\) −22.2990 22.2990i −1.29392 1.29392i
\(298\) 0.843346 + 1.63140i 0.0488537 + 0.0945045i
\(299\) −0.0141480 + 0.0141480i −0.000818201 + 0.000818201i
\(300\) −23.7506 14.4240i −1.37124 0.832768i
\(301\) −16.0956 + 5.85869i −0.927735 + 0.337689i
\(302\) 7.66201 24.0612i 0.440899 1.38457i
\(303\) −25.5580 + 25.5580i −1.46827 + 1.46827i
\(304\) 6.16367 12.8336i 0.353511 0.736056i
\(305\) −0.730117 20.6175i −0.0418064 1.18055i
\(306\) −12.1293 + 6.27017i −0.693384 + 0.358442i
\(307\) −25.6773 −1.46548 −0.732741 0.680508i \(-0.761759\pi\)
−0.732741 + 0.680508i \(0.761759\pi\)
\(308\) 17.2705 + 30.3100i 0.984076 + 1.72708i
\(309\) −4.28284 4.28284i −0.243642 0.243642i
\(310\) 6.46742 + 11.4944i 0.367325 + 0.652838i
\(311\) −5.96810 −0.338420 −0.169210 0.985580i \(-0.554122\pi\)
−0.169210 + 0.985580i \(0.554122\pi\)
\(312\) −3.70676 4.91733i −0.209854 0.278389i
\(313\) −4.81266 + 4.81266i −0.272028 + 0.272028i −0.829916 0.557888i \(-0.811612\pi\)
0.557888 + 0.829916i \(0.311612\pi\)
\(314\) 10.0378 + 3.19643i 0.566468 + 0.180385i
\(315\) 25.7175 + 10.9009i 1.44902 + 0.614196i
\(316\) 1.71353 2.41770i 0.0963939 0.136006i
\(317\) 18.9684i 1.06537i −0.846314 0.532684i \(-0.821183\pi\)
0.846314 0.532684i \(-0.178817\pi\)
\(318\) −21.4032 6.81559i −1.20023 0.382199i
\(319\) 36.1033i 2.02140i
\(320\) 9.22592 + 15.3259i 0.515745 + 0.856742i
\(321\) 0.261941i 0.0146201i
\(322\) −0.0647523 + 0.0702641i −0.00360851 + 0.00391567i
\(323\) 7.27832 0.404976
\(324\) −1.42343 1.00885i −0.0790793 0.0560472i
\(325\) 3.90771 0.277111i 0.216761 0.0153713i
\(326\) −27.7357 8.83213i −1.53614 0.489166i
\(327\) 19.8827 + 19.8827i 1.09952 + 1.09952i
\(328\) −13.4249 17.8093i −0.741266 0.983352i
\(329\) 23.1479 + 10.7935i 1.27619 + 0.595063i
\(330\) −55.7872 15.6132i −3.07098 0.859476i
\(331\) −8.37259 + 8.37259i −0.460199 + 0.460199i −0.898721 0.438521i \(-0.855502\pi\)
0.438521 + 0.898721i \(0.355502\pi\)
\(332\) 17.4579 24.6321i 0.958126 1.35186i
\(333\) 14.6062 0.800413
\(334\) 2.42113 + 4.68353i 0.132478 + 0.256271i
\(335\) −22.7970 21.2377i −1.24554 1.16034i
\(336\) −18.6449 22.7413i −1.01716 1.24064i
\(337\) −4.80682 4.80682i −0.261844 0.261844i 0.563959 0.825803i \(-0.309278\pi\)
−0.825803 + 0.563959i \(0.809278\pi\)
\(338\) −16.6908 5.31499i −0.907860 0.289098i
\(339\) −21.9680 21.9680i −1.19314 1.19314i
\(340\) −5.02071 + 7.64364i −0.272286 + 0.414535i
\(341\) 19.4427 + 19.4427i 1.05288 + 1.05288i
\(342\) −10.9135 21.1115i −0.590134 1.14158i
\(343\) 16.0396 + 9.25914i 0.866056 + 0.499947i
\(344\) −14.6223 + 11.0225i −0.788379 + 0.594293i
\(345\) −0.00561549 0.158574i −0.000302328 0.00853732i
\(346\) −8.37813 + 26.3100i −0.450411 + 1.41444i
\(347\) 3.28835 0.176528 0.0882640 0.996097i \(-0.471868\pi\)
0.0882640 + 0.996097i \(0.471868\pi\)
\(348\) −5.11376 30.0018i −0.274127 1.60826i
\(349\) 0.915717 + 0.915717i 0.0490172 + 0.0490172i 0.731191 0.682173i \(-0.238965\pi\)
−0.682173 + 0.731191i \(0.738965\pi\)
\(350\) 18.5919 2.08344i 0.993780 0.111364i
\(351\) −3.74784 −0.200045
\(352\) 27.1336 + 25.5850i 1.44622 + 1.36368i
\(353\) 1.62492 + 1.62492i 0.0864859 + 0.0864859i 0.749026 0.662540i \(-0.230522\pi\)
−0.662540 + 0.749026i \(0.730522\pi\)
\(354\) −2.40076 4.64413i −0.127599 0.246833i
\(355\) 9.10924 + 8.48614i 0.483468 + 0.450398i
\(356\) −7.45430 + 10.5176i −0.395077 + 0.557431i
\(357\) 6.35332 13.6255i 0.336253 0.721136i
\(358\) 1.99683 1.03225i 0.105535 0.0545561i
\(359\) 15.3617 0.810757 0.405379 0.914149i \(-0.367140\pi\)
0.405379 + 0.914149i \(0.367140\pi\)
\(360\) 29.6995 + 3.10178i 1.56530 + 0.163478i
\(361\) 6.33179i 0.333252i
\(362\) −10.4467 20.2084i −0.549065 1.06213i
\(363\) −90.2069 −4.73463
\(364\) 3.99848 + 1.09579i 0.209577 + 0.0574352i
\(365\) −0.272606 7.69801i −0.0142688 0.402932i
\(366\) 16.6496 + 32.2076i 0.870288 + 1.68352i
\(367\) −14.0530 + 14.0530i −0.733563 + 0.733563i −0.971324 0.237761i \(-0.923587\pi\)
0.237761 + 0.971324i \(0.423587\pi\)
\(368\) −0.0442233 + 0.0920787i −0.00230530 + 0.00479993i
\(369\) −37.2290 −1.93806
\(370\) 8.52585 4.79714i 0.443238 0.249391i
\(371\) 14.2108 5.17264i 0.737788 0.268550i
\(372\) −18.9107 13.4029i −0.980476 0.694908i
\(373\) 27.4072i 1.41909i −0.704660 0.709545i \(-0.748900\pi\)
0.704660 0.709545i \(-0.251100\pi\)
\(374\) −5.78497 + 18.1667i −0.299134 + 0.939377i
\(375\) −19.5157 + 24.1726i −1.00779 + 1.24827i
\(376\) 27.0390 + 3.79549i 1.39443 + 0.195737i
\(377\) 3.03398 + 3.03398i 0.156258 + 0.156258i
\(378\) −17.8831 + 0.730044i −0.919807 + 0.0375494i
\(379\) −9.57095 9.57095i −0.491627 0.491627i 0.417192 0.908819i \(-0.363014\pi\)
−0.908819 + 0.417192i \(0.863014\pi\)
\(380\) −13.3041 8.73875i −0.682485 0.448289i
\(381\) 25.6401 25.6401i 1.31358 1.31358i
\(382\) −14.4334 4.59615i −0.738477 0.235160i
\(383\) 11.4848 + 11.4848i 0.586845 + 0.586845i 0.936776 0.349931i \(-0.113795\pi\)
−0.349931 + 0.936776i \(0.613795\pi\)
\(384\) −26.1718 17.4178i −1.33558 0.888846i
\(385\) 36.1552 14.6292i 1.84264 0.745571i
\(386\) 19.7144 10.1913i 1.00344 0.518722i
\(387\) 30.5668i 1.55380i
\(388\) 4.49273 0.765781i 0.228084 0.0388767i
\(389\) 9.44128 + 9.44128i 0.478692 + 0.478692i 0.904713 0.426021i \(-0.140085\pi\)
−0.426021 + 0.904713i \(0.640085\pi\)
\(390\) −6.00020 + 3.37607i −0.303832 + 0.170954i
\(391\) −0.0522207 −0.00264091
\(392\) 19.2925 + 4.44979i 0.974417 + 0.224749i
\(393\) 12.5788 + 12.5788i 0.634518 + 0.634518i
\(394\) 15.2415 + 4.85348i 0.767856 + 0.244515i
\(395\) −2.42418 2.25836i −0.121974 0.113630i
\(396\) 61.3686 10.4602i 3.08389 0.525645i
\(397\) 0.486141 0.0243987 0.0121994 0.999926i \(-0.496117\pi\)
0.0121994 + 0.999926i \(0.496117\pi\)
\(398\) −8.05961 + 25.3098i −0.403992 + 1.26866i
\(399\) 23.7157 + 11.0582i 1.18727 + 0.553603i
\(400\) 18.3548 7.94371i 0.917738 0.397186i
\(401\) 5.27669 0.263505 0.131753 0.991283i \(-0.457940\pi\)
0.131753 + 0.991283i \(0.457940\pi\)
\(402\) 52.1745 + 16.6144i 2.60223 + 0.828650i
\(403\) 3.26777 0.162779
\(404\) −4.37118 25.6451i −0.217474 1.27589i
\(405\) −1.32962 + 1.42724i −0.0660692 + 0.0709203i
\(406\) 15.0678 + 13.8859i 0.747804 + 0.689143i
\(407\) 14.4214 14.4214i 0.714842 0.714842i
\(408\) 2.23412 15.9159i 0.110606 0.787953i
\(409\) 15.8641i 0.784431i 0.919873 + 0.392216i \(0.128291\pi\)
−0.919873 + 0.392216i \(0.871709\pi\)
\(410\) −21.7311 + 12.2272i −1.07322 + 0.603859i
\(411\) 25.6358 + 25.6358i 1.26452 + 1.26452i
\(412\) 4.29743 0.732492i 0.211719 0.0360873i
\(413\) 3.19005 + 1.48746i 0.156972 + 0.0731933i
\(414\) 0.0783025 + 0.151471i 0.00384836 + 0.00744441i
\(415\) −24.6981 23.0087i −1.21238 1.12945i
\(416\) 4.43026 0.130140i 0.217211 0.00638065i
\(417\) −36.5213 36.5213i −1.78845 1.78845i
\(418\) −31.6199 10.0690i −1.54658 0.492490i
\(419\) 25.8374 + 25.8374i 1.26224 + 1.26224i 0.950004 + 0.312238i \(0.101079\pi\)
0.312238 + 0.950004i \(0.398921\pi\)
\(420\) −27.9728 + 17.2779i −1.36493 + 0.843076i
\(421\) 19.3466 19.3466i 0.942895 0.942895i −0.0555608 0.998455i \(-0.517695\pi\)
0.998455 + 0.0555608i \(0.0176947\pi\)
\(422\) 12.6736 + 24.5163i 0.616941 + 1.19343i
\(423\) 32.2286 32.2286i 1.56701 1.56701i
\(424\) 12.9100 9.73175i 0.626964 0.472616i
\(425\) 7.72313 + 6.70031i 0.374627 + 0.325013i
\(426\) −20.8479 6.63876i −1.01008 0.321649i
\(427\) −22.1234 10.3158i −1.07063 0.499214i
\(428\) −0.153817 0.109017i −0.00743500 0.00526953i
\(429\) −10.1493 + 10.1493i −0.490013 + 0.490013i
\(430\) 10.0391 + 17.8423i 0.484130 + 0.860432i
\(431\) 37.6790 1.81493 0.907467 0.420123i \(-0.138013\pi\)
0.907467 + 0.420123i \(0.138013\pi\)
\(432\) −18.0534 + 6.33850i −0.868593 + 0.304961i
\(433\) 2.87849 + 2.87849i 0.138332 + 0.138332i 0.772882 0.634550i \(-0.218815\pi\)
−0.634550 + 0.772882i \(0.718815\pi\)
\(434\) 15.5924 0.636531i 0.748459 0.0305544i
\(435\) −34.0054 + 1.20422i −1.63044 + 0.0577378i
\(436\) −19.9505 + 3.40054i −0.955454 + 0.162856i
\(437\) 0.0908923i 0.00434797i
\(438\) 6.21651 + 12.0255i 0.297036 + 0.574598i
\(439\) 39.8563i 1.90224i 0.308824 + 0.951119i \(0.400065\pi\)
−0.308824 + 0.951119i \(0.599935\pi\)
\(440\) 32.3863 26.2612i 1.54396 1.25195i
\(441\) 25.3169 21.2452i 1.20557 1.01168i
\(442\) 1.04051 + 2.01280i 0.0494920 + 0.0957393i
\(443\) 8.55071i 0.406257i 0.979152 + 0.203128i \(0.0651109\pi\)
−0.979152 + 0.203128i \(0.934889\pi\)
\(444\) −9.94146 + 14.0268i −0.471801 + 0.665684i
\(445\) 10.5458 + 9.82442i 0.499918 + 0.465722i
\(446\) −2.93947 5.68622i −0.139188 0.269250i
\(447\) −2.55157 + 2.55157i −0.120685 + 0.120685i
\(448\) 21.1139 1.48394i 0.997539 0.0701098i
\(449\) 0.708673i 0.0334443i 0.999860 + 0.0167222i \(0.00532308\pi\)
−0.999860 + 0.0167222i \(0.994677\pi\)
\(450\) 7.85444 32.4485i 0.370262 1.52964i
\(451\) −36.7580 + 36.7580i −1.73087 + 1.73087i
\(452\) 22.0429 3.75718i 1.03681 0.176723i
\(453\) 49.6163 2.33118
\(454\) 3.55558 + 1.13223i 0.166872 + 0.0531383i
\(455\) 1.80896 4.26772i 0.0848054 0.200074i
\(456\) 27.7022 + 3.88858i 1.29728 + 0.182100i
\(457\) 15.9723 15.9723i 0.747154 0.747154i −0.226790 0.973944i \(-0.572823\pi\)
0.973944 + 0.226790i \(0.0728230\pi\)
\(458\) 12.7864 6.60987i 0.597469 0.308859i
\(459\) −6.91669 6.91669i −0.322844 0.322844i
\(460\) 0.0954545 + 0.0626991i 0.00445059 + 0.00292336i
\(461\) −4.27821 + 4.27821i −0.199256 + 0.199256i −0.799681 0.600425i \(-0.794998\pi\)
0.600425 + 0.799681i \(0.294998\pi\)
\(462\) −46.4511 + 50.4050i −2.16110 + 2.34505i
\(463\) −22.1706 + 22.1706i −1.03035 + 1.03035i −0.0308291 + 0.999525i \(0.509815\pi\)
−0.999525 + 0.0308291i \(0.990185\pi\)
\(464\) 19.7459 + 9.48349i 0.916679 + 0.440260i
\(465\) −17.6644 + 18.9614i −0.819167 + 0.879315i
\(466\) 1.78470 + 3.45240i 0.0826748 + 0.159929i
\(467\) −28.6116 −1.32399 −0.661993 0.749510i \(-0.730289\pi\)
−0.661993 + 0.749510i \(0.730289\pi\)
\(468\) 4.27814 6.03621i 0.197757 0.279024i
\(469\) −34.6417 + 12.6093i −1.59960 + 0.582245i
\(470\) 8.22743 29.3973i 0.379503 1.35600i
\(471\) 20.6989i 0.953755i
\(472\) 3.72629 + 0.523062i 0.171516 + 0.0240759i
\(473\) 30.1801 + 30.1801i 1.38768 + 1.38768i
\(474\) 5.54810 + 1.76673i 0.254833 + 0.0811486i
\(475\) −11.6622 + 13.4424i −0.535097 + 0.616781i
\(476\) 5.35694 + 9.40155i 0.245535 + 0.430919i
\(477\) 26.9874i 1.23567i
\(478\) 5.87308 18.4434i 0.268629 0.843580i
\(479\) −2.72906 −0.124694 −0.0623470 0.998055i \(-0.519859\pi\)
−0.0623470 + 0.998055i \(0.519859\pi\)
\(480\) −23.1932 + 26.4103i −1.05862 + 1.20546i
\(481\) 2.42384i 0.110517i
\(482\) −9.54679 + 29.9800i −0.434844 + 1.36555i
\(483\) −0.170156 0.0793408i −0.00774237 0.00361013i
\(484\) 37.5431 52.9711i 1.70650 2.40778i
\(485\) −0.180330 5.09228i −0.00818838 0.231229i
\(486\) 7.19802 22.6041i 0.326509 1.02534i
\(487\) −8.39679 + 8.39679i −0.380495 + 0.380495i −0.871280 0.490785i \(-0.836710\pi\)
0.490785 + 0.871280i \(0.336710\pi\)
\(488\) −25.8423 3.62750i −1.16982 0.164209i
\(489\) 57.1935i 2.58638i
\(490\) 7.80028 20.7161i 0.352381 0.935857i
\(491\) 20.8530 20.8530i 0.941081 0.941081i −0.0572772 0.998358i \(-0.518242\pi\)
0.998358 + 0.0572772i \(0.0182419\pi\)
\(492\) 25.3393 35.7523i 1.14239 1.61184i
\(493\) 11.1985i 0.504355i
\(494\) −3.50337 + 1.81105i −0.157624 + 0.0814830i
\(495\) −2.46323 69.5581i −0.110714 3.12640i
\(496\) 15.7409 5.52659i 0.706786 0.248151i
\(497\) 13.8421 5.03844i 0.620904 0.226005i
\(498\) 56.5254 + 17.9999i 2.53296 + 0.806593i
\(499\) −7.32472 + 7.32472i −0.327899 + 0.327899i −0.851787 0.523888i \(-0.824481\pi\)
0.523888 + 0.851787i \(0.324481\pi\)
\(500\) −6.07239 21.5204i −0.271566 0.962420i
\(501\) −7.32522 + 7.32522i −0.327267 + 0.327267i
\(502\) −1.90985 3.69449i −0.0852409 0.164893i
\(503\) −6.68944 + 6.68944i −0.298267 + 0.298267i −0.840335 0.542068i \(-0.817642\pi\)
0.542068 + 0.840335i \(0.317642\pi\)
\(504\) 19.2376 29.6355i 0.856912 1.32007i
\(505\) −29.0674 + 1.02935i −1.29348 + 0.0458054i
\(506\) 0.226867 + 0.0722433i 0.0100855 + 0.00321160i
\(507\) 34.4179i 1.52855i
\(508\) 4.38521 + 25.7275i 0.194562 + 1.14147i
\(509\) 6.22166 + 6.22166i 0.275770 + 0.275770i 0.831418 0.555648i \(-0.187530\pi\)
−0.555648 + 0.831418i \(0.687530\pi\)
\(510\) −17.3040 4.84288i −0.766235 0.214446i
\(511\) −8.26028 3.85162i −0.365413 0.170386i
\(512\) 21.1205 8.11951i 0.933401 0.358835i
\(513\) 12.0388 12.0388i 0.531526 0.531526i
\(514\) −13.6203 + 7.04097i −0.600766 + 0.310564i
\(515\) −0.172491 4.87092i −0.00760088 0.214638i
\(516\) −29.3544 20.8048i −1.29226 0.915881i
\(517\) 63.6419i 2.79897i
\(518\) −0.472140 11.5655i −0.0207446 0.508159i
\(519\) −54.2536 −2.38147
\(520\) 0.514729 4.92851i 0.0225724 0.216129i
\(521\) 10.5965 0.464241 0.232121 0.972687i \(-0.425434\pi\)
0.232121 + 0.972687i \(0.425434\pi\)
\(522\) 32.4823 16.7916i 1.42171 0.734949i
\(523\) 16.7758 0.733553 0.366777 0.930309i \(-0.380461\pi\)
0.366777 + 0.930309i \(0.380461\pi\)
\(524\) −12.6217 + 2.15135i −0.551381 + 0.0939822i
\(525\) 14.9851 + 33.5663i 0.654001 + 1.46496i
\(526\) 4.50967 + 8.72369i 0.196631 + 0.380371i
\(527\) 6.03072 + 6.03072i 0.262702 + 0.262702i
\(528\) −31.7243 + 66.0541i −1.38062 + 2.87463i
\(529\) 22.9993i 0.999972i
\(530\) −8.86354 15.7530i −0.385008 0.684265i
\(531\) 4.44148 4.44148i 0.192744 0.192744i
\(532\) −16.3638 + 9.32398i −0.709460 + 0.404246i
\(533\) 6.17800i 0.267599i
\(534\) −24.1356 7.68571i −1.04445 0.332593i
\(535\) −0.143679 + 0.154229i −0.00621179 + 0.00666790i
\(536\) −31.4707 + 23.7231i −1.35933 + 1.02468i
\(537\) 3.12311 + 3.12311i 0.134772 + 0.134772i
\(538\) 3.34913 + 6.47868i 0.144391 + 0.279316i
\(539\) 4.02023 45.9732i 0.173164 1.98020i
\(540\) 4.33850 + 20.9476i 0.186699 + 0.901443i
\(541\) 8.59244 + 8.59244i 0.369418 + 0.369418i 0.867265 0.497847i \(-0.165876\pi\)
−0.497847 + 0.867265i \(0.665876\pi\)
\(542\) −10.4290 + 32.7506i −0.447966 + 1.40676i
\(543\) 31.6068 31.6068i 1.35638 1.35638i
\(544\) 8.41627 + 7.93592i 0.360845 + 0.340250i
\(545\) 0.800777 + 22.6128i 0.0343015 + 0.968627i
\(546\) 0.332276 + 8.13941i 0.0142201 + 0.348334i
\(547\) 36.4365i 1.55791i 0.627078 + 0.778956i \(0.284251\pi\)
−0.627078 + 0.778956i \(0.715749\pi\)
\(548\) −25.7231 + 4.38448i −1.09884 + 0.187296i
\(549\) −30.8022 + 30.8022i −1.31461 + 1.31461i
\(550\) −24.2830 39.7931i −1.03543 1.69679i
\(551\) −19.4914 −0.830364
\(552\) −0.198759 0.0278999i −0.00845974 0.00118750i
\(553\) −3.68371 + 1.34085i −0.156647 + 0.0570186i
\(554\) −29.9571 9.53950i −1.27276 0.405294i
\(555\) 14.0644 + 13.1024i 0.597002 + 0.556165i
\(556\) 36.6457 6.24622i 1.55412 0.264899i
\(557\) 28.9409i 1.22627i −0.789979 0.613133i \(-0.789909\pi\)
0.789979 0.613133i \(-0.210091\pi\)
\(558\) 8.44991 26.5355i 0.357713 1.12334i
\(559\) 5.07244 0.214541
\(560\) 1.49604 23.6170i 0.0632192 0.998000i
\(561\) −37.4613 −1.58162
\(562\) −1.96495 + 6.17059i −0.0828866 + 0.260291i
\(563\) 39.1244i 1.64890i −0.565937 0.824448i \(-0.691485\pi\)
0.565937 0.824448i \(-0.308515\pi\)
\(564\) 9.01441 + 52.8863i 0.379575 + 2.22691i
\(565\) −0.884762 24.9845i −0.0372222 1.05110i
\(566\) −21.6939 6.90819i −0.911864 0.290373i
\(567\) 0.789427 + 2.16879i 0.0331528 + 0.0910808i
\(568\) 12.5751 9.47927i 0.527637 0.397741i
\(569\) 12.0263 0.504167 0.252084 0.967705i \(-0.418884\pi\)
0.252084 + 0.967705i \(0.418884\pi\)
\(570\) 8.42923 30.1184i 0.353062 1.26152i
\(571\) 6.36452 6.36452i 0.266347 0.266347i −0.561279 0.827626i \(-0.689691\pi\)
0.827626 + 0.561279i \(0.189691\pi\)
\(572\) −1.73583 10.1839i −0.0725787 0.425809i
\(573\) 29.7630i 1.24337i
\(574\) 1.20341 + 29.4788i 0.0502296 + 1.23042i
\(575\) 0.0836741 0.0964472i 0.00348945 0.00402213i
\(576\) 10.3991 36.3118i 0.433297 1.51299i
\(577\) −4.25134 + 4.25134i −0.176986 + 0.176986i −0.790040 0.613055i \(-0.789940\pi\)
0.613055 + 0.790040i \(0.289940\pi\)
\(578\) 5.50047 17.2733i 0.228789 0.718473i
\(579\) 30.8341 + 30.8341i 1.28142 + 1.28142i
\(580\) 13.4455 20.4698i 0.558296 0.849962i
\(581\) −37.5305 + 13.6608i −1.55703 + 0.566747i
\(582\) 4.11226 + 7.95491i 0.170459 + 0.329742i
\(583\) −26.6460 26.6460i −1.10357 1.10357i
\(584\) −9.64881 1.35441i −0.399270 0.0560459i
\(585\) −6.05239 5.63839i −0.250235 0.233119i
\(586\) −14.7903 4.70980i −0.610982 0.194560i
\(587\) 9.58043i 0.395427i −0.980260 0.197713i \(-0.936648\pi\)
0.980260 0.197713i \(-0.0633515\pi\)
\(588\) 3.17096 + 38.7730i 0.130768 + 1.59897i
\(589\) −10.4967 + 10.4967i −0.432509 + 0.432509i
\(590\) 1.13383 4.05129i 0.0466792 0.166789i
\(591\) 31.4293i 1.29283i
\(592\) −4.09929 11.6756i −0.168480 0.479865i
\(593\) −5.54327 5.54327i −0.227635 0.227635i 0.584069 0.811704i \(-0.301460\pi\)
−0.811704 + 0.584069i \(0.801460\pi\)
\(594\) 20.4801 + 39.6175i 0.840310 + 1.62553i
\(595\) 11.2146 4.53766i 0.459753 0.186026i
\(596\) −0.436394 2.56027i −0.0178754 0.104873i
\(597\) −52.1910 −2.13604
\(598\) 0.0251361 0.0129940i 0.00102789 0.000531364i
\(599\) 17.6136 0.719670 0.359835 0.933016i \(-0.382833\pi\)
0.359835 + 0.933016i \(0.382833\pi\)
\(600\) 25.8155 + 29.6285i 1.05391 + 1.20958i
\(601\) 4.82475 0.196806 0.0984029 0.995147i \(-0.468627\pi\)
0.0984029 + 0.995147i \(0.468627\pi\)
\(602\) 24.2035 0.988062i 0.986460 0.0402704i
\(603\) 65.7872i 2.67906i
\(604\) −20.6497 + 29.1356i −0.840225 + 1.18551i
\(605\) −53.1131 49.4800i −2.15936 2.01165i
\(606\) 45.4076 23.4733i 1.84456 0.953537i
\(607\) −11.2432 + 11.2432i −0.456346 + 0.456346i −0.897454 0.441108i \(-0.854586\pi\)
0.441108 + 0.897454i \(0.354586\pi\)
\(608\) −13.8128 + 14.6489i −0.560183 + 0.594090i
\(609\) −17.0143 + 36.4892i −0.689454 + 1.47862i
\(610\) −7.86328 + 28.0962i −0.318375 + 1.13758i
\(611\) −5.34822 5.34822i −0.216366 0.216366i
\(612\) 19.0353 3.24454i 0.769455 0.131153i
\(613\) 32.7565i 1.32302i −0.749935 0.661512i \(-0.769915\pi\)
0.749935 0.661512i \(-0.230085\pi\)
\(614\) 34.6012 + 11.0184i 1.39639 + 0.444665i
\(615\) −35.8482 33.3961i −1.44554 1.34666i
\(616\) −10.2663 48.2549i −0.413643 1.94425i
\(617\) −7.76697 + 7.76697i −0.312687 + 0.312687i −0.845950 0.533263i \(-0.820966\pi\)
0.533263 + 0.845950i \(0.320966\pi\)
\(618\) 3.93350 + 7.60911i 0.158228 + 0.306083i
\(619\) 15.4096 15.4096i 0.619366 0.619366i −0.326003 0.945369i \(-0.605702\pi\)
0.945369 + 0.326003i \(0.105702\pi\)
\(620\) −3.78277 18.2644i −0.151920 0.733516i
\(621\) −0.0863763 + 0.0863763i −0.00346616 + 0.00346616i
\(622\) 8.04225 + 2.56096i 0.322465 + 0.102685i
\(623\) 16.0250 5.83301i 0.642030 0.233695i
\(624\) 2.88494 + 8.21690i 0.115490 + 0.328939i
\(625\) −24.7498 + 3.52796i −0.989993 + 0.141118i
\(626\) 8.55042 4.42010i 0.341743 0.176663i
\(627\) 65.2030i 2.60396i
\(628\) −12.1548 8.61465i −0.485028 0.343762i
\(629\) 4.47322 4.47322i 0.178359 0.178359i
\(630\) −29.9777 25.7250i −1.19434 1.02491i
\(631\) 24.4893i 0.974902i 0.873150 + 0.487451i \(0.162073\pi\)
−0.873150 + 0.487451i \(0.837927\pi\)
\(632\) −3.34651 + 2.52265i −0.133117 + 0.100346i
\(633\) −38.3444 + 38.3444i −1.52405 + 1.52405i
\(634\) −8.13949 + 25.5606i −0.323260 + 1.01514i
\(635\) 29.1607 1.03265i 1.15721 0.0409796i
\(636\) 25.9170 + 18.3686i 1.02768 + 0.728361i
\(637\) −3.52556 4.20125i −0.139688 0.166459i
\(638\) 15.4922 48.6507i 0.613344 1.92610i
\(639\) 26.2872i 1.03991i
\(640\) −5.85584 24.6112i −0.231472 0.972841i
\(641\) 7.48701 0.295719 0.147859 0.989008i \(-0.452762\pi\)
0.147859 + 0.989008i \(0.452762\pi\)
\(642\) 0.112401 0.352976i 0.00443612 0.0139309i
\(643\) 23.7187i 0.935373i −0.883894 0.467687i \(-0.845088\pi\)
0.883894 0.467687i \(-0.154912\pi\)
\(644\) 0.117407 0.0668980i 0.00462650 0.00263615i
\(645\) −27.4198 + 29.4331i −1.07965 + 1.15893i
\(646\) −9.80783 3.12319i −0.385884 0.122880i
\(647\) 29.1694 + 29.1694i 1.14677 + 1.14677i 0.987184 + 0.159584i \(0.0510154\pi\)
0.159584 + 0.987184i \(0.448985\pi\)
\(648\) 1.48522 + 1.97027i 0.0583450 + 0.0773995i
\(649\) 8.77059i 0.344276i
\(650\) −5.38470 1.30341i −0.211205 0.0511241i
\(651\) 10.4878 + 28.8132i 0.411050 + 1.12928i
\(652\) 33.5851 + 23.8033i 1.31529 + 0.932209i
\(653\) −24.8919 −0.974097 −0.487048 0.873375i \(-0.661926\pi\)
−0.487048 + 0.873375i \(0.661926\pi\)
\(654\) −18.2609 35.3246i −0.714059 1.38130i
\(655\) 0.506612 + 14.3060i 0.0197950 + 0.558983i
\(656\) 10.4485 + 29.7594i 0.407945 + 1.16191i
\(657\) −11.5007 + 11.5007i −0.448686 + 0.448686i
\(658\) −26.5612 24.4776i −1.03546 0.954237i
\(659\) 15.9582 15.9582i 0.621643 0.621643i −0.324308 0.945951i \(-0.605132\pi\)
0.945951 + 0.324308i \(0.105132\pi\)
\(660\) 68.4757 + 44.9781i 2.66541 + 1.75077i
\(661\) 3.52942 + 3.52942i 0.137278 + 0.137278i 0.772407 0.635128i \(-0.219053\pi\)
−0.635128 + 0.772407i \(0.719053\pi\)
\(662\) 14.8752 7.68966i 0.578140 0.298867i
\(663\) −3.14810 + 3.14810i −0.122262 + 0.122262i
\(664\) −34.0951 + 25.7014i −1.32314 + 0.997407i
\(665\) 7.89799 + 19.5195i 0.306271 + 0.756932i
\(666\) −19.6824 6.26763i −0.762677 0.242866i
\(667\) 0.139848 0.00541493
\(668\) −1.25283 7.35018i −0.0484734 0.284387i
\(669\) 8.89346 8.89346i 0.343841 0.343841i
\(670\) 21.6067 + 38.4010i 0.834739 + 1.48356i
\(671\) 60.8252i 2.34813i
\(672\) 15.3663 + 38.6456i 0.592766 + 1.49079i
\(673\) 7.28950 7.28950i 0.280990 0.280990i −0.552514 0.833504i \(-0.686331\pi\)
0.833504 + 0.552514i \(0.186331\pi\)
\(674\) 4.41474 + 8.54004i 0.170049 + 0.328950i
\(675\) 23.8573 1.69181i 0.918267 0.0651179i
\(676\) 20.2108 + 14.3243i 0.777339 + 0.550936i
\(677\) 29.8134i 1.14582i 0.819618 + 0.572911i \(0.194186\pi\)
−0.819618 + 0.572911i \(0.805814\pi\)
\(678\) 20.1761 + 39.0295i 0.774860 + 1.49892i
\(679\) −5.46422 2.54787i −0.209698 0.0977784i
\(680\) 10.0456 8.14569i 0.385230 0.312373i
\(681\) 7.33192i 0.280960i
\(682\) −17.8568 34.5428i −0.683771 1.32271i
\(683\) 11.9084i 0.455661i 0.973701 + 0.227831i \(0.0731632\pi\)
−0.973701 + 0.227831i \(0.926837\pi\)
\(684\) 5.64725 + 33.1316i 0.215928 + 1.26682i
\(685\) 1.03248 + 29.1558i 0.0394491 + 1.11399i
\(686\) −17.6408 19.3598i −0.673529 0.739161i
\(687\) 19.9984 + 19.9984i 0.762986 + 0.762986i
\(688\) 24.4339 8.57871i 0.931535 0.327060i
\(689\) −4.47845 −0.170615
\(690\) −0.0604783 + 0.216094i −0.00230237 + 0.00822656i
\(691\) 27.4899 27.4899i 1.04577 1.04577i 0.0468649 0.998901i \(-0.485077\pi\)
0.998901 0.0468649i \(-0.0149230\pi\)
\(692\) 22.5797 31.8587i 0.858353 1.21109i
\(693\) −74.6386 34.8027i −2.83529 1.32205i
\(694\) −4.43119 1.41106i −0.168206 0.0535632i
\(695\) −1.47089 41.5360i −0.0557942 1.57555i
\(696\) −5.98301 + 42.6229i −0.226786 + 1.61562i
\(697\) −11.4016 + 11.4016i −0.431866 + 0.431866i
\(698\) −0.841023 1.62691i −0.0318332 0.0615794i
\(699\) −5.39968 + 5.39968i −0.204235 + 0.204235i
\(700\) −25.9474 5.17044i −0.980719 0.195424i
\(701\) 6.87992 + 6.87992i 0.259851 + 0.259851i 0.824993 0.565142i \(-0.191179\pi\)
−0.565142 + 0.824993i \(0.691179\pi\)
\(702\) 5.05037 + 1.60823i 0.190614 + 0.0606988i
\(703\) 7.78582 + 7.78582i 0.293648 + 0.293648i
\(704\) −25.5849 46.1200i −0.964266 1.73821i
\(705\) 59.9439 2.12276i 2.25762 0.0799479i
\(706\) −1.49238 2.88692i −0.0561665 0.108651i
\(707\) −14.5436 + 31.1905i −0.546968 + 1.17304i
\(708\) 1.24229 + 7.28834i 0.0466881 + 0.273913i
\(709\) 28.2024 + 28.2024i 1.05916 + 1.05916i 0.998136 + 0.0610286i \(0.0194381\pi\)
0.0610286 + 0.998136i \(0.480562\pi\)
\(710\) −8.63359 15.3443i −0.324013 0.575860i
\(711\) 6.99565i 0.262357i
\(712\) 14.5582 10.9742i 0.545590 0.411274i
\(713\) 0.0753121 0.0753121i 0.00282046 0.00282046i
\(714\) −14.4082 + 15.6346i −0.539212 + 0.585110i
\(715\) −11.5429 + 0.408763i −0.431680 + 0.0152869i
\(716\) −3.13375 + 0.534144i −0.117114 + 0.0199619i
\(717\) 38.0319 1.42033
\(718\) −20.7005 6.59182i −0.772534 0.246005i
\(719\) −40.6755 −1.51694 −0.758470 0.651708i \(-0.774053\pi\)
−0.758470 + 0.651708i \(0.774053\pi\)
\(720\) −38.6902 16.9241i −1.44190 0.630723i
\(721\) −5.22669 2.43712i −0.194652 0.0907629i
\(722\) −2.71703 + 8.53234i −0.101117 + 0.317541i
\(723\) −61.8214 −2.29916
\(724\) 5.40569 + 31.7145i 0.200901 + 1.17866i
\(725\) −20.6827 17.9435i −0.768135 0.666406i
\(726\) 121.557 + 38.7086i 4.51142 + 1.43661i
\(727\) 12.7287 + 12.7287i 0.472082 + 0.472082i 0.902588 0.430506i \(-0.141665\pi\)
−0.430506 + 0.902588i \(0.641665\pi\)
\(728\) −4.91790 3.19241i −0.182269 0.118319i
\(729\) 43.9946 1.62943
\(730\) −2.93594 + 10.4904i −0.108664 + 0.388266i
\(731\) 9.36125 + 9.36125i 0.346238 + 0.346238i
\(732\) −8.61543 50.5456i −0.318436 1.86822i
\(733\) 0.240800i 0.00889414i −0.999990 0.00444707i \(-0.998584\pi\)
0.999990 0.00444707i \(-0.00141555\pi\)
\(734\) 24.9673 12.9068i 0.921561 0.476397i
\(735\) 43.4359 + 2.25320i 1.60216 + 0.0831106i
\(736\) 0.0991045 0.105103i 0.00365304 0.00387415i
\(737\) 64.9550 + 64.9550i 2.39265 + 2.39265i
\(738\) 50.1675 + 15.9753i 1.84669 + 0.588058i
\(739\) −17.5908 + 17.5908i −0.647089 + 0.647089i −0.952288 0.305200i \(-0.901277\pi\)
0.305200 + 0.952288i \(0.401277\pi\)
\(740\) −13.5474 + 2.80583i −0.498013 + 0.103144i
\(741\) −5.47940 5.47940i −0.201291 0.201291i
\(742\) −21.3693 + 0.872359i −0.784490 + 0.0320253i
\(743\) 28.2699 + 28.2699i 1.03712 + 1.03712i 0.999284 + 0.0378385i \(0.0120472\pi\)
0.0378385 + 0.999284i \(0.487953\pi\)
\(744\) 19.7317 + 26.1757i 0.723398 + 0.959649i
\(745\) −2.90193 + 0.102765i −0.106318 + 0.00376500i
\(746\) −11.7607 + 36.9323i −0.430589 + 1.35219i
\(747\) 71.2733i 2.60775i
\(748\) 15.5910 21.9980i 0.570062 0.804325i
\(749\) 0.0853060 + 0.234361i 0.00311701 + 0.00856338i
\(750\) 36.6709 24.1992i 1.33903 0.883631i
\(751\) 7.00331 0.255555 0.127777 0.991803i \(-0.459216\pi\)
0.127777 + 0.991803i \(0.459216\pi\)
\(752\) −34.8075 16.7172i −1.26930 0.609615i
\(753\) 5.77833 5.77833i 0.210574 0.210574i
\(754\) −2.78650 5.39032i −0.101478 0.196304i
\(755\) 29.2137 + 27.2154i 1.06319 + 0.990469i
\(756\) 24.4115 + 6.69003i 0.887836 + 0.243314i
\(757\) 11.7588 0.427381 0.213690 0.976901i \(-0.431452\pi\)
0.213690 + 0.976901i \(0.431452\pi\)
\(758\) 8.79027 + 17.0042i 0.319277 + 0.617621i
\(759\) 0.467820i 0.0169808i
\(760\) 14.1779 + 17.4847i 0.514287 + 0.634238i
\(761\) 24.5182 0.888782 0.444391 0.895833i \(-0.353420\pi\)
0.444391 + 0.895833i \(0.353420\pi\)
\(762\) −45.5535 + 23.5487i −1.65023 + 0.853079i
\(763\) 24.2645 + 11.3141i 0.878433 + 0.409598i
\(764\) 17.4773 + 12.3870i 0.632308 + 0.448146i
\(765\) −0.764042 21.5755i −0.0276240 0.780063i
\(766\) −10.5480 20.4044i −0.381114 0.737242i
\(767\) −0.737046 0.737046i −0.0266132 0.0266132i
\(768\) 27.7935 + 34.7017i 1.00291 + 1.25219i
\(769\) −44.3175 −1.59813 −0.799066 0.601244i \(-0.794672\pi\)
−0.799066 + 0.601244i \(0.794672\pi\)
\(770\) −54.9981 + 4.19888i −1.98199 + 0.151317i
\(771\) −21.3027 21.3027i −0.767198 0.767198i
\(772\) −30.9391 + 5.27353i −1.11352 + 0.189799i
\(773\) −43.9140 −1.57948 −0.789739 0.613443i \(-0.789784\pi\)
−0.789739 + 0.613443i \(0.789784\pi\)
\(774\) 13.1165 41.1900i 0.471462 1.48054i
\(775\) −20.8013 + 1.47510i −0.747206 + 0.0529873i
\(776\) −6.38274 0.895950i −0.229127 0.0321627i
\(777\) 21.3719 7.77922i 0.766712 0.279078i
\(778\) −8.67117 16.7738i −0.310877 0.601372i
\(779\) −19.8449 19.8449i −0.711018 0.711018i
\(780\) 9.53421 1.97465i 0.341380 0.0707036i
\(781\) −25.9547 25.9547i −0.928733 0.928733i
\(782\) 0.0703695 + 0.0224084i 0.00251641 + 0.000801321i
\(783\) 18.5230 + 18.5230i 0.661959 + 0.661959i
\(784\) −24.0879 14.2748i −0.860283 0.509816i
\(785\) −11.3537 + 12.1874i −0.405231 + 0.434985i
\(786\) −11.5528 22.3482i −0.412074 0.797133i
\(787\) 45.6907 1.62870 0.814349 0.580375i \(-0.197094\pi\)
0.814349 + 0.580375i \(0.197094\pi\)
\(788\) −18.4559 13.0805i −0.657463 0.465975i
\(789\) −13.6442 + 13.6442i −0.485746 + 0.485746i
\(790\) 2.29760 + 4.08347i 0.0817449 + 0.145283i
\(791\) −26.8093 12.5007i −0.953230 0.444475i
\(792\) −87.1852 12.2382i −3.09799 0.434867i
\(793\) 5.11151 + 5.11151i 0.181515 + 0.181515i
\(794\) −0.655095 0.208607i −0.0232485 0.00740320i
\(795\) 24.2089 25.9865i 0.858602 0.921645i
\(796\) 21.7213 30.6475i 0.769891 1.08627i
\(797\) −38.4266 −1.36114 −0.680569 0.732684i \(-0.738267\pi\)
−0.680569 + 0.732684i \(0.738267\pi\)
\(798\) −27.2127 25.0780i −0.963318 0.887752i
\(799\) 19.7404i 0.698365i
\(800\) −28.1425 + 2.82828i −0.994988 + 0.0999949i
\(801\) 30.4328i 1.07529i
\(802\) −7.11055 2.26427i −0.251082 0.0799542i
\(803\) 22.7105i 0.801435i
\(804\) −63.1779 44.7771i −2.22811 1.57917i
\(805\) −0.0566667 0.140049i −0.00199724 0.00493607i
\(806\) −4.40346 1.40223i −0.155105 0.0493914i
\(807\) −10.1329 + 10.1329i −0.356695 + 0.356695i
\(808\) −5.11420 + 36.4335i −0.179917 + 1.28173i
\(809\) 32.3853 1.13861 0.569304 0.822127i \(-0.307213\pi\)
0.569304 + 0.822127i \(0.307213\pi\)
\(810\) 2.40415 1.35272i 0.0844734 0.0475297i
\(811\) −11.7394 11.7394i −0.412226 0.412226i 0.470288 0.882513i \(-0.344150\pi\)
−0.882513 + 0.470288i \(0.844150\pi\)
\(812\) −14.3460 25.1775i −0.503445 0.883557i
\(813\) −67.5346 −2.36854
\(814\) −25.6218 + 13.2451i −0.898043 + 0.464240i
\(815\) 31.3717 33.6751i 1.09890 1.17959i
\(816\) −9.84021 + 20.4886i −0.344476 + 0.717244i
\(817\) −16.2936 + 16.2936i −0.570042 + 0.570042i
\(818\) 6.80744 21.3776i 0.238017 0.747449i
\(819\) −9.19702 + 3.34765i −0.321370 + 0.116977i
\(820\) 34.5304 7.15164i 1.20585 0.249746i
\(821\) −8.71813 + 8.71813i −0.304265 + 0.304265i −0.842680 0.538415i \(-0.819023\pi\)
0.538415 + 0.842680i \(0.319023\pi\)
\(822\) −23.5447 45.5458i −0.821216 1.58859i
\(823\) 13.0386 + 13.0386i 0.454498 + 0.454498i 0.896844 0.442346i \(-0.145854\pi\)
−0.442346 + 0.896844i \(0.645854\pi\)
\(824\) −6.10528 0.857003i −0.212688 0.0298551i
\(825\) 60.0249 69.1879i 2.08980 2.40881i
\(826\) −3.66043 3.37330i −0.127363 0.117372i
\(827\) −39.6826 −1.37990 −0.689950 0.723857i \(-0.742368\pi\)
−0.689950 + 0.723857i \(0.742368\pi\)
\(828\) −0.0405181 0.237714i −0.00140810 0.00826113i
\(829\) 9.48891 + 9.48891i 0.329563 + 0.329563i 0.852420 0.522857i \(-0.175134\pi\)
−0.522857 + 0.852420i \(0.675134\pi\)
\(830\) 23.4085 + 41.6033i 0.812520 + 1.44407i
\(831\) 61.7742i 2.14292i
\(832\) −6.02579 1.72569i −0.208907 0.0598276i
\(833\) 1.24699 14.2599i 0.0432057 0.494077i
\(834\) 33.5423 + 64.8855i 1.16147 + 2.24680i
\(835\) −8.33104 + 0.295023i −0.288308 + 0.0102097i
\(836\) 38.2884 + 27.1367i 1.32423 + 0.938544i
\(837\) 19.9504 0.689586
\(838\) −23.7299 45.9041i −0.819737 1.58573i
\(839\) 31.0888i 1.07331i −0.843803 0.536653i \(-0.819688\pi\)
0.843803 0.536653i \(-0.180312\pi\)
\(840\) 45.1085 11.2793i 1.55639 0.389174i
\(841\) 0.989751i 0.0341293i
\(842\) −34.3721 + 17.7685i −1.18454 + 0.612343i
\(843\) −12.7243 −0.438248
\(844\) −6.55802 38.4750i −0.225737 1.32437i
\(845\) 18.8788 20.2650i 0.649451 0.697137i
\(846\) −57.2590 + 29.5998i −1.96861 + 1.01766i
\(847\) −80.7090 + 29.3776i −2.77320 + 1.00942i
\(848\) −21.5727 + 7.57414i −0.740810 + 0.260097i
\(849\) 44.7348i 1.53529i
\(850\) −7.53207 12.3430i −0.258348 0.423362i
\(851\) −0.0558620 0.0558620i −0.00191492 0.00191492i
\(852\) 25.2446 + 17.8920i 0.864866 + 0.612970i
\(853\) −1.65153 −0.0565471 −0.0282736 0.999600i \(-0.509001\pi\)
−0.0282736 + 0.999600i \(0.509001\pi\)
\(854\) 25.3856 + 23.3942i 0.868677 + 0.800534i
\(855\) 37.5530 1.32985i 1.28429 0.0454798i
\(856\) 0.160494 + 0.212909i 0.00548557 + 0.00727707i
\(857\) −19.4507 19.4507i −0.664422 0.664422i 0.291997 0.956419i \(-0.405680\pi\)
−0.956419 + 0.291997i \(0.905680\pi\)
\(858\) 18.0317 9.32143i 0.615593 0.318228i
\(859\) −13.4018 + 13.4018i −0.457263 + 0.457263i −0.897756 0.440493i \(-0.854804\pi\)
0.440493 + 0.897756i \(0.354804\pi\)
\(860\) −5.87184 28.3511i −0.200228 0.966765i
\(861\) −54.4738 + 19.8281i −1.85646 + 0.675740i
\(862\) −50.7740 16.1684i −1.72937 0.550698i
\(863\) 0.399827 0.399827i 0.0136103 0.0136103i −0.700269 0.713879i \(-0.746937\pi\)
0.713879 + 0.700269i \(0.246937\pi\)
\(864\) 27.0476 0.794530i 0.920176 0.0270305i
\(865\) −31.9441 29.7591i −1.08613 1.01184i
\(866\) −2.64370 5.11407i −0.0898366 0.173783i
\(867\) 35.6190 1.20968
\(868\) −21.2845 5.83309i −0.722444 0.197988i
\(869\) 6.90715 + 6.90715i 0.234309 + 0.234309i
\(870\) 46.3404 + 12.9693i 1.57109 + 0.439701i
\(871\) 10.9171 0.369913
\(872\) 28.3433 + 3.97857i 0.959824 + 0.134731i
\(873\) −7.60779 + 7.60779i −0.257485 + 0.257485i
\(874\) −0.0390027 + 0.122481i −0.00131929 + 0.00414298i
\(875\) −9.58864 + 27.9832i −0.324155 + 0.946004i
\(876\) −3.21677 18.8723i −0.108685 0.637637i
\(877\) 45.1892i 1.52593i 0.646440 + 0.762965i \(0.276257\pi\)
−0.646440 + 0.762965i \(0.723743\pi\)
\(878\) 17.1027 53.7080i 0.577188 1.81256i
\(879\) 30.4989i 1.02870i
\(880\) −54.9108 + 21.4908i −1.85104 + 0.724455i
\(881\) 7.65639i 0.257950i 0.991648 + 0.128975i \(0.0411687\pi\)
−0.991648 + 0.128975i \(0.958831\pi\)
\(882\) −43.2321 + 17.7651i −1.45570 + 0.598180i
\(883\) 16.4633 0.554035 0.277017 0.960865i \(-0.410654\pi\)
0.277017 + 0.960865i \(0.410654\pi\)
\(884\) −0.538418 3.15883i −0.0181090 0.106243i
\(885\) 8.26096 0.292541i 0.277689 0.00983366i
\(886\) 3.66919 11.5224i 0.123269 0.387104i
\(887\) −19.9656 19.9656i −0.670378 0.670378i 0.287425 0.957803i \(-0.407201\pi\)
−0.957803 + 0.287425i \(0.907201\pi\)
\(888\) 19.4156 14.6358i 0.651544 0.491144i
\(889\) 14.5903 31.2906i 0.489342 1.04945i
\(890\) −9.99512 17.7641i −0.335037 0.595454i
\(891\) 4.06661 4.06661i 0.136237 0.136237i
\(892\) 1.52105 + 8.92376i 0.0509284 + 0.298790i
\(893\) 34.3590 1.14978
\(894\) 4.53325 2.34344i 0.151615 0.0783765i
\(895\) 0.125783 + 3.55194i 0.00420447 + 0.118728i
\(896\) −29.0886 7.06050i −0.971783 0.235875i
\(897\) 0.0393138 + 0.0393138i 0.00131265 + 0.00131265i
\(898\) 0.304098 0.954965i 0.0101479 0.0318676i
\(899\) −16.1504 16.1504i −0.538644 0.538644i
\(900\) −24.5081 + 40.3553i −0.816937 + 1.34518i
\(901\) −8.26504 8.26504i −0.275349 0.275349i
\(902\) 65.3061 33.7597i 2.17446 1.12408i
\(903\) 16.2798 + 44.7256i 0.541759 + 1.48837i
\(904\) −31.3159 4.39584i −1.04155 0.146203i
\(905\) 35.9467 1.27296i 1.19491 0.0423147i
\(906\) −66.8599 21.2908i −2.22127 0.707339i
\(907\) 10.4238 0.346117 0.173059 0.984912i \(-0.444635\pi\)
0.173059 + 0.984912i \(0.444635\pi\)
\(908\) −4.30544 3.05146i −0.142881 0.101266i
\(909\) 43.4263 + 43.4263i 1.44036 + 1.44036i
\(910\) −4.26896 + 4.97468i −0.141515 + 0.164909i
\(911\) 26.0811 0.864105 0.432053 0.901848i \(-0.357789\pi\)
0.432053 + 0.901848i \(0.357789\pi\)
\(912\) −35.6613 17.1273i −1.18086 0.567141i
\(913\) 70.3717 + 70.3717i 2.32896 + 2.32896i
\(914\) −28.3772 + 14.6695i −0.938635 + 0.485224i
\(915\) −57.2908 + 2.02881i −1.89397 + 0.0670704i
\(916\) −20.0665 + 3.42032i −0.663017 + 0.113010i
\(917\) 15.3509 + 7.15788i 0.506933 + 0.236374i
\(918\) 6.35251 + 12.2885i 0.209664 + 0.405582i
\(919\) 50.6701 1.67145 0.835726 0.549146i \(-0.185047\pi\)
0.835726 + 0.549146i \(0.185047\pi\)
\(920\) −0.101724 0.125450i −0.00335374 0.00413596i
\(921\) 71.3508i 2.35109i
\(922\) 7.60088 3.92924i 0.250322 0.129403i
\(923\) −4.36226 −0.143586
\(924\) 84.2240 47.9903i 2.77076 1.57876i
\(925\) 1.09414 + 15.4292i 0.0359752 + 0.507308i
\(926\) 39.3893 20.3622i 1.29441 0.669142i
\(927\) −7.27708 + 7.27708i −0.239011 + 0.239011i
\(928\) −22.5389 21.2525i −0.739876 0.697648i
\(929\) 4.52113 0.148333 0.0741667 0.997246i \(-0.476370\pi\)
0.0741667 + 0.997246i \(0.476370\pi\)
\(930\) 31.9400 17.9713i 1.04735 0.589303i
\(931\) 24.8200 + 2.17044i 0.813442 + 0.0711333i
\(932\) −0.923505 5.41808i −0.0302504 0.177475i
\(933\) 16.5838i 0.542930i
\(934\) 38.5552 + 12.2775i 1.26157 + 0.401731i
\(935\) −22.0569 20.5482i −0.721339 0.671997i
\(936\) −8.35515 + 6.29825i −0.273097 + 0.205865i
\(937\) 34.2842 + 34.2842i 1.12002 + 1.12002i 0.991738 + 0.128278i \(0.0409448\pi\)
0.128278 + 0.991738i \(0.459055\pi\)
\(938\) 52.0918 2.12655i 1.70086 0.0694344i
\(939\) 13.3732 + 13.3732i 0.436417 + 0.436417i
\(940\) −23.7014 + 36.0836i −0.773056 + 1.17692i
\(941\) −28.6524 + 28.6524i −0.934041 + 0.934041i −0.997955 0.0639142i \(-0.979642\pi\)
0.0639142 + 0.997955i \(0.479642\pi\)
\(942\) 8.88208 27.8926i 0.289394 0.908790i
\(943\) 0.142384 + 0.142384i 0.00463666 + 0.00463666i
\(944\) −4.79687 2.30383i −0.156125 0.0749833i
\(945\) 11.0441 26.0552i 0.359263 0.847576i
\(946\) −27.7184 53.6195i −0.901202 1.74332i
\(947\) 26.0324i 0.845939i −0.906144 0.422969i \(-0.860988\pi\)
0.906144 0.422969i \(-0.139012\pi\)
\(948\) −6.71817 4.76148i −0.218196 0.154646i
\(949\) 1.90850 + 1.90850i 0.0619525 + 0.0619525i
\(950\) 21.4835 13.1099i 0.697017 0.425341i
\(951\) −52.7083 −1.70918
\(952\) −3.18441 14.9677i −0.103207 0.485105i
\(953\) −26.5668 26.5668i −0.860583 0.860583i 0.130822 0.991406i \(-0.458238\pi\)
−0.991406 + 0.130822i \(0.958238\pi\)
\(954\) −11.5805 + 36.3666i −0.374934 + 1.17741i
\(955\) 16.3255 17.5242i 0.528281 0.567070i
\(956\) −15.8284 + 22.3330i −0.511928 + 0.722301i
\(957\) 100.322 3.24295
\(958\) 3.67752 + 1.17106i 0.118815 + 0.0378354i
\(959\) 31.2854 + 14.5878i 1.01026 + 0.471066i
\(960\) 42.5867 25.6365i 1.37448 0.827415i
\(961\) 13.6051 0.438875
\(962\) −1.04009 + 3.26622i −0.0335338 + 0.105307i
\(963\) 0.445070 0.0143422
\(964\) 25.7294 36.3027i 0.828687 1.16923i
\(965\) 1.24184 + 35.0679i 0.0399763 + 1.12887i
\(966\) 0.195246 + 0.179930i 0.00628195 + 0.00578917i
\(967\) −16.0970 + 16.0970i −0.517645 + 0.517645i −0.916858 0.399213i \(-0.869283\pi\)
0.399213 + 0.916858i \(0.369283\pi\)
\(968\) −73.3212 + 55.2707i −2.35663 + 1.77647i
\(969\) 20.2246i 0.649708i
\(970\) −1.94214 + 6.93944i −0.0623584 + 0.222812i
\(971\) −29.2299 29.2299i −0.938031 0.938031i 0.0601576 0.998189i \(-0.480840\pi\)
−0.998189 + 0.0601576i \(0.980840\pi\)
\(972\) −19.3992 + 27.3712i −0.622231 + 0.877932i
\(973\) −44.5698 20.7821i −1.42884 0.666244i
\(974\) 14.9182 7.71188i 0.478009 0.247105i
\(975\) −0.770021 10.8585i −0.0246604 0.347751i
\(976\) 33.2669 + 15.9773i 1.06485 + 0.511422i
\(977\) −12.0405 12.0405i −0.385209 0.385209i 0.487766 0.872975i \(-0.337812\pi\)
−0.872975 + 0.487766i \(0.837812\pi\)
\(978\) −24.5423 + 77.0706i −0.784775 + 2.46445i
\(979\) −30.0478 30.0478i −0.960333 0.960333i
\(980\) −19.4006 + 24.5686i −0.619731 + 0.784815i
\(981\) 33.7832 33.7832i 1.07862 1.07862i
\(982\) −37.0484 + 19.1520i −1.18226 + 0.611166i
\(983\) 3.21227 3.21227i 0.102455 0.102455i −0.654021 0.756476i \(-0.726919\pi\)
0.756476 + 0.654021i \(0.226919\pi\)
\(984\) −49.4874 + 37.3044i −1.57760 + 1.18922i
\(985\) −17.2395 + 18.5053i −0.549297 + 0.589629i
\(986\) 4.80537 15.0904i 0.153034 0.480577i
\(987\) 29.9923 64.3222i 0.954666 2.04740i
\(988\) 5.49807 0.937139i 0.174917 0.0298144i
\(989\) 0.116904 0.116904i 0.00371733 0.00371733i
\(990\) −26.5287 + 94.7893i −0.843137 + 3.01260i
\(991\) 13.9052 0.441714 0.220857 0.975306i \(-0.429115\pi\)
0.220857 + 0.975306i \(0.429115\pi\)
\(992\) −23.5830 + 0.692757i −0.748760 + 0.0219950i
\(993\) 23.2653 + 23.2653i 0.738303 + 0.738303i
\(994\) −20.8148 + 0.849727i −0.660207 + 0.0269517i
\(995\) −30.7297 28.6277i −0.974196 0.907558i
\(996\) −68.4463 48.5111i −2.16880 1.53713i
\(997\) 33.3954i 1.05764i 0.848733 + 0.528822i \(0.177366\pi\)
−0.848733 + 0.528822i \(0.822634\pi\)
\(998\) 13.0135 6.72725i 0.411934 0.212948i
\(999\) 14.7980i 0.468187i
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 560.2.r.a.237.7 184
5.3 odd 4 560.2.bn.a.13.38 yes 184
7.6 odd 2 inner 560.2.r.a.237.8 yes 184
16.5 even 4 560.2.bn.a.517.37 yes 184
35.13 even 4 560.2.bn.a.13.37 yes 184
80.53 odd 4 inner 560.2.r.a.293.7 yes 184
112.69 odd 4 560.2.bn.a.517.38 yes 184
560.293 even 4 inner 560.2.r.a.293.8 yes 184
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
560.2.r.a.237.7 184 1.1 even 1 trivial
560.2.r.a.237.8 yes 184 7.6 odd 2 inner
560.2.r.a.293.7 yes 184 80.53 odd 4 inner
560.2.r.a.293.8 yes 184 560.293 even 4 inner
560.2.bn.a.13.37 yes 184 35.13 even 4
560.2.bn.a.13.38 yes 184 5.3 odd 4
560.2.bn.a.517.37 yes 184 16.5 even 4
560.2.bn.a.517.38 yes 184 112.69 odd 4