Properties

Label 115.2.g.a.31.1
Level $115$
Weight $2$
Character 115.31
Analytic conductor $0.918$
Analytic rank $0$
Dimension $10$
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] = [115,2,Mod(6,115)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(115, base_ring=CyclotomicField(22))
 
chi = DirichletCharacter(H, H._module([0, 18]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("115.6");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 115 = 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 115.g (of order \(11\), degree \(10\), 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: \(0.918279623245\)
Analytic rank: \(0\)
Dimension: \(10\)
Coefficient field: \(\Q(\zeta_{22})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label 31.1
Root \(-0.415415 + 0.909632i\) of defining polynomial
Character \(\chi\) \(=\) 115.31
Dual form 115.2.g.a.26.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.0125459 + 0.0872586i) q^{2} +(-0.415415 - 0.909632i) q^{3} +(1.91153 + 0.561276i) q^{4} +(0.654861 + 0.755750i) q^{5} +(0.0845850 - 0.0248364i) q^{6} +(-1.30075 - 0.835939i) q^{7} +(-0.146201 + 0.320135i) q^{8} +(1.30972 - 1.51150i) q^{9} +O(q^{10})\) \(q+(-0.0125459 + 0.0872586i) q^{2} +(-0.415415 - 0.909632i) q^{3} +(1.91153 + 0.561276i) q^{4} +(0.654861 + 0.755750i) q^{5} +(0.0845850 - 0.0248364i) q^{6} +(-1.30075 - 0.835939i) q^{7} +(-0.146201 + 0.320135i) q^{8} +(1.30972 - 1.51150i) q^{9} +(-0.0741615 + 0.0476607i) q^{10} +(0.289532 + 2.01374i) q^{11} +(-0.283524 - 1.97195i) q^{12} +(1.80075 - 1.15727i) q^{13} +(0.0892619 - 0.103014i) q^{14} +(0.415415 - 0.909632i) q^{15} +(3.32584 + 2.13739i) q^{16} +(-4.18251 + 1.22809i) q^{17} +(0.115460 + 0.133248i) q^{18} +(-7.12381 - 2.09174i) q^{19} +(0.827602 + 1.81219i) q^{20} +(-0.220047 + 1.53046i) q^{21} -0.179348 q^{22} +(-2.79310 + 3.89854i) q^{23} +0.351939 q^{24} +(-0.142315 + 0.989821i) q^{25} +(0.0783898 + 0.171650i) q^{26} +(-4.79746 - 1.40866i) q^{27} +(-2.01722 - 2.32800i) q^{28} +(-4.30111 + 1.26292i) q^{29} +(0.0741615 + 0.0476607i) q^{30} +(-0.376329 + 0.824045i) q^{31} +(-0.689173 + 0.795348i) q^{32} +(1.71148 - 1.09990i) q^{33} +(-0.0546886 - 0.380367i) q^{34} +(-0.220047 - 1.53046i) q^{35} +(3.35194 - 2.15416i) q^{36} +(7.26571 - 8.38507i) q^{37} +(0.271897 - 0.595371i) q^{38} +(-1.80075 - 1.15727i) q^{39} +(-0.337683 + 0.0991526i) q^{40} +(3.95750 + 4.56720i) q^{41} +(-0.130785 - 0.0384020i) q^{42} +(2.24116 + 4.90745i) q^{43} +(-0.576814 + 4.01183i) q^{44} +2.00000 q^{45} +(-0.305139 - 0.292633i) q^{46} -2.72825 q^{47} +(0.562632 - 3.91319i) q^{48} +(-1.91476 - 4.19273i) q^{49} +(-0.0845850 - 0.0248364i) q^{50} +(2.85459 + 3.29437i) q^{51} +(4.09173 - 1.20144i) q^{52} +(-0.230732 - 0.148283i) q^{53} +(0.183106 - 0.400947i) q^{54} +(-1.33228 + 1.53753i) q^{55} +(0.457783 - 0.294199i) q^{56} +(1.05662 + 7.34898i) q^{57} +(-0.0562393 - 0.391153i) q^{58} +(6.74757 - 4.33640i) q^{59} +(1.30463 - 1.50563i) q^{60} +(-1.33718 + 2.92802i) q^{61} +(-0.0671837 - 0.0431763i) q^{62} +(-2.96714 + 0.871230i) q^{63} +(5.11714 + 5.90549i) q^{64} +(2.05384 + 0.603063i) q^{65} +(0.0745040 + 0.163141i) q^{66} +(0.279610 - 1.94473i) q^{67} -8.68428 q^{68} +(4.70653 + 0.921186i) q^{69} +0.136307 q^{70} +(1.58700 - 11.0378i) q^{71} +(0.292401 + 0.640269i) q^{72} +(9.95039 + 2.92170i) q^{73} +(0.640515 + 0.739194i) q^{74} +(0.959493 - 0.281733i) q^{75} +(-12.4433 - 7.99684i) q^{76} +(1.30675 - 2.86139i) q^{77} +(0.123574 - 0.142612i) q^{78} +(2.70849 - 1.74064i) q^{79} +(0.562632 + 3.91319i) q^{80} +(-0.142315 - 0.989821i) q^{81} +(-0.448178 + 0.288027i) q^{82} +(2.85563 - 3.29557i) q^{83} +(-1.27964 + 2.80202i) q^{84} +(-3.66709 - 2.35670i) q^{85} +(-0.456334 + 0.133992i) q^{86} +(2.93553 + 3.38779i) q^{87} +(-0.686997 - 0.201720i) q^{88} +(0.266861 + 0.584343i) q^{89} +(-0.0250918 + 0.174517i) q^{90} -3.30972 q^{91} +(-7.52725 + 5.88446i) q^{92} +0.905910 q^{93} +(0.0342284 - 0.238063i) q^{94} +(-3.08427 - 6.75361i) q^{95} +(1.00977 + 0.296494i) q^{96} +(3.62848 + 4.18748i) q^{97} +(0.389875 - 0.114478i) q^{98} +(3.42297 + 2.19981i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q + 5 q^{2} + q^{3} - q^{4} + q^{5} + 6 q^{6} + 5 q^{7} - 16 q^{8} + 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 10 q + 5 q^{2} + q^{3} - q^{4} + q^{5} + 6 q^{6} + 5 q^{7} - 16 q^{8} + 2 q^{9} - 5 q^{10} + 8 q^{11} + q^{12} - 3 q^{14} - q^{15} + 5 q^{16} - 23 q^{17} - 10 q^{18} - 13 q^{19} + q^{20} + 6 q^{21} + 4 q^{22} - 21 q^{23} - 6 q^{24} - q^{25} + 11 q^{26} - 5 q^{27} - 6 q^{28} + 2 q^{29} + 5 q^{30} - 20 q^{31} - 15 q^{32} + 3 q^{33} + 16 q^{34} + 6 q^{35} + 24 q^{36} + 13 q^{37} + 21 q^{38} - 6 q^{40} - 5 q^{41} + 3 q^{42} + 15 q^{43} + 19 q^{44} + 20 q^{45} - 16 q^{46} - 52 q^{47} + 6 q^{48} + 4 q^{49} - 6 q^{50} - 10 q^{51} + 22 q^{52} + 6 q^{53} - 30 q^{54} + 3 q^{55} + 3 q^{56} + 2 q^{57} + 45 q^{58} + 5 q^{59} + 10 q^{60} - 3 q^{61} - 54 q^{62} - 10 q^{63} - 34 q^{64} - 4 q^{66} + 20 q^{67} + 32 q^{68} - q^{69} - 8 q^{70} - 22 q^{71} + 32 q^{72} + 43 q^{73} + q^{74} + q^{75} - 2 q^{76} + 4 q^{77} + 11 q^{78} + 51 q^{79} + 6 q^{80} - q^{81} + 58 q^{82} - 17 q^{83} + 6 q^{84} + q^{85} - 9 q^{86} - 2 q^{87} + 7 q^{88} + 57 q^{89} + 10 q^{90} - 22 q^{91} - 43 q^{92} + 20 q^{93} - 81 q^{94} - 9 q^{95} - 7 q^{96} + 52 q^{97} + 24 q^{98} + 6 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/115\mathbb{Z}\right)^\times\).

\(n\) \(47\) \(51\)
\(\chi(n)\) \(1\) \(e\left(\frac{3}{11}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.0125459 + 0.0872586i −0.00887129 + 0.0617012i −0.993776 0.111395i \(-0.964468\pi\)
0.984905 + 0.173096i \(0.0553772\pi\)
\(3\) −0.415415 0.909632i −0.239840 0.525176i 0.750986 0.660318i \(-0.229578\pi\)
−0.990826 + 0.135141i \(0.956851\pi\)
\(4\) 1.91153 + 0.561276i 0.955765 + 0.280638i
\(5\) 0.654861 + 0.755750i 0.292863 + 0.337981i
\(6\) 0.0845850 0.0248364i 0.0345317 0.0101394i
\(7\) −1.30075 0.835939i −0.491636 0.315955i 0.271227 0.962515i \(-0.412571\pi\)
−0.762863 + 0.646560i \(0.776207\pi\)
\(8\) −0.146201 + 0.320135i −0.0516897 + 0.113185i
\(9\) 1.30972 1.51150i 0.436574 0.503833i
\(10\) −0.0741615 + 0.0476607i −0.0234519 + 0.0150716i
\(11\) 0.289532 + 2.01374i 0.0872971 + 0.607165i 0.985765 + 0.168126i \(0.0537717\pi\)
−0.898468 + 0.439038i \(0.855319\pi\)
\(12\) −0.283524 1.97195i −0.0818462 0.569253i
\(13\) 1.80075 1.15727i 0.499437 0.320969i −0.266554 0.963820i \(-0.585885\pi\)
0.765991 + 0.642851i \(0.222249\pi\)
\(14\) 0.0892619 0.103014i 0.0238563 0.0275316i
\(15\) 0.415415 0.909632i 0.107260 0.234866i
\(16\) 3.32584 + 2.13739i 0.831460 + 0.534347i
\(17\) −4.18251 + 1.22809i −1.01441 + 0.297857i −0.746355 0.665548i \(-0.768198\pi\)
−0.268052 + 0.963405i \(0.586380\pi\)
\(18\) 0.115460 + 0.133248i 0.0272141 + 0.0314068i
\(19\) −7.12381 2.09174i −1.63431 0.479878i −0.669499 0.742813i \(-0.733491\pi\)
−0.964814 + 0.262935i \(0.915310\pi\)
\(20\) 0.827602 + 1.81219i 0.185057 + 0.405219i
\(21\) −0.220047 + 1.53046i −0.0480182 + 0.333974i
\(22\) −0.179348 −0.0382372
\(23\) −2.79310 + 3.89854i −0.582402 + 0.812901i
\(24\) 0.351939 0.0718392
\(25\) −0.142315 + 0.989821i −0.0284630 + 0.197964i
\(26\) 0.0783898 + 0.171650i 0.0153735 + 0.0336633i
\(27\) −4.79746 1.40866i −0.923273 0.271097i
\(28\) −2.01722 2.32800i −0.381219 0.439951i
\(29\) −4.30111 + 1.26292i −0.798695 + 0.234518i −0.655519 0.755179i \(-0.727550\pi\)
−0.143177 + 0.989697i \(0.545732\pi\)
\(30\) 0.0741615 + 0.0476607i 0.0135400 + 0.00870161i
\(31\) −0.376329 + 0.824045i −0.0675906 + 0.148003i −0.940412 0.340037i \(-0.889561\pi\)
0.872822 + 0.488039i \(0.162288\pi\)
\(32\) −0.689173 + 0.795348i −0.121830 + 0.140599i
\(33\) 1.71148 1.09990i 0.297931 0.191469i
\(34\) −0.0546886 0.380367i −0.00937901 0.0652325i
\(35\) −0.220047 1.53046i −0.0371948 0.258695i
\(36\) 3.35194 2.15416i 0.558656 0.359027i
\(37\) 7.26571 8.38507i 1.19447 1.37850i 0.287248 0.957856i \(-0.407260\pi\)
0.907227 0.420641i \(-0.138195\pi\)
\(38\) 0.271897 0.595371i 0.0441075 0.0965819i
\(39\) −1.80075 1.15727i −0.288350 0.185311i
\(40\) −0.337683 + 0.0991526i −0.0533923 + 0.0156774i
\(41\) 3.95750 + 4.56720i 0.618058 + 0.713277i 0.975337 0.220720i \(-0.0708408\pi\)
−0.357279 + 0.933998i \(0.616295\pi\)
\(42\) −0.130785 0.0384020i −0.0201806 0.00592556i
\(43\) 2.24116 + 4.90745i 0.341773 + 0.748379i 0.999990 0.00444961i \(-0.00141636\pi\)
−0.658217 + 0.752828i \(0.728689\pi\)
\(44\) −0.576814 + 4.01183i −0.0869579 + 0.604806i
\(45\) 2.00000 0.298142
\(46\) −0.305139 0.292633i −0.0449903 0.0431464i
\(47\) −2.72825 −0.397956 −0.198978 0.980004i \(-0.563762\pi\)
−0.198978 + 0.980004i \(0.563762\pi\)
\(48\) 0.562632 3.91319i 0.0812089 0.564821i
\(49\) −1.91476 4.19273i −0.273537 0.598962i
\(50\) −0.0845850 0.0248364i −0.0119621 0.00351240i
\(51\) 2.85459 + 3.29437i 0.399723 + 0.461305i
\(52\) 4.09173 1.20144i 0.567420 0.166610i
\(53\) −0.230732 0.148283i −0.0316935 0.0203682i 0.524698 0.851288i \(-0.324178\pi\)
−0.556392 + 0.830920i \(0.687815\pi\)
\(54\) 0.183106 0.400947i 0.0249176 0.0545620i
\(55\) −1.33228 + 1.53753i −0.179644 + 0.207321i
\(56\) 0.457783 0.294199i 0.0611738 0.0393140i
\(57\) 1.05662 + 7.34898i 0.139953 + 0.973396i
\(58\) −0.0562393 0.391153i −0.00738458 0.0513609i
\(59\) 6.74757 4.33640i 0.878458 0.564551i −0.0218707 0.999761i \(-0.506962\pi\)
0.900329 + 0.435210i \(0.143326\pi\)
\(60\) 1.30463 1.50563i 0.168427 0.194375i
\(61\) −1.33718 + 2.92802i −0.171208 + 0.374894i −0.975713 0.219052i \(-0.929704\pi\)
0.804505 + 0.593946i \(0.202431\pi\)
\(62\) −0.0671837 0.0431763i −0.00853233 0.00548340i
\(63\) −2.96714 + 0.871230i −0.373824 + 0.109765i
\(64\) 5.11714 + 5.90549i 0.639642 + 0.738187i
\(65\) 2.05384 + 0.603063i 0.254748 + 0.0748008i
\(66\) 0.0745040 + 0.163141i 0.00917081 + 0.0200813i
\(67\) 0.279610 1.94473i 0.0341598 0.237587i −0.965587 0.260080i \(-0.916251\pi\)
0.999747 + 0.0224928i \(0.00716029\pi\)
\(68\) −8.68428 −1.05312
\(69\) 4.70653 + 0.921186i 0.566600 + 0.110898i
\(70\) 0.136307 0.0162918
\(71\) 1.58700 11.0378i 0.188342 1.30995i −0.647959 0.761675i \(-0.724377\pi\)
0.836301 0.548271i \(-0.184714\pi\)
\(72\) 0.292401 + 0.640269i 0.0344598 + 0.0754564i
\(73\) 9.95039 + 2.92170i 1.16461 + 0.341959i 0.806221 0.591615i \(-0.201509\pi\)
0.358385 + 0.933574i \(0.383328\pi\)
\(74\) 0.640515 + 0.739194i 0.0744584 + 0.0859295i
\(75\) 0.959493 0.281733i 0.110793 0.0325317i
\(76\) −12.4433 7.99684i −1.42735 0.917300i
\(77\) 1.30675 2.86139i 0.148919 0.326086i
\(78\) 0.123574 0.142612i 0.0139920 0.0161476i
\(79\) 2.70849 1.74064i 0.304729 0.195837i −0.379335 0.925259i \(-0.623847\pi\)
0.684064 + 0.729422i \(0.260211\pi\)
\(80\) 0.562632 + 3.91319i 0.0629042 + 0.437508i
\(81\) −0.142315 0.989821i −0.0158128 0.109980i
\(82\) −0.448178 + 0.288027i −0.0494930 + 0.0318072i
\(83\) 2.85563 3.29557i 0.313446 0.361736i −0.577065 0.816698i \(-0.695802\pi\)
0.890510 + 0.454963i \(0.150347\pi\)
\(84\) −1.27964 + 2.80202i −0.139620 + 0.305725i
\(85\) −3.66709 2.35670i −0.397752 0.255620i
\(86\) −0.456334 + 0.133992i −0.0492078 + 0.0144487i
\(87\) 2.93553 + 3.38779i 0.314722 + 0.363209i
\(88\) −0.686997 0.201720i −0.0732341 0.0215035i
\(89\) 0.266861 + 0.584343i 0.0282872 + 0.0619403i 0.923248 0.384204i \(-0.125524\pi\)
−0.894961 + 0.446144i \(0.852797\pi\)
\(90\) −0.0250918 + 0.174517i −0.00264491 + 0.0183957i
\(91\) −3.30972 −0.346953
\(92\) −7.52725 + 5.88446i −0.784770 + 0.613498i
\(93\) 0.905910 0.0939385
\(94\) 0.0342284 0.238063i 0.00353038 0.0245544i
\(95\) −3.08427 6.75361i −0.316439 0.692906i
\(96\) 1.00977 + 0.296494i 0.103059 + 0.0302608i
\(97\) 3.62848 + 4.18748i 0.368416 + 0.425175i 0.909442 0.415831i \(-0.136509\pi\)
−0.541026 + 0.841006i \(0.681964\pi\)
\(98\) 0.389875 0.114478i 0.0393833 0.0115640i
\(99\) 3.42297 + 2.19981i 0.344021 + 0.221089i
\(100\) −0.827602 + 1.81219i −0.0827602 + 0.181219i
\(101\) −2.94535 + 3.39912i −0.293073 + 0.338225i −0.883122 0.469143i \(-0.844563\pi\)
0.590049 + 0.807367i \(0.299108\pi\)
\(102\) −0.323276 + 0.207757i −0.0320091 + 0.0205710i
\(103\) −1.38513 9.63380i −0.136481 0.949247i −0.936848 0.349737i \(-0.886271\pi\)
0.800367 0.599510i \(-0.204638\pi\)
\(104\) 0.107212 + 0.745675i 0.0105130 + 0.0731194i
\(105\) −1.30075 + 0.835939i −0.126940 + 0.0815793i
\(106\) 0.0158337 0.0182730i 0.00153790 0.00177483i
\(107\) −3.07272 + 6.72833i −0.297051 + 0.650452i −0.998031 0.0627299i \(-0.980019\pi\)
0.700979 + 0.713182i \(0.252747\pi\)
\(108\) −8.37985 5.38540i −0.806351 0.518210i
\(109\) −9.99029 + 2.93341i −0.956897 + 0.280970i −0.722656 0.691208i \(-0.757079\pi\)
−0.234241 + 0.972179i \(0.575260\pi\)
\(110\) −0.117448 0.135542i −0.0111983 0.0129235i
\(111\) −10.6456 3.12583i −1.01044 0.296691i
\(112\) −2.53935 5.56040i −0.239946 0.525408i
\(113\) −2.78825 + 19.3927i −0.262297 + 1.82431i 0.253189 + 0.967417i \(0.418520\pi\)
−0.515486 + 0.856898i \(0.672389\pi\)
\(114\) −0.654518 −0.0613012
\(115\) −4.77541 + 0.442111i −0.445309 + 0.0412271i
\(116\) −8.93053 −0.829179
\(117\) 0.609264 4.23753i 0.0563265 0.391760i
\(118\) 0.293734 + 0.643187i 0.0270404 + 0.0592102i
\(119\) 6.46699 + 1.89888i 0.592828 + 0.174070i
\(120\) 0.230471 + 0.265977i 0.0210390 + 0.0242803i
\(121\) 6.58311 1.93298i 0.598465 0.175725i
\(122\) −0.238719 0.153415i −0.0216126 0.0138896i
\(123\) 2.51047 5.49716i 0.226361 0.495662i
\(124\) −1.18188 + 1.36396i −0.106136 + 0.122487i
\(125\) −0.841254 + 0.540641i −0.0752440 + 0.0483564i
\(126\) −0.0387969 0.269839i −0.00345631 0.0240391i
\(127\) 2.49696 + 17.3667i 0.221569 + 1.54105i 0.732105 + 0.681192i \(0.238538\pi\)
−0.510536 + 0.859856i \(0.670553\pi\)
\(128\) −2.35017 + 1.51036i −0.207727 + 0.133498i
\(129\) 3.53296 4.07725i 0.311060 0.358982i
\(130\) −0.0783898 + 0.171650i −0.00687524 + 0.0150547i
\(131\) −10.9767 7.05427i −0.959035 0.616334i −0.0353039 0.999377i \(-0.511240\pi\)
−0.923731 + 0.383043i \(0.874876\pi\)
\(132\) 3.88890 1.14188i 0.338486 0.0993883i
\(133\) 7.51770 + 8.67589i 0.651867 + 0.752295i
\(134\) 0.166187 + 0.0487968i 0.0143563 + 0.00421540i
\(135\) −2.07708 4.54816i −0.178766 0.391443i
\(136\) 0.218329 1.51851i 0.0187216 0.130211i
\(137\) 21.5268 1.83916 0.919580 0.392903i \(-0.128529\pi\)
0.919580 + 0.392903i \(0.128529\pi\)
\(138\) −0.139429 + 0.399128i −0.0118690 + 0.0339760i
\(139\) −16.3719 −1.38864 −0.694322 0.719665i \(-0.744295\pi\)
−0.694322 + 0.719665i \(0.744295\pi\)
\(140\) 0.438384 3.04903i 0.0370502 0.257690i
\(141\) 1.13336 + 2.48170i 0.0954458 + 0.208997i
\(142\) 0.943233 + 0.276958i 0.0791544 + 0.0232418i
\(143\) 2.85181 + 3.29117i 0.238480 + 0.275221i
\(144\) 7.58658 2.22762i 0.632215 0.185635i
\(145\) −3.77108 2.42352i −0.313171 0.201263i
\(146\) −0.379780 + 0.831602i −0.0314308 + 0.0688239i
\(147\) −3.01843 + 3.48345i −0.248956 + 0.287310i
\(148\) 18.5950 11.9502i 1.52850 0.982304i
\(149\) −2.74972 19.1247i −0.225266 1.56676i −0.717665 0.696389i \(-0.754789\pi\)
0.492399 0.870370i \(-0.336120\pi\)
\(150\) 0.0125459 + 0.0872586i 0.00102437 + 0.00712464i
\(151\) 16.8366 10.8202i 1.37015 0.880539i 0.371297 0.928514i \(-0.378913\pi\)
0.998849 + 0.0479750i \(0.0152768\pi\)
\(152\) 1.71114 1.97476i 0.138792 0.160174i
\(153\) −3.62165 + 7.93032i −0.292793 + 0.641128i
\(154\) 0.233287 + 0.149924i 0.0187988 + 0.0120812i
\(155\) −0.869215 + 0.255224i −0.0698170 + 0.0205001i
\(156\) −2.79263 3.22287i −0.223590 0.258036i
\(157\) −5.54048 1.62683i −0.442179 0.129835i 0.0530620 0.998591i \(-0.483102\pi\)
−0.495241 + 0.868756i \(0.664920\pi\)
\(158\) 0.117905 + 0.258177i 0.00938006 + 0.0205395i
\(159\) −0.0390330 + 0.271480i −0.00309552 + 0.0215298i
\(160\) −1.05240 −0.0831992
\(161\) 6.89206 2.73614i 0.543170 0.215638i
\(162\) 0.0881559 0.00692618
\(163\) −1.25289 + 8.71401i −0.0981335 + 0.682534i 0.880064 + 0.474856i \(0.157500\pi\)
−0.978197 + 0.207678i \(0.933409\pi\)
\(164\) 5.00143 + 10.9516i 0.390546 + 0.855176i
\(165\) 1.95204 + 0.573170i 0.151966 + 0.0446212i
\(166\) 0.251740 + 0.290524i 0.0195388 + 0.0225490i
\(167\) 18.7367 5.50159i 1.44989 0.425726i 0.540384 0.841418i \(-0.318279\pi\)
0.909505 + 0.415692i \(0.136461\pi\)
\(168\) −0.457783 0.294199i −0.0353187 0.0226980i
\(169\) −3.49698 + 7.65732i −0.268998 + 0.589024i
\(170\) 0.251649 0.290419i 0.0193006 0.0222741i
\(171\) −12.4919 + 8.02803i −0.955276 + 0.613919i
\(172\) 1.52960 + 10.6386i 0.116631 + 0.811188i
\(173\) −3.07149 21.3627i −0.233521 1.62417i −0.682676 0.730721i \(-0.739184\pi\)
0.449155 0.893454i \(-0.351725\pi\)
\(174\) −0.332443 + 0.213648i −0.0252024 + 0.0161966i
\(175\) 1.01255 1.16854i 0.0765413 0.0883333i
\(176\) −3.34120 + 7.31621i −0.251852 + 0.551480i
\(177\) −6.74757 4.33640i −0.507178 0.325944i
\(178\) −0.0543370 + 0.0159548i −0.00407273 + 0.00119586i
\(179\) 10.0553 + 11.6044i 0.751567 + 0.867354i 0.994719 0.102634i \(-0.0327270\pi\)
−0.243152 + 0.969988i \(0.578182\pi\)
\(180\) 3.82306 + 1.12255i 0.284954 + 0.0836700i
\(181\) 0.340209 + 0.744955i 0.0252876 + 0.0553720i 0.921854 0.387537i \(-0.126674\pi\)
−0.896567 + 0.442909i \(0.853947\pi\)
\(182\) 0.0415234 0.288802i 0.00307792 0.0214074i
\(183\) 3.21890 0.237948
\(184\) −0.839703 1.46414i −0.0619037 0.107938i
\(185\) 11.0950 0.815724
\(186\) −0.0113655 + 0.0790485i −0.000833356 + 0.00579612i
\(187\) −3.68403 8.06690i −0.269403 0.589910i
\(188\) −5.21513 1.53130i −0.380353 0.111682i
\(189\) 5.06273 + 5.84270i 0.368259 + 0.424994i
\(190\) 0.628006 0.184399i 0.0455603 0.0133777i
\(191\) −3.58868 2.30630i −0.259668 0.166878i 0.404329 0.914613i \(-0.367505\pi\)
−0.663997 + 0.747735i \(0.731141\pi\)
\(192\) 3.24609 7.10794i 0.234266 0.512972i
\(193\) −3.16580 + 3.65352i −0.227879 + 0.262986i −0.858162 0.513379i \(-0.828393\pi\)
0.630283 + 0.776366i \(0.282939\pi\)
\(194\) −0.410917 + 0.264080i −0.0295021 + 0.0189598i
\(195\) −0.304632 2.11876i −0.0218152 0.151728i
\(196\) −1.30684 9.08924i −0.0933454 0.649232i
\(197\) −0.220925 + 0.141980i −0.0157403 + 0.0101157i −0.548487 0.836159i \(-0.684796\pi\)
0.532747 + 0.846275i \(0.321160\pi\)
\(198\) −0.234896 + 0.271085i −0.0166934 + 0.0192652i
\(199\) −1.79719 + 3.93530i −0.127399 + 0.278966i −0.962574 0.271019i \(-0.912639\pi\)
0.835175 + 0.549985i \(0.185367\pi\)
\(200\) −0.296070 0.190272i −0.0209353 0.0134543i
\(201\) −1.88514 + 0.553528i −0.132968 + 0.0390429i
\(202\) −0.259650 0.299652i −0.0182689 0.0210835i
\(203\) 6.65037 + 1.95273i 0.466765 + 0.137054i
\(204\) 3.60758 + 7.89950i 0.252581 + 0.553076i
\(205\) −0.860048 + 5.98176i −0.0600684 + 0.417785i
\(206\) 0.858010 0.0597804
\(207\) 2.23445 + 9.32777i 0.155305 + 0.648325i
\(208\) 8.46252 0.586770
\(209\) 2.14964 14.9511i 0.148694 1.03419i
\(210\) −0.0566239 0.123989i −0.00390742 0.00855605i
\(211\) 6.30147 + 1.85028i 0.433811 + 0.127378i 0.491345 0.870965i \(-0.336506\pi\)
−0.0575338 + 0.998344i \(0.518324\pi\)
\(212\) −0.357824 0.412951i −0.0245755 0.0283616i
\(213\) −10.6996 + 3.14169i −0.733125 + 0.215265i
\(214\) −0.548554 0.352535i −0.0374984 0.0240988i
\(215\) −2.24116 + 4.90745i −0.152846 + 0.334685i
\(216\) 1.15235 1.32989i 0.0784077 0.0904874i
\(217\) 1.17836 0.757286i 0.0799923 0.0514079i
\(218\) −0.130629 0.908542i −0.00884728 0.0615342i
\(219\) −1.47587 10.2649i −0.0997301 0.693638i
\(220\) −3.40967 + 2.19126i −0.229880 + 0.147735i
\(221\) −6.11040 + 7.05178i −0.411030 + 0.474354i
\(222\) 0.406315 0.889705i 0.0272701 0.0597131i
\(223\) −7.74566 4.97783i −0.518688 0.333340i 0.254965 0.966950i \(-0.417936\pi\)
−0.773653 + 0.633610i \(0.781572\pi\)
\(224\) 1.56130 0.458439i 0.104319 0.0306308i
\(225\) 1.30972 + 1.51150i 0.0873148 + 0.100767i
\(226\) −1.65720 0.486598i −0.110235 0.0323680i
\(227\) −3.68538 8.06985i −0.244607 0.535615i 0.747012 0.664810i \(-0.231488\pi\)
−0.991619 + 0.129196i \(0.958760\pi\)
\(228\) −2.10504 + 14.6408i −0.139409 + 0.969614i
\(229\) −8.38484 −0.554086 −0.277043 0.960858i \(-0.589354\pi\)
−0.277043 + 0.960858i \(0.589354\pi\)
\(230\) 0.0213338 0.422242i 0.00140671 0.0278418i
\(231\) −3.14566 −0.206969
\(232\) 0.224520 1.56157i 0.0147405 0.102522i
\(233\) −9.97561 21.8435i −0.653524 1.43102i −0.888435 0.459002i \(-0.848207\pi\)
0.234911 0.972017i \(-0.424520\pi\)
\(234\) 0.362117 + 0.106327i 0.0236723 + 0.00695082i
\(235\) −1.78662 2.06187i −0.116547 0.134502i
\(236\) 15.3321 4.50191i 0.998034 0.293049i
\(237\) −2.70849 1.74064i −0.175935 0.113067i
\(238\) −0.246828 + 0.540478i −0.0159995 + 0.0350340i
\(239\) 7.35914 8.49290i 0.476023 0.549360i −0.466054 0.884756i \(-0.654325\pi\)
0.942077 + 0.335396i \(0.108870\pi\)
\(240\) 3.32584 2.13739i 0.214682 0.137968i
\(241\) 4.00004 + 27.8209i 0.257665 + 1.79210i 0.549355 + 0.835589i \(0.314874\pi\)
−0.291689 + 0.956513i \(0.594217\pi\)
\(242\) 0.0860778 + 0.598684i 0.00553329 + 0.0384849i
\(243\) −13.4601 + 8.65025i −0.863463 + 0.554914i
\(244\) −4.19948 + 4.84646i −0.268844 + 0.310263i
\(245\) 1.91476 4.19273i 0.122329 0.267864i
\(246\) 0.448178 + 0.288027i 0.0285748 + 0.0183639i
\(247\) −15.2489 + 4.47747i −0.970262 + 0.284895i
\(248\) −0.208786 0.240952i −0.0132579 0.0153004i
\(249\) −4.18403 1.22854i −0.265152 0.0778556i
\(250\) −0.0366213 0.0801894i −0.00231613 0.00507163i
\(251\) 3.91272 27.2135i 0.246969 1.71770i −0.368572 0.929599i \(-0.620153\pi\)
0.615541 0.788105i \(-0.288938\pi\)
\(252\) −6.16077 −0.388092
\(253\) −8.65932 4.49583i −0.544407 0.282650i
\(254\) −1.54672 −0.0970501
\(255\) −0.620362 + 4.31471i −0.0388486 + 0.270198i
\(256\) 6.38987 + 13.9919i 0.399367 + 0.874492i
\(257\) −17.0432 5.00435i −1.06313 0.312163i −0.297018 0.954872i \(-0.595992\pi\)
−0.766110 + 0.642709i \(0.777810\pi\)
\(258\) 0.311451 + 0.359434i 0.0193901 + 0.0223774i
\(259\) −16.4603 + 4.83317i −1.02279 + 0.300318i
\(260\) 3.58750 + 2.30555i 0.222487 + 0.142984i
\(261\) −3.72435 + 8.15519i −0.230531 + 0.504794i
\(262\) 0.753257 0.869305i 0.0465364 0.0537059i
\(263\) −7.35320 + 4.72561i −0.453417 + 0.291394i −0.747348 0.664433i \(-0.768673\pi\)
0.293930 + 0.955827i \(0.405037\pi\)
\(264\) 0.101897 + 0.708712i 0.00627135 + 0.0436182i
\(265\) −0.0390330 0.271480i −0.00239778 0.0166769i
\(266\) −0.851362 + 0.547137i −0.0522004 + 0.0335471i
\(267\) 0.420680 0.485490i 0.0257452 0.0297115i
\(268\) 1.62601 3.56047i 0.0993246 0.217491i
\(269\) 2.46553 + 1.58450i 0.150326 + 0.0966086i 0.613642 0.789585i \(-0.289704\pi\)
−0.463316 + 0.886193i \(0.653340\pi\)
\(270\) 0.422925 0.124182i 0.0257384 0.00755747i
\(271\) 4.29616 + 4.95803i 0.260973 + 0.301179i 0.871081 0.491139i \(-0.163419\pi\)
−0.610108 + 0.792318i \(0.708874\pi\)
\(272\) −16.5353 4.85519i −1.00260 0.294389i
\(273\) 1.37491 + 3.01063i 0.0832132 + 0.182212i
\(274\) −0.270073 + 1.87840i −0.0163157 + 0.113478i
\(275\) −2.03445 −0.122682
\(276\) 8.47963 + 4.40253i 0.510414 + 0.265001i
\(277\) −22.7888 −1.36924 −0.684622 0.728898i \(-0.740033\pi\)
−0.684622 + 0.728898i \(0.740033\pi\)
\(278\) 0.205400 1.42859i 0.0123191 0.0856809i
\(279\) 0.752658 + 1.64809i 0.0450604 + 0.0986686i
\(280\) 0.522125 + 0.153310i 0.0312029 + 0.00916201i
\(281\) 9.32744 + 10.7644i 0.556429 + 0.642153i 0.962369 0.271747i \(-0.0876013\pi\)
−0.405940 + 0.913900i \(0.633056\pi\)
\(282\) −0.230769 + 0.0677599i −0.0137421 + 0.00403504i
\(283\) 19.9441 + 12.8173i 1.18555 + 0.761910i 0.976399 0.215973i \(-0.0692923\pi\)
0.209155 + 0.977882i \(0.432929\pi\)
\(284\) 9.22884 20.2083i 0.547631 1.19914i
\(285\) −4.86205 + 5.61110i −0.288003 + 0.332373i
\(286\) −0.322961 + 0.207554i −0.0190971 + 0.0122730i
\(287\) −1.32981 9.24901i −0.0784960 0.545952i
\(288\) 0.299543 + 2.08337i 0.0176507 + 0.122764i
\(289\) 1.68384 1.08214i 0.0990493 0.0636551i
\(290\) 0.258785 0.298654i 0.0151964 0.0175375i
\(291\) 2.30175 5.04012i 0.134931 0.295457i
\(292\) 17.3806 + 11.1698i 1.01712 + 0.653664i
\(293\) 4.10110 1.20419i 0.239589 0.0703497i −0.159734 0.987160i \(-0.551064\pi\)
0.399323 + 0.916810i \(0.369245\pi\)
\(294\) −0.266092 0.307087i −0.0155188 0.0179097i
\(295\) 7.69595 + 2.25973i 0.448075 + 0.131567i
\(296\) 1.62210 + 3.55191i 0.0942827 + 0.206450i
\(297\) 1.44766 10.0687i 0.0840017 0.584245i
\(298\) 1.70330 0.0986692
\(299\) −0.518014 + 10.2526i −0.0299575 + 0.592926i
\(300\) 1.99223 0.115021
\(301\) 1.18715 8.25681i 0.0684262 0.475915i
\(302\) 0.732929 + 1.60489i 0.0421753 + 0.0923511i
\(303\) 4.31549 + 1.26714i 0.247918 + 0.0727954i
\(304\) −19.2218 22.1831i −1.10244 1.27229i
\(305\) −3.08851 + 0.906870i −0.176848 + 0.0519272i
\(306\) −0.646552 0.415514i −0.0369609 0.0237533i
\(307\) −3.71586 + 8.13661i −0.212076 + 0.464381i −0.985536 0.169463i \(-0.945797\pi\)
0.773461 + 0.633844i \(0.218524\pi\)
\(308\) 4.10393 4.73619i 0.233843 0.269869i
\(309\) −8.18781 + 5.26199i −0.465788 + 0.299344i
\(310\) −0.0113655 0.0790485i −0.000645515 0.00448965i
\(311\) 3.32224 + 23.1067i 0.188387 + 1.31026i 0.836185 + 0.548447i \(0.184781\pi\)
−0.647798 + 0.761812i \(0.724310\pi\)
\(312\) 0.633752 0.407288i 0.0358792 0.0230581i
\(313\) 14.7416 17.0127i 0.833244 0.961615i −0.166457 0.986049i \(-0.553233\pi\)
0.999701 + 0.0244337i \(0.00777827\pi\)
\(314\) 0.211465 0.463045i 0.0119337 0.0261311i
\(315\) −2.60149 1.67188i −0.146578 0.0941997i
\(316\) 6.15434 1.80708i 0.346209 0.101656i
\(317\) −8.34970 9.63606i −0.468966 0.541215i 0.471158 0.882049i \(-0.343836\pi\)
−0.940124 + 0.340834i \(0.889291\pi\)
\(318\) −0.0231993 0.00681193i −0.00130095 0.000381994i
\(319\) −3.78849 8.29564i −0.212115 0.464467i
\(320\) −1.11206 + 7.73455i −0.0621661 + 0.432375i
\(321\) 7.39676 0.412847
\(322\) 0.152285 + 0.635719i 0.00848651 + 0.0354272i
\(323\) 32.3642 1.80079
\(324\) 0.283524 1.97195i 0.0157513 0.109553i
\(325\) 0.889217 + 1.94711i 0.0493249 + 0.108006i
\(326\) −0.744654 0.218650i −0.0412426 0.0121099i
\(327\) 6.81845 + 7.86891i 0.377061 + 0.435151i
\(328\) −2.04071 + 0.599206i −0.112679 + 0.0330856i
\(329\) 3.54876 + 2.28065i 0.195650 + 0.125736i
\(330\) −0.0745040 + 0.163141i −0.00410131 + 0.00898062i
\(331\) 10.7382 12.3926i 0.590227 0.681158i −0.379545 0.925173i \(-0.623919\pi\)
0.969771 + 0.244015i \(0.0784647\pi\)
\(332\) 7.30834 4.69678i 0.401097 0.257769i
\(333\) −3.15798 21.9642i −0.173056 1.20363i
\(334\) 0.244993 + 1.70396i 0.0134054 + 0.0932366i
\(335\) 1.65284 1.06221i 0.0903041 0.0580349i
\(336\) −4.00303 + 4.61974i −0.218383 + 0.252028i
\(337\) 11.3983 24.9589i 0.620907 1.35960i −0.293951 0.955821i \(-0.594970\pi\)
0.914858 0.403776i \(-0.132303\pi\)
\(338\) −0.624294 0.401210i −0.0339571 0.0218229i
\(339\) 18.7985 5.51975i 1.02100 0.299792i
\(340\) −5.68700 6.56314i −0.308421 0.355936i
\(341\) −1.76837 0.519240i −0.0957626 0.0281184i
\(342\) −0.543793 1.19074i −0.0294050 0.0643879i
\(343\) −2.55459 + 17.7675i −0.137935 + 0.959357i
\(344\) −1.89870 −0.102371
\(345\) 2.38594 + 4.16021i 0.128454 + 0.223978i
\(346\) 1.90261 0.102285
\(347\) −0.858953 + 5.97415i −0.0461110 + 0.320709i 0.953691 + 0.300789i \(0.0972501\pi\)
−0.999802 + 0.0199196i \(0.993659\pi\)
\(348\) 3.70988 + 8.12350i 0.198870 + 0.435465i
\(349\) −8.00915 2.35170i −0.428720 0.125883i 0.0602518 0.998183i \(-0.480810\pi\)
−0.488972 + 0.872300i \(0.662628\pi\)
\(350\) 0.0892619 + 0.103014i 0.00477125 + 0.00550632i
\(351\) −10.2692 + 3.01532i −0.548130 + 0.160946i
\(352\) −1.80116 1.15753i −0.0960021 0.0616968i
\(353\) −10.8642 + 23.7892i −0.578242 + 1.26617i 0.364049 + 0.931380i \(0.381394\pi\)
−0.942291 + 0.334794i \(0.891333\pi\)
\(354\) 0.463042 0.534379i 0.0246104 0.0284019i
\(355\) 9.38108 6.02885i 0.497896 0.319978i
\(356\) 0.182134 + 1.26677i 0.00965310 + 0.0671388i
\(357\) −0.959204 6.67141i −0.0507664 0.353088i
\(358\) −1.13874 + 0.731822i −0.0601841 + 0.0386780i
\(359\) −3.70672 + 4.27779i −0.195633 + 0.225773i −0.845088 0.534628i \(-0.820452\pi\)
0.649454 + 0.760401i \(0.274997\pi\)
\(360\) −0.292401 + 0.640269i −0.0154109 + 0.0337451i
\(361\) 30.3894 + 19.5301i 1.59944 + 1.02790i
\(362\) −0.0692719 + 0.0203401i −0.00364085 + 0.00106905i
\(363\) −4.49302 5.18522i −0.235822 0.272154i
\(364\) −6.32663 1.85767i −0.331605 0.0973682i
\(365\) 4.30805 + 9.43331i 0.225494 + 0.493762i
\(366\) −0.0403840 + 0.280877i −0.00211091 + 0.0146817i
\(367\) −12.3147 −0.642822 −0.321411 0.946940i \(-0.604157\pi\)
−0.321411 + 0.946940i \(0.604157\pi\)
\(368\) −17.6221 + 6.99596i −0.918615 + 0.364690i
\(369\) 12.0866 0.629201
\(370\) −0.139197 + 0.968138i −0.00723652 + 0.0503311i
\(371\) 0.176169 + 0.385756i 0.00914624 + 0.0200275i
\(372\) 1.73167 + 0.508465i 0.0897831 + 0.0263627i
\(373\) −19.0734 22.0119i −0.987585 1.13973i −0.990189 0.139737i \(-0.955374\pi\)
0.00260397 0.999997i \(-0.499171\pi\)
\(374\) 0.750126 0.220257i 0.0387881 0.0113892i
\(375\) 0.841254 + 0.540641i 0.0434421 + 0.0279186i
\(376\) 0.398872 0.873407i 0.0205702 0.0450426i
\(377\) −6.28366 + 7.25173i −0.323625 + 0.373483i
\(378\) −0.573343 + 0.368465i −0.0294896 + 0.0189518i
\(379\) 4.74698 + 33.0160i 0.243836 + 1.69592i 0.632519 + 0.774545i \(0.282021\pi\)
−0.388683 + 0.921372i \(0.627070\pi\)
\(380\) −2.10504 14.6408i −0.107986 0.751060i
\(381\) 14.7601 9.48571i 0.756181 0.485968i
\(382\) 0.246268 0.284209i 0.0126002 0.0145414i
\(383\) 12.9139 28.2775i 0.659870 1.44491i −0.222773 0.974870i \(-0.571511\pi\)
0.882643 0.470044i \(-0.155762\pi\)
\(384\) 2.35017 + 1.51036i 0.119931 + 0.0770753i
\(385\) 3.01824 0.886235i 0.153824 0.0451667i
\(386\) −0.279084 0.322080i −0.0142050 0.0163934i
\(387\) 10.3529 + 3.03988i 0.526267 + 0.154526i
\(388\) 4.58560 + 10.0411i 0.232799 + 0.509758i
\(389\) 1.80544 12.5571i 0.0915394 0.636670i −0.891465 0.453089i \(-0.850322\pi\)
0.983005 0.183581i \(-0.0587690\pi\)
\(390\) 0.188702 0.00955531
\(391\) 6.89440 19.7358i 0.348665 0.998085i
\(392\) 1.62218 0.0819324
\(393\) −1.85692 + 12.9152i −0.0936692 + 0.651484i
\(394\) −0.00961727 0.0210589i −0.000484511 0.00106093i
\(395\) 3.08917 + 0.907063i 0.155433 + 0.0456393i
\(396\) 5.30841 + 6.12623i 0.266757 + 0.307855i
\(397\) −11.8219 + 3.47123i −0.593325 + 0.174216i −0.564590 0.825371i \(-0.690966\pi\)
−0.0287344 + 0.999587i \(0.509148\pi\)
\(398\) −0.320841 0.206192i −0.0160823 0.0103355i
\(399\) 4.76890 10.4424i 0.238744 0.522776i
\(400\) −2.58895 + 2.98780i −0.129447 + 0.149390i
\(401\) −28.3895 + 18.2448i −1.41770 + 0.911102i −0.417705 + 0.908583i \(0.637166\pi\)
−0.999997 + 0.00251937i \(0.999198\pi\)
\(402\) −0.0246493 0.171440i −0.00122940 0.00855063i
\(403\) 0.275970 + 1.91941i 0.0137470 + 0.0956126i
\(404\) −7.53797 + 4.84436i −0.375028 + 0.241016i
\(405\) 0.654861 0.755750i 0.0325403 0.0375535i
\(406\) −0.253827 + 0.555804i −0.0125972 + 0.0275841i
\(407\) 18.9890 + 12.2035i 0.941249 + 0.604904i
\(408\) −1.47199 + 0.432214i −0.0728741 + 0.0213978i
\(409\) −10.6316 12.2695i −0.525698 0.606688i 0.429350 0.903138i \(-0.358743\pi\)
−0.955048 + 0.296450i \(0.904197\pi\)
\(410\) −0.511170 0.150093i −0.0252449 0.00741257i
\(411\) −8.94256 19.5815i −0.441104 0.965883i
\(412\) 2.75950 19.1927i 0.135951 0.945558i
\(413\) −12.4018 −0.610254
\(414\) −0.841961 + 0.0779495i −0.0413801 + 0.00383101i
\(415\) 4.36066 0.214057
\(416\) −0.320594 + 2.22978i −0.0157184 + 0.109324i
\(417\) 6.80112 + 14.8924i 0.333052 + 0.729282i
\(418\) 1.27764 + 0.375150i 0.0624916 + 0.0183492i
\(419\) 8.76692 + 10.1176i 0.428292 + 0.494275i 0.928345 0.371719i \(-0.121232\pi\)
−0.500053 + 0.865995i \(0.666686\pi\)
\(420\) −2.95561 + 0.867845i −0.144219 + 0.0423465i
\(421\) −10.9478 7.03572i −0.533563 0.342900i 0.245954 0.969282i \(-0.420899\pi\)
−0.779517 + 0.626382i \(0.784535\pi\)
\(422\) −0.240510 + 0.526644i −0.0117079 + 0.0256366i
\(423\) −3.57325 + 4.12375i −0.173737 + 0.200504i
\(424\) 0.0812036 0.0521864i 0.00394360 0.00253439i
\(425\) −0.620362 4.31471i −0.0300920 0.209294i
\(426\) −0.139903 0.973048i −0.00677833 0.0471443i
\(427\) 4.18698 2.69081i 0.202622 0.130217i
\(428\) −9.65005 + 11.1367i −0.466453 + 0.538315i
\(429\) 1.80906 3.96130i 0.0873424 0.191253i
\(430\) −0.400100 0.257128i −0.0192945 0.0123998i
\(431\) −8.97982 + 2.63671i −0.432543 + 0.127006i −0.490754 0.871298i \(-0.663279\pi\)
0.0582112 + 0.998304i \(0.481460\pi\)
\(432\) −12.9447 14.9390i −0.622804 0.718754i
\(433\) 32.5898 + 9.56922i 1.56616 + 0.459867i 0.945882 0.324511i \(-0.105200\pi\)
0.620283 + 0.784378i \(0.287018\pi\)
\(434\) 0.0512961 + 0.112323i 0.00246229 + 0.00539167i
\(435\) −0.637953 + 4.43706i −0.0305875 + 0.212741i
\(436\) −20.7432 −0.993419
\(437\) 28.0522 21.9300i 1.34192 1.04905i
\(438\) 0.914218 0.0436830
\(439\) −4.53831 + 31.5646i −0.216602 + 1.50650i 0.533854 + 0.845577i \(0.320743\pi\)
−0.750456 + 0.660921i \(0.770166\pi\)
\(440\) −0.297437 0.651296i −0.0141798 0.0310493i
\(441\) −8.84511 2.59716i −0.421196 0.123674i
\(442\) −0.538668 0.621656i −0.0256218 0.0295691i
\(443\) −29.3691 + 8.62354i −1.39537 + 0.409717i −0.891091 0.453825i \(-0.850059\pi\)
−0.504277 + 0.863542i \(0.668241\pi\)
\(444\) −18.5950 11.9502i −0.882477 0.567134i
\(445\) −0.266861 + 0.584343i −0.0126504 + 0.0277005i
\(446\) 0.531535 0.613424i 0.0251689 0.0290465i
\(447\) −16.2542 + 10.4459i −0.768797 + 0.494076i
\(448\) −1.71947 11.9592i −0.0812373 0.565018i
\(449\) 2.39840 + 16.6812i 0.113187 + 0.787236i 0.964785 + 0.263040i \(0.0847251\pi\)
−0.851597 + 0.524196i \(0.824366\pi\)
\(450\) −0.148323 + 0.0953214i −0.00699201 + 0.00449349i
\(451\) −8.05133 + 9.29173i −0.379122 + 0.437530i
\(452\) −16.2145 + 35.5048i −0.762666 + 1.67001i
\(453\) −16.8366 10.8202i −0.791054 0.508380i
\(454\) 0.750400 0.220337i 0.0352180 0.0103409i
\(455\) −2.16741 2.50132i −0.101610 0.117264i
\(456\) −2.50714 0.736163i −0.117408 0.0344740i
\(457\) −1.12972 2.47375i −0.0528463 0.115717i 0.881367 0.472432i \(-0.156624\pi\)
−0.934213 + 0.356715i \(0.883897\pi\)
\(458\) 0.105195 0.731650i 0.00491546 0.0341877i
\(459\) 21.7954 1.01732
\(460\) −9.37648 1.83521i −0.437181 0.0855672i
\(461\) −35.7457 −1.66484 −0.832421 0.554143i \(-0.813046\pi\)
−0.832421 + 0.554143i \(0.813046\pi\)
\(462\) 0.0394651 0.274486i 0.00183608 0.0127702i
\(463\) −17.3020 37.8860i −0.804091 1.76071i −0.630961 0.775814i \(-0.717339\pi\)
−0.173130 0.984899i \(-0.555388\pi\)
\(464\) −17.0041 4.99286i −0.789397 0.231788i
\(465\) 0.593245 + 0.684641i 0.0275111 + 0.0317495i
\(466\) 2.03119 0.596411i 0.0940931 0.0276282i
\(467\) 14.8682 + 9.55519i 0.688017 + 0.442161i 0.837380 0.546621i \(-0.184086\pi\)
−0.149364 + 0.988782i \(0.547722\pi\)
\(468\) 3.54305 7.75819i 0.163777 0.358623i
\(469\) −1.98938 + 2.29587i −0.0918610 + 0.106013i
\(470\) 0.202331 0.130030i 0.00933284 0.00599785i
\(471\) 0.821781 + 5.71561i 0.0378657 + 0.263361i
\(472\) 0.401733 + 2.79411i 0.0184913 + 0.128609i
\(473\) −9.23343 + 5.93396i −0.424553 + 0.272844i
\(474\) 0.185866 0.214501i 0.00853712 0.00985237i
\(475\) 3.08427 6.75361i 0.141516 0.309877i
\(476\) 11.2961 + 7.25953i 0.517754 + 0.332740i
\(477\) −0.526324 + 0.154543i −0.0240987 + 0.00707602i
\(478\) 0.648752 + 0.748699i 0.0296732 + 0.0342447i
\(479\) 11.4723 + 3.36858i 0.524184 + 0.153914i 0.533110 0.846046i \(-0.321023\pi\)
−0.00892633 + 0.999960i \(0.502841\pi\)
\(480\) 0.437181 + 0.957293i 0.0199545 + 0.0436942i
\(481\) 3.37991 23.5078i 0.154111 1.07186i
\(482\) −2.47780 −0.112861
\(483\) −5.35195 5.13260i −0.243522 0.233541i
\(484\) 13.6687 0.621306
\(485\) −0.788543 + 5.48444i −0.0358059 + 0.249036i
\(486\) −0.585941 1.28303i −0.0265788 0.0581995i
\(487\) 18.1024 + 5.31536i 0.820300 + 0.240862i 0.664845 0.746981i \(-0.268497\pi\)
0.155455 + 0.987843i \(0.450316\pi\)
\(488\) −0.741863 0.856156i −0.0335826 0.0387563i
\(489\) 8.44701 2.48026i 0.381987 0.112161i
\(490\) 0.341830 + 0.219681i 0.0154423 + 0.00992416i
\(491\) 9.10363 19.9342i 0.410841 0.899616i −0.585214 0.810879i \(-0.698990\pi\)
0.996055 0.0887373i \(-0.0282832\pi\)
\(492\) 7.88425 9.09891i 0.355450 0.410211i
\(493\) 16.4384 10.5643i 0.740349 0.475794i
\(494\) −0.199387 1.38677i −0.00897086 0.0623937i
\(495\) 0.579064 + 4.02748i 0.0260270 + 0.181022i
\(496\) −3.01291 + 1.93628i −0.135284 + 0.0869416i
\(497\) −11.2912 + 13.0308i −0.506480 + 0.584509i
\(498\) 0.159693 0.349679i 0.00715602 0.0156695i
\(499\) 8.48768 + 5.45470i 0.379961 + 0.244186i 0.716655 0.697428i \(-0.245672\pi\)
−0.336694 + 0.941614i \(0.609309\pi\)
\(500\) −1.91153 + 0.561276i −0.0854862 + 0.0251010i
\(501\) −12.7879 14.7581i −0.571323 0.659341i
\(502\) 2.32553 + 0.682837i 0.103793 + 0.0304765i
\(503\) 5.56885 + 12.1941i 0.248303 + 0.543707i 0.992210 0.124576i \(-0.0397569\pi\)
−0.743907 + 0.668283i \(0.767030\pi\)
\(504\) 0.154886 1.07726i 0.00689918 0.0479849i
\(505\) −4.49768 −0.200144
\(506\) 0.500939 0.699196i 0.0222694 0.0310831i
\(507\) 8.41804 0.373858
\(508\) −4.97451 + 34.5985i −0.220708 + 1.53506i
\(509\) 8.03460 + 17.5933i 0.356127 + 0.779810i 0.999894 + 0.0145879i \(0.00464363\pi\)
−0.643766 + 0.765222i \(0.722629\pi\)
\(510\) −0.368713 0.108264i −0.0163269 0.00479400i
\(511\) −10.5006 12.1183i −0.464518 0.536082i
\(512\) −6.66205 + 1.95615i −0.294424 + 0.0864506i
\(513\) 31.2297 + 20.0701i 1.37882 + 0.886116i
\(514\) 0.650495 1.42439i 0.0286921 0.0628270i
\(515\) 6.37367 7.35561i 0.280858 0.324127i
\(516\) 9.04182 5.81083i 0.398044 0.255807i
\(517\) −0.789915 5.49398i −0.0347404 0.241625i
\(518\) −0.215227 1.49694i −0.00945652 0.0657716i
\(519\) −18.1562 + 11.6683i −0.796970 + 0.512182i
\(520\) −0.493335 + 0.569338i −0.0216342 + 0.0249671i
\(521\) −4.67119 + 10.2285i −0.204648 + 0.448117i −0.983930 0.178557i \(-0.942857\pi\)
0.779281 + 0.626674i \(0.215584\pi\)
\(522\) −0.664885 0.427296i −0.0291012 0.0187022i
\(523\) 17.3487 5.09404i 0.758605 0.222747i 0.120519 0.992711i \(-0.461544\pi\)
0.638087 + 0.769964i \(0.279726\pi\)
\(524\) −17.0228 19.6454i −0.743645 0.858212i
\(525\) −1.48357 0.435615i −0.0647482 0.0190118i
\(526\) −0.320098 0.700917i −0.0139569 0.0305614i
\(527\) 0.561992 3.90874i 0.0244808 0.170267i
\(528\) 8.04304 0.350028
\(529\) −7.39715 21.7780i −0.321615 0.946870i
\(530\) 0.0241787 0.00105026
\(531\) 2.28297 15.8784i 0.0990725 0.689064i
\(532\) 9.50074 + 20.8037i 0.411909 + 0.901955i
\(533\) 12.4119 + 3.64448i 0.537621 + 0.157860i
\(534\) 0.0370854 + 0.0427988i 0.00160484 + 0.00185209i
\(535\) −7.09714 + 2.08391i −0.306836 + 0.0900952i
\(536\) 0.581697 + 0.373834i 0.0251255 + 0.0161472i
\(537\) 6.37863 13.9672i 0.275258 0.602731i
\(538\) −0.169194 + 0.195260i −0.00729445 + 0.00841825i
\(539\) 7.88869 5.06975i 0.339790 0.218370i
\(540\) −1.41762 9.85975i −0.0610046 0.424296i
\(541\) 1.97456 + 13.7333i 0.0848928 + 0.590442i 0.987217 + 0.159384i \(0.0509507\pi\)
−0.902324 + 0.431059i \(0.858140\pi\)
\(542\) −0.486530 + 0.312674i −0.0208983 + 0.0134305i
\(543\) 0.536306 0.618931i 0.0230151 0.0265609i
\(544\) 1.90571 4.17292i 0.0817065 0.178912i
\(545\) −8.75918 5.62918i −0.375202 0.241128i
\(546\) −0.279953 + 0.0822015i −0.0119809 + 0.00351790i
\(547\) 19.7384 + 22.7793i 0.843952 + 0.973973i 0.999905 0.0137919i \(-0.00439025\pi\)
−0.155953 + 0.987764i \(0.549845\pi\)
\(548\) 41.1491 + 12.0825i 1.75780 + 0.516138i
\(549\) 2.67436 + 5.85603i 0.114139 + 0.249929i
\(550\) 0.0255239 0.177523i 0.00108834 0.00756960i
\(551\) 33.2819 1.41786
\(552\) −0.983001 + 1.37204i −0.0418393 + 0.0583981i
\(553\) −4.97813 −0.211692
\(554\) 0.285906 1.98852i 0.0121470 0.0844840i
\(555\) −4.60905 10.0924i −0.195643 0.428399i
\(556\) −31.2953 9.18913i −1.32722 0.389706i
\(557\) −14.1622 16.3440i −0.600071 0.692519i 0.371724 0.928343i \(-0.378767\pi\)
−0.971796 + 0.235824i \(0.924221\pi\)
\(558\) −0.153253 + 0.0449991i −0.00648771 + 0.00190496i
\(559\) 9.71499 + 6.24345i 0.410900 + 0.264070i
\(560\) 2.53935 5.56040i 0.107307 0.234970i
\(561\) −5.80751 + 6.70222i −0.245193 + 0.282968i
\(562\) −1.05631 + 0.678850i −0.0445578 + 0.0286356i
\(563\) −0.0407395 0.283349i −0.00171696 0.0119418i 0.988945 0.148283i \(-0.0473747\pi\)
−0.990662 + 0.136341i \(0.956466\pi\)
\(564\) 0.773524 + 5.37998i 0.0325712 + 0.226538i
\(565\) −16.4820 + 10.5923i −0.693402 + 0.445622i
\(566\) −1.36864 + 1.57949i −0.0575281 + 0.0663910i
\(567\) −0.642315 + 1.40647i −0.0269747 + 0.0590663i
\(568\) 3.30156 + 2.12179i 0.138531 + 0.0890282i
\(569\) 1.66147 0.487852i 0.0696525 0.0204518i −0.246721 0.969087i \(-0.579353\pi\)
0.316373 + 0.948635i \(0.397535\pi\)
\(570\) −0.428618 0.494652i −0.0179528 0.0207187i
\(571\) −19.8922 5.84086i −0.832461 0.244433i −0.162387 0.986727i \(-0.551919\pi\)
−0.670074 + 0.742295i \(0.733738\pi\)
\(572\) 3.60407 + 7.89181i 0.150694 + 0.329973i
\(573\) −0.607097 + 4.22245i −0.0253618 + 0.176395i
\(574\) 0.823739 0.0343822
\(575\) −3.46135 3.31949i −0.144348 0.138432i
\(576\) 15.6282 0.651174
\(577\) −3.43290 + 23.8763i −0.142913 + 0.993985i 0.784549 + 0.620067i \(0.212895\pi\)
−0.927462 + 0.373917i \(0.878014\pi\)
\(578\) 0.0733005 + 0.160506i 0.00304890 + 0.00667616i
\(579\) 4.63848 + 1.36198i 0.192769 + 0.0566020i
\(580\) −5.84826 6.74925i −0.242836 0.280247i
\(581\) −6.46934 + 1.89957i −0.268394 + 0.0788074i
\(582\) 0.410917 + 0.264080i 0.0170330 + 0.0109465i
\(583\) 0.231798 0.507567i 0.00960009 0.0210213i
\(584\) −2.39009 + 2.75831i −0.0989026 + 0.114140i
\(585\) 3.60149 2.31454i 0.148903 0.0956944i
\(586\) 0.0536241 + 0.372964i 0.00221519 + 0.0154070i
\(587\) 4.77952 + 33.2423i 0.197272 + 1.37206i 0.812157 + 0.583439i \(0.198293\pi\)
−0.614885 + 0.788617i \(0.710798\pi\)
\(588\) −7.72499 + 4.96455i −0.318573 + 0.204734i
\(589\) 4.40458 5.08316i 0.181488 0.209448i
\(590\) −0.293734 + 0.643187i −0.0120928 + 0.0264796i
\(591\) 0.220925 + 0.141980i 0.00908764 + 0.00584027i
\(592\) 42.0867 12.3578i 1.72975 0.507901i
\(593\) −19.5470 22.5585i −0.802700 0.926365i 0.195827 0.980639i \(-0.437261\pi\)
−0.998526 + 0.0542739i \(0.982716\pi\)
\(594\) 0.860418 + 0.252641i 0.0353034 + 0.0103660i
\(595\) 2.79990 + 6.13093i 0.114785 + 0.251344i
\(596\) 5.47807 38.1008i 0.224391 1.56067i
\(597\) 4.32625 0.177062
\(598\) −0.888133 0.173830i −0.0363185 0.00710843i
\(599\) 4.70186 0.192113 0.0960564 0.995376i \(-0.469377\pi\)
0.0960564 + 0.995376i \(0.469377\pi\)
\(600\) −0.0500861 + 0.348356i −0.00204476 + 0.0142216i
\(601\) 8.89729 + 19.4823i 0.362928 + 0.794701i 0.999720 + 0.0236658i \(0.00753375\pi\)
−0.636792 + 0.771036i \(0.719739\pi\)
\(602\) 0.705584 + 0.207178i 0.0287575 + 0.00844395i
\(603\) −2.57325 2.96969i −0.104791 0.120935i
\(604\) 38.2569 11.2332i 1.55665 0.457073i
\(605\) 5.77187 + 3.70935i 0.234660 + 0.150807i
\(606\) −0.164711 + 0.360666i −0.00669091 + 0.0146511i
\(607\) 25.2756 29.1696i 1.02591 1.18396i 0.0431477 0.999069i \(-0.486261\pi\)
0.982759 0.184891i \(-0.0591932\pi\)
\(608\) 6.57319 4.22433i 0.266578 0.171319i
\(609\) −0.986403 6.86058i −0.0399711 0.278005i
\(610\) −0.0403840 0.280877i −0.00163510 0.0113724i
\(611\) −4.91289 + 3.15732i −0.198754 + 0.127732i
\(612\) −11.3740 + 13.1263i −0.459766 + 0.530599i
\(613\) 7.81638 17.1155i 0.315700 0.691288i −0.683554 0.729900i \(-0.739567\pi\)
0.999254 + 0.0386125i \(0.0122938\pi\)
\(614\) −0.663370 0.426322i −0.0267714 0.0172050i
\(615\) 5.79848 1.70259i 0.233817 0.0686550i
\(616\) 0.724983 + 0.836675i 0.0292104 + 0.0337106i
\(617\) −15.2099 4.46602i −0.612326 0.179795i −0.0391580 0.999233i \(-0.512468\pi\)
−0.573168 + 0.819438i \(0.694286\pi\)
\(618\) −0.356430 0.780473i −0.0143377 0.0313952i
\(619\) 4.22984 29.4192i 0.170012 1.18246i −0.708842 0.705367i \(-0.750782\pi\)
0.878854 0.477091i \(-0.158309\pi\)
\(620\) −1.80478 −0.0724817
\(621\) 18.8915 14.7685i 0.758091 0.592641i
\(622\) −2.05794 −0.0825158
\(623\) 0.141357 0.983162i 0.00566336 0.0393896i
\(624\) −3.51546 7.69778i −0.140731 0.308158i
\(625\) −0.959493 0.281733i −0.0383797 0.0112693i
\(626\) 1.29956 + 1.49977i 0.0519408 + 0.0599429i
\(627\) −14.4930 + 4.25553i −0.578794 + 0.169949i
\(628\) −9.67769 6.21947i −0.386182 0.248184i
\(629\) −20.0912 + 43.9936i −0.801089 + 1.75414i
\(630\) 0.178524 0.206027i 0.00711256 0.00820833i
\(631\) −14.0318 + 9.01768i −0.558597 + 0.358988i −0.789273 0.614042i \(-0.789542\pi\)
0.230677 + 0.973030i \(0.425906\pi\)
\(632\) 0.161257 + 1.12156i 0.00641444 + 0.0446134i
\(633\) −0.934652 6.50065i −0.0371491 0.258378i
\(634\) 0.945584 0.607690i 0.0375539 0.0241345i
\(635\) −11.4897 + 13.2599i −0.455956 + 0.526202i
\(636\) −0.226988 + 0.497034i −0.00900066 + 0.0197087i
\(637\) −8.30012 5.33416i −0.328863 0.211347i
\(638\) 0.771397 0.226502i 0.0305399 0.00896732i
\(639\) −14.6051 16.8552i −0.577769 0.666781i
\(640\) −2.68049 0.787062i −0.105956 0.0311114i
\(641\) −12.5542 27.4898i −0.495859 1.08578i −0.977793 0.209573i \(-0.932793\pi\)
0.481934 0.876208i \(-0.339935\pi\)
\(642\) −0.0927990 + 0.645431i −0.00366248 + 0.0254731i
\(643\) −7.45857 −0.294137 −0.147069 0.989126i \(-0.546984\pi\)
−0.147069 + 0.989126i \(0.546984\pi\)
\(644\) 14.7101 1.36187i 0.579659 0.0536653i
\(645\) 5.39498 0.212427
\(646\) −0.406038 + 2.82406i −0.0159754 + 0.111111i
\(647\) 3.17102 + 6.94356i 0.124666 + 0.272980i 0.961666 0.274222i \(-0.0884204\pi\)
−0.837001 + 0.547202i \(0.815693\pi\)
\(648\) 0.337683 + 0.0991526i 0.0132654 + 0.00389508i
\(649\) 10.6860 + 12.3323i 0.419462 + 0.484085i
\(650\) −0.181059 + 0.0531636i −0.00710170 + 0.00208525i
\(651\) −1.17836 0.757286i −0.0461836 0.0296804i
\(652\) −7.28589 + 15.9539i −0.285337 + 0.624802i
\(653\) −25.4564 + 29.3782i −0.996185 + 1.14966i −0.00745135 + 0.999972i \(0.502372\pi\)
−0.988734 + 0.149686i \(0.952174\pi\)
\(654\) −0.772173 + 0.496246i −0.0301944 + 0.0194047i
\(655\) −1.85692 12.9152i −0.0725559 0.504637i
\(656\) 3.40014 + 23.6485i 0.132753 + 0.923319i
\(657\) 17.4484 11.2134i 0.680726 0.437476i
\(658\) −0.243529 + 0.281047i −0.00949374 + 0.0109564i
\(659\) −5.38310 + 11.7873i −0.209696 + 0.459170i −0.985030 0.172381i \(-0.944854\pi\)
0.775335 + 0.631551i \(0.217581\pi\)
\(660\) 3.40967 + 2.19126i 0.132721 + 0.0852947i
\(661\) 28.9778 8.50866i 1.12711 0.330949i 0.335537 0.942027i \(-0.391082\pi\)
0.791570 + 0.611078i \(0.209264\pi\)
\(662\) 0.946639 + 1.09248i 0.0367922 + 0.0424604i
\(663\) 8.95287 + 2.62880i 0.347701 + 0.102094i
\(664\) 0.637531 + 1.39600i 0.0247410 + 0.0541753i
\(665\) −1.63375 + 11.3630i −0.0633542 + 0.440638i
\(666\) 1.95619 0.0758007
\(667\) 7.08990 20.2955i 0.274522 0.785844i
\(668\) 38.9037 1.50523
\(669\) −1.31033 + 9.11356i −0.0506604 + 0.352351i
\(670\) 0.0719509 + 0.157551i 0.00277971 + 0.00608671i
\(671\) −6.28342 1.84498i −0.242569 0.0712246i
\(672\) −1.06560 1.22977i −0.0411064 0.0474393i
\(673\) 2.27218 0.667173i 0.0875862 0.0257176i −0.237646 0.971352i \(-0.576376\pi\)
0.325232 + 0.945634i \(0.394558\pi\)
\(674\) 2.03488 + 1.30773i 0.0783805 + 0.0503721i
\(675\) 2.07708 4.54816i 0.0799467 0.175059i
\(676\) −10.9824 + 12.6744i −0.422402 + 0.487478i
\(677\) −29.1912 + 18.7600i −1.12191 + 0.721006i −0.963856 0.266425i \(-0.914158\pi\)
−0.158052 + 0.987431i \(0.550521\pi\)
\(678\) 0.245801 + 1.70958i 0.00943993 + 0.0656562i
\(679\) −1.21925 8.48004i −0.0467904 0.325434i
\(680\) 1.29059 0.829413i 0.0494919 0.0318065i
\(681\) −5.80963 + 6.70467i −0.222626 + 0.256924i
\(682\) 0.0674940 0.147791i 0.00258448 0.00565922i
\(683\) −19.5711 12.5776i −0.748869 0.481269i 0.109702 0.993965i \(-0.465010\pi\)
−0.858570 + 0.512696i \(0.828647\pi\)
\(684\) −28.3845 + 8.33444i −1.08531 + 0.318675i
\(685\) 14.0971 + 16.2689i 0.538621 + 0.621602i
\(686\) −1.51832 0.445819i −0.0579698 0.0170215i
\(687\) 3.48319 + 7.62712i 0.132892 + 0.290993i
\(688\) −3.03539 + 21.1116i −0.115723 + 0.804872i
\(689\) −0.587093 −0.0223665
\(690\) −0.392948 + 0.156000i −0.0149593 + 0.00593882i
\(691\) −45.0096 −1.71225 −0.856123 0.516772i \(-0.827133\pi\)
−0.856123 + 0.516772i \(0.827133\pi\)
\(692\) 6.11911 42.5593i 0.232614 1.61786i
\(693\) −2.61351 5.72279i −0.0992790 0.217391i
\(694\) −0.510520 0.149902i −0.0193791 0.00569020i
\(695\) −10.7213 12.3730i −0.406682 0.469336i
\(696\) −1.51372 + 0.444470i −0.0573776 + 0.0168476i
\(697\) −22.1612 14.2422i −0.839417 0.539461i
\(698\) 0.305688 0.669363i 0.0115705 0.0253358i
\(699\) −15.7256 + 18.1483i −0.594796 + 0.686431i
\(700\) 2.59138 1.66538i 0.0979451 0.0629455i
\(701\) −3.34738 23.2815i −0.126429 0.879332i −0.950029 0.312161i \(-0.898947\pi\)
0.823600 0.567171i \(-0.191962\pi\)
\(702\) −0.134276 0.933908i −0.00506791 0.0352481i
\(703\) −69.2989 + 44.5357i −2.61366 + 1.67969i
\(704\) −10.4105 + 12.0144i −0.392362 + 0.452810i
\(705\) −1.13336 + 2.48170i −0.0426847 + 0.0934664i
\(706\) −1.93952 1.24645i −0.0729946 0.0469108i
\(707\) 6.67261 1.95925i 0.250949 0.0736854i
\(708\) −10.4643 12.0764i −0.393271 0.453859i
\(709\) 32.8793 + 9.65422i 1.23481 + 0.362572i 0.833062 0.553180i \(-0.186586\pi\)
0.401745 + 0.915752i \(0.368404\pi\)
\(710\) 0.408375 + 0.894217i 0.0153261 + 0.0335594i
\(711\) 0.916390 6.37363i 0.0343673 0.239030i
\(712\) −0.226084 −0.00847285
\(713\) −2.16144 3.76877i −0.0809467 0.141142i
\(714\) 0.594172 0.0222363
\(715\) −0.619758 + 4.31051i −0.0231776 + 0.161204i
\(716\) 12.7077 + 27.8260i 0.474909 + 1.03990i
\(717\) −10.7825 3.16603i −0.402680 0.118238i
\(718\) −0.326770 0.377112i −0.0121949 0.0140737i
\(719\) −22.3827 + 6.57217i −0.834735 + 0.245100i −0.671050 0.741412i \(-0.734156\pi\)
−0.163685 + 0.986513i \(0.552338\pi\)
\(720\) 6.65168 + 4.27477i 0.247893 + 0.159311i
\(721\) −6.25157 + 13.6890i −0.232821 + 0.509806i
\(722\) −2.08543 + 2.40672i −0.0776117 + 0.0895687i
\(723\) 23.6451 15.1958i 0.879371 0.565138i
\(724\) 0.232195 + 1.61495i 0.00862947 + 0.0600193i
\(725\) −0.637953 4.43706i −0.0236930 0.164788i
\(726\) 0.508824 0.327001i 0.0188842 0.0121362i
\(727\) −26.3834 + 30.4481i −0.978507 + 1.12926i 0.0130932 + 0.999914i \(0.495832\pi\)
−0.991600 + 0.129343i \(0.958713\pi\)
\(728\) 0.483883 1.05956i 0.0179339 0.0392698i
\(729\) 10.9363 + 7.02833i 0.405048 + 0.260309i
\(730\) −0.877186 + 0.257565i −0.0324661 + 0.00953291i
\(731\) −15.4005 17.7731i −0.569607 0.657361i
\(732\) 6.15303 + 1.80669i 0.227422 + 0.0667773i
\(733\) −9.43781 20.6659i −0.348594 0.763313i −0.999990 0.00457542i \(-0.998544\pi\)
0.651396 0.758738i \(-0.274184\pi\)
\(734\) 0.154499 1.07456i 0.00570266 0.0396629i
\(735\) −4.60926 −0.170015
\(736\) −1.17576 4.90825i −0.0433391 0.180921i
\(737\) 3.99714 0.147236
\(738\) −0.151637 + 1.05466i −0.00558182 + 0.0388224i
\(739\) −7.47356 16.3648i −0.274919 0.601989i 0.720930 0.693008i \(-0.243715\pi\)
−0.995849 + 0.0910188i \(0.970988\pi\)
\(740\) 21.2085 + 6.22738i 0.779640 + 0.228923i
\(741\) 10.4075 + 12.0109i 0.382328 + 0.441230i
\(742\) −0.0358708 + 0.0105326i −0.00131686 + 0.000386664i
\(743\) −4.89833 3.14797i −0.179702 0.115488i 0.447697 0.894185i \(-0.352244\pi\)
−0.627399 + 0.778698i \(0.715881\pi\)
\(744\) −0.132445 + 0.290013i −0.00485566 + 0.0106324i
\(745\) 12.6528 14.6021i 0.463563 0.534981i
\(746\) 2.16002 1.38816i 0.0790840 0.0508242i
\(747\) −1.24117 8.63256i −0.0454122 0.315849i
\(748\) −2.51438 17.4879i −0.0919347 0.639420i
\(749\) 9.62131 6.18324i 0.351555 0.225931i
\(750\) −0.0577299 + 0.0666238i −0.00210800 + 0.00243276i
\(751\) 3.84740 8.42462i 0.140393 0.307419i −0.826354 0.563151i \(-0.809589\pi\)
0.966748 + 0.255732i \(0.0823164\pi\)
\(752\) −9.07372 5.83133i −0.330885 0.212647i
\(753\) −26.3797 + 7.74578i −0.961330 + 0.282272i
\(754\) −0.553942 0.639283i −0.0201734 0.0232813i
\(755\) 19.2030 + 5.63852i 0.698870 + 0.205207i
\(756\) 6.39819 + 14.0101i 0.232700 + 0.509542i
\(757\) 1.15607 8.04064i 0.0420180 0.292242i −0.957968 0.286877i \(-0.907383\pi\)
0.999986 0.00536536i \(-0.00170786\pi\)
\(758\) −2.94048 −0.106803
\(759\) −0.492336 + 9.74443i −0.0178707 + 0.353700i
\(760\) 2.61299 0.0947830
\(761\) −4.15984 + 28.9323i −0.150794 + 1.04880i 0.764099 + 0.645099i \(0.223184\pi\)
−0.914893 + 0.403697i \(0.867725\pi\)
\(762\) 0.642532 + 1.40695i 0.0232765 + 0.0509684i
\(763\) 15.4470 + 4.53565i 0.559219 + 0.164201i
\(764\) −5.56539 6.42281i −0.201349 0.232369i
\(765\) −8.36501 + 2.45619i −0.302438 + 0.0888037i
\(766\) 2.30544 + 1.48162i 0.0832990 + 0.0535330i
\(767\) 7.13228 15.6175i 0.257532 0.563915i
\(768\) 10.0730 11.6249i 0.363478 0.419476i
\(769\) 12.2803 7.89208i 0.442840 0.284596i −0.300158 0.953889i \(-0.597040\pi\)
0.742998 + 0.669294i \(0.233403\pi\)
\(770\) 0.0394651 + 0.274486i 0.00142222 + 0.00989179i
\(771\) 2.52790 + 17.5820i 0.0910403 + 0.633199i
\(772\) −8.10215 + 5.20693i −0.291603 + 0.187402i
\(773\) 11.3054 13.0471i 0.406625 0.469271i −0.515091 0.857136i \(-0.672242\pi\)
0.921716 + 0.387865i \(0.126787\pi\)
\(774\) −0.395142 + 0.865241i −0.0142031 + 0.0311004i
\(775\) −0.762100 0.489772i −0.0273755 0.0175931i
\(776\) −1.87104 + 0.549388i −0.0671666 + 0.0197219i
\(777\) 11.2342 + 12.9650i 0.403026 + 0.465117i
\(778\) 1.07306 + 0.315080i 0.0384712 + 0.0112962i
\(779\) −18.6391 40.8139i −0.667815 1.46231i
\(780\) 0.606897 4.22106i 0.0217304 0.151138i
\(781\) 22.6867 0.811795
\(782\) 1.63563 + 0.849200i 0.0584899 + 0.0303673i
\(783\) 22.4134 0.800991
\(784\) 2.59332 18.0369i 0.0926186 0.644176i
\(785\) −2.39877 5.25257i −0.0856156 0.187472i
\(786\) −1.10366 0.324065i −0.0393663 0.0115590i
\(787\) −10.0471 11.5950i −0.358142 0.413318i 0.547875 0.836561i \(-0.315437\pi\)
−0.906016 + 0.423243i \(0.860892\pi\)
\(788\) −0.501995 + 0.147399i −0.0178828 + 0.00525087i
\(789\) 7.35320 + 4.72561i 0.261781 + 0.168236i
\(790\) −0.117905 + 0.258177i −0.00419489 + 0.00918553i
\(791\) 19.8380 22.8942i 0.705356 0.814025i
\(792\) −1.20467 + 0.774198i −0.0428063 + 0.0275099i
\(793\) 0.980582 + 6.82010i 0.0348215 + 0.242189i
\(794\) −0.154578 1.07511i −0.00548577 0.0381544i
\(795\) −0.230732 + 0.148283i −0.00818323 + 0.00525904i
\(796\) −5.64417 + 6.51371i −0.200052 + 0.230872i
\(797\) 10.4360 22.8517i 0.369663 0.809448i −0.629803 0.776755i \(-0.716864\pi\)
0.999465 0.0326932i \(-0.0104084\pi\)
\(798\) 0.851362 + 0.547137i 0.0301379 + 0.0193685i
\(799\) 11.4109 3.35055i 0.403690 0.118534i
\(800\) −0.689173 0.795348i −0.0243659 0.0281198i
\(801\) 1.23275 + 0.361967i 0.0435570 + 0.0127895i
\(802\) −1.23584 2.70612i −0.0436392 0.0955565i
\(803\) −3.00258 + 20.8834i −0.105959 + 0.736959i
\(804\) −3.91419 −0.138043
\(805\) 6.58118 + 3.41688i 0.231956 + 0.120429i
\(806\) −0.170947 −0.00602136
\(807\) 0.417094 2.90095i 0.0146824 0.102118i
\(808\) −0.657563 1.43986i −0.0231330 0.0506542i
\(809\) −21.8919 6.42804i −0.769678 0.225998i −0.126761 0.991933i \(-0.540458\pi\)
−0.642917 + 0.765935i \(0.722276\pi\)
\(810\) 0.0577299 + 0.0666238i 0.00202842 + 0.00234092i
\(811\) 41.7803 12.2678i 1.46711 0.430781i 0.551949 0.833878i \(-0.313884\pi\)
0.915157 + 0.403097i \(0.132066\pi\)
\(812\) 11.6164 + 7.46538i 0.407654 + 0.261984i
\(813\) 2.72530 5.96757i 0.0955803 0.209292i
\(814\) −1.30309 + 1.50385i −0.0456734 + 0.0527099i
\(815\) −7.40607 + 4.75959i −0.259423 + 0.166721i
\(816\) 2.45256 + 17.0579i 0.0858567 + 0.597147i
\(817\) −5.70046 39.6476i −0.199434 1.38709i
\(818\) 1.20400 0.773766i 0.0420970 0.0270541i
\(819\) −4.33481 + 5.00264i −0.151471 + 0.174806i
\(820\) −5.00143 + 10.9516i −0.174657 + 0.382446i
\(821\) 40.9122 + 26.2927i 1.42785 + 0.917621i 0.999905 + 0.0138148i \(0.00439753\pi\)
0.427942 + 0.903806i \(0.359239\pi\)
\(822\) 1.82085 0.534648i 0.0635093 0.0186480i
\(823\) −0.752583 0.868528i −0.0262334 0.0302750i 0.742481 0.669867i \(-0.233649\pi\)
−0.768715 + 0.639592i \(0.779103\pi\)
\(824\) 3.28662 + 0.965039i 0.114495 + 0.0336187i
\(825\) 0.845139 + 1.85060i 0.0294240 + 0.0644295i
\(826\) 0.155592 1.08217i 0.00541374 0.0376534i
\(827\) −15.3873 −0.535069 −0.267534 0.963548i \(-0.586209\pi\)
−0.267534 + 0.963548i \(0.586209\pi\)
\(828\) −0.964240 + 19.0844i −0.0335096 + 0.663230i
\(829\) −43.7168 −1.51835 −0.759174 0.650888i \(-0.774397\pi\)
−0.759174 + 0.650888i \(0.774397\pi\)
\(830\) −0.0547084 + 0.380505i −0.00189896 + 0.0132075i
\(831\) 9.46680 + 20.7294i 0.328400 + 0.719095i
\(832\) 16.0489 + 4.71239i 0.556396 + 0.163373i
\(833\) 13.1576 + 15.1846i 0.455883 + 0.526117i
\(834\) −1.38481 + 0.406618i −0.0479522 + 0.0140800i
\(835\) 16.4278 + 10.5575i 0.568506 + 0.365357i
\(836\) 12.5008 27.3729i 0.432349 0.946712i
\(837\) 2.96623 3.42321i 0.102528 0.118323i
\(838\) −0.992833 + 0.638055i −0.0342969 + 0.0220413i
\(839\) 1.60650 + 11.1735i 0.0554627 + 0.385751i 0.998579 + 0.0532888i \(0.0169704\pi\)
−0.943116 + 0.332462i \(0.892121\pi\)
\(840\) −0.0774431 0.538629i −0.00267204 0.0185845i
\(841\) −7.49181 + 4.81469i −0.258338 + 0.166024i
\(842\) 0.751277 0.867020i 0.0258907 0.0298795i
\(843\) 5.91692 12.9563i 0.203790 0.446237i
\(844\) 11.0069 + 7.07372i 0.378874 + 0.243488i
\(845\) −8.07705 + 2.37164i −0.277859 + 0.0815867i
\(846\) −0.315003 0.363533i −0.0108300 0.0124985i
\(847\) −10.1788 2.98877i −0.349748 0.102695i
\(848\) −0.450441 0.986328i −0.0154682 0.0338707i
\(849\) 3.37394 23.4663i 0.115793 0.805361i
\(850\) 0.384279 0.0131807
\(851\) 12.3956 + 51.7460i 0.424917 + 1.77383i
\(852\) −22.2160 −0.761106
\(853\) −2.37985 + 16.5522i −0.0814845 + 0.566737i 0.907651 + 0.419727i \(0.137874\pi\)
−0.989135 + 0.147010i \(0.953035\pi\)
\(854\) 0.182267 + 0.399108i 0.00623704 + 0.0136572i
\(855\) −14.2476 4.18348i −0.487258 0.143072i
\(856\) −1.70474 1.96737i −0.0582667 0.0672433i
\(857\) −5.93618 + 1.74302i −0.202776 + 0.0595405i −0.381543 0.924351i \(-0.624607\pi\)
0.178767 + 0.983891i \(0.442789\pi\)
\(858\) 0.322961 + 0.207554i 0.0110257 + 0.00708579i
\(859\) −3.60612 + 7.89631i −0.123039 + 0.269419i −0.961122 0.276125i \(-0.910950\pi\)
0.838082 + 0.545544i \(0.183677\pi\)
\(860\) −7.03847 + 8.12282i −0.240010 + 0.276986i
\(861\) −7.86077 + 5.05181i −0.267894 + 0.172165i
\(862\) −0.117416 0.816646i −0.00399921 0.0278151i
\(863\) −1.61006 11.1982i −0.0548072 0.381192i −0.998701 0.0509446i \(-0.983777\pi\)
0.943894 0.330248i \(-0.107132\pi\)
\(864\) 4.42666 2.84484i 0.150598 0.0967834i
\(865\) 14.1334 16.3109i 0.480551 0.554586i
\(866\) −1.24386 + 2.72368i −0.0422682 + 0.0925546i
\(867\) −1.68384 1.08214i −0.0571861 0.0367513i
\(868\) 2.67752 0.786189i 0.0908808 0.0266850i
\(869\) 4.28939 + 4.95022i 0.145508 + 0.167925i
\(870\) −0.379168 0.111334i −0.0128550 0.00377457i
\(871\) −1.74707 3.82555i −0.0591973 0.129624i
\(872\) 0.521499 3.62711i 0.0176602 0.122829i
\(873\) 11.0817 0.375058
\(874\) 1.56164 + 2.72293i 0.0528232 + 0.0921045i
\(875\) 1.54620 0.0522711
\(876\) 2.94027 20.4500i 0.0993426 0.690943i
\(877\) 10.2913 + 22.5349i 0.347514 + 0.760950i 0.999995 + 0.00314460i \(0.00100096\pi\)
−0.652481 + 0.757805i \(0.726272\pi\)
\(878\) −2.69735 0.792013i −0.0910311 0.0267291i
\(879\) −2.79903 3.23025i −0.0944090 0.108954i
\(880\) −7.71724 + 2.26599i −0.260148 + 0.0763864i
\(881\) 28.0492 + 18.0261i 0.945000 + 0.607315i 0.919808 0.392368i \(-0.128344\pi\)
0.0251917 + 0.999683i \(0.491980\pi\)
\(882\) 0.337594 0.739229i 0.0113674 0.0248911i
\(883\) 8.56278 9.88198i 0.288161 0.332555i −0.593150 0.805092i \(-0.702116\pi\)
0.881311 + 0.472537i \(0.156662\pi\)
\(884\) −15.6382 + 10.0501i −0.525969 + 0.338020i
\(885\) −1.14149 7.93921i −0.0383706 0.266874i
\(886\) −0.384017 2.67090i −0.0129013 0.0897305i
\(887\) 18.6668 11.9964i 0.626770 0.402800i −0.188343 0.982103i \(-0.560312\pi\)
0.815112 + 0.579303i \(0.196675\pi\)
\(888\) 2.55708 2.95103i 0.0858101 0.0990301i
\(889\) 11.2696 24.6770i 0.377971 0.827641i
\(890\) −0.0476410 0.0306170i −0.00159693 0.00102628i
\(891\) 1.95204 0.573170i 0.0653957 0.0192019i
\(892\) −12.0121 13.8627i −0.402195 0.464158i
\(893\) 19.4355 + 5.70679i 0.650385 + 0.190970i
\(894\) −0.707574 1.54937i −0.0236648 0.0518187i
\(895\) −2.18522 + 15.1985i −0.0730439 + 0.508031i
\(896\) 4.31954 0.144306
\(897\) 9.54133 3.78790i 0.318576 0.126474i
\(898\) −1.48567 −0.0495775
\(899\) 0.577928 4.01958i 0.0192750 0.134060i
\(900\) 1.65520 + 3.62439i 0.0551734 + 0.120813i
\(901\) 1.14714 + 0.336832i 0.0382169 + 0.0112215i
\(902\) −0.709772 0.819121i −0.0236328 0.0272737i
\(903\) −8.00382 + 2.35013i −0.266351 + 0.0782076i
\(904\) −5.80064 3.72784i −0.192926 0.123986i
\(905\) −0.340209 + 0.744955i −0.0113089 + 0.0247631i
\(906\) 1.15539 1.33339i 0.0383853 0.0442990i
\(907\) −18.0240 + 11.5834i −0.598479 + 0.384619i −0.804521 0.593924i \(-0.797578\pi\)
0.206042 + 0.978543i \(0.433942\pi\)
\(908\) −2.51530 17.4943i −0.0834730 0.580568i
\(909\) 1.28017 + 8.90379i 0.0424606 + 0.295320i
\(910\) 0.245454 0.157744i 0.00813672 0.00522915i
\(911\) 25.5067 29.4363i 0.845076 0.975269i −0.154844 0.987939i \(-0.549488\pi\)
0.999920 + 0.0126696i \(0.00403297\pi\)
\(912\) −12.1935 + 26.6999i −0.403766 + 0.884123i
\(913\) 7.46321 + 4.79631i 0.246996 + 0.158735i
\(914\) 0.230030 0.0675428i 0.00760870 0.00223412i
\(915\) 2.10793 + 2.43268i 0.0696861 + 0.0804221i
\(916\) −16.0279 4.70621i −0.529576 0.155497i
\(917\) 8.38091 + 18.3516i 0.276762 + 0.606024i
\(918\) −0.273443 + 1.90184i −0.00902496 + 0.0627700i
\(919\) 29.9408 0.987657 0.493829 0.869559i \(-0.335597\pi\)
0.493829 + 0.869559i \(0.335597\pi\)
\(920\) 0.556632 1.59341i 0.0183516 0.0525332i
\(921\) 8.94494 0.294746
\(922\) 0.448462 3.11912i 0.0147693 0.102723i
\(923\) −9.91594 21.7129i −0.326387 0.714688i
\(924\) −6.01302 1.76558i −0.197814 0.0580834i
\(925\) 7.26571 + 8.38507i 0.238895 + 0.275700i
\(926\) 3.52295 1.03443i 0.115771 0.0339935i
\(927\) −16.3756 10.5240i −0.537846 0.345653i
\(928\) 1.95974 4.29124i 0.0643318 0.140867i
\(929\) 8.14358 9.39819i 0.267182 0.308345i −0.606266 0.795262i \(-0.707333\pi\)
0.873448 + 0.486917i \(0.161879\pi\)
\(930\) −0.0671837 + 0.0431763i −0.00220304 + 0.00141581i
\(931\) 4.87026 + 33.8734i 0.159616 + 1.11016i
\(932\) −6.80843 47.3537i −0.223017 1.55112i
\(933\) 19.6385 12.6209i 0.642934 0.413189i
\(934\) −1.02031 + 1.17750i −0.0333855 + 0.0385289i
\(935\) 3.68403 8.06690i 0.120481 0.263816i
\(936\) 1.26750 + 0.814576i 0.0414297 + 0.0266252i
\(937\) −9.15473 + 2.68807i −0.299072 + 0.0878155i −0.427826 0.903861i \(-0.640720\pi\)
0.128754 + 0.991677i \(0.458902\pi\)
\(938\) −0.175376 0.202394i −0.00572621 0.00660840i
\(939\) −21.5992 6.34209i −0.704863 0.206966i
\(940\) −2.25790 4.94412i −0.0736447 0.161259i
\(941\) 0.484266 3.36814i 0.0157866 0.109798i −0.980405 0.196995i \(-0.936882\pi\)
0.996191 + 0.0871966i \(0.0277908\pi\)
\(942\) −0.509046 −0.0165856
\(943\) −28.8591 + 2.67180i −0.939782 + 0.0870058i
\(944\) 31.7099 1.03207
\(945\) −1.10024 + 7.65231i −0.0357907 + 0.248930i
\(946\) −0.401948 0.880143i −0.0130684 0.0286159i
\(947\) −11.9343 3.50424i −0.387814 0.113872i 0.0820124 0.996631i \(-0.473865\pi\)
−0.469826 + 0.882759i \(0.655683\pi\)
\(948\) −4.20038 4.84750i −0.136422 0.157439i
\(949\) 21.2993 6.25405i 0.691405 0.203015i
\(950\) 0.550616 + 0.353859i 0.0178643 + 0.0114807i
\(951\) −5.29668 + 11.5981i −0.171757 + 0.376095i
\(952\) −1.55338 + 1.79269i −0.0503452 + 0.0581015i
\(953\) 11.2590 7.23572i 0.364715 0.234388i −0.345429 0.938445i \(-0.612266\pi\)
0.710143 + 0.704057i \(0.248630\pi\)
\(954\) −0.00688198 0.0478652i −0.000222812 0.00154969i
\(955\) −0.607097 4.22245i −0.0196452 0.136635i
\(956\) 18.8341 12.1039i 0.609137 0.391469i
\(957\) −5.97219 + 6.89227i −0.193053 + 0.222795i
\(958\) −0.437868 + 0.958797i −0.0141469 + 0.0309773i
\(959\) −28.0009 17.9951i −0.904197 0.581092i
\(960\) 7.49756 2.20148i 0.241983 0.0710526i
\(961\) 19.7633 + 22.8080i 0.637524 + 0.735742i
\(962\) 2.00885 + 0.589852i 0.0647680 + 0.0190176i
\(963\) 6.14545 + 13.4567i 0.198034 + 0.433635i
\(964\) −7.96900 + 55.4256i −0.256664 + 1.78514i
\(965\) −4.83431 −0.155622
\(966\) 0.515009 0.402610i 0.0165701 0.0129538i
\(967\) −24.7635 −0.796341 −0.398170 0.917311i \(-0.630355\pi\)
−0.398170 + 0.917311i \(0.630355\pi\)
\(968\) −0.343642 + 2.39008i −0.0110451 + 0.0768202i
\(969\) −13.4446 29.4395i −0.431902 0.945734i
\(970\) −0.468672 0.137614i −0.0150481 0.00441853i
\(971\) −11.6629 13.4597i −0.374281 0.431944i 0.537092 0.843523i \(-0.319523\pi\)
−0.911374 + 0.411580i \(0.864977\pi\)
\(972\) −30.5845 + 8.98041i −0.980997 + 0.288047i
\(973\) 21.2956 + 13.6859i 0.682707 + 0.438749i
\(974\) −0.690922 + 1.51291i −0.0221386 + 0.0484767i
\(975\) 1.40176 1.61772i 0.0448923 0.0518085i
\(976\) −10.7056 + 6.88004i −0.342676 + 0.220225i
\(977\) −1.03522 7.20015i −0.0331198 0.230353i 0.966538 0.256525i \(-0.0825775\pi\)
−0.999657 + 0.0261716i \(0.991668\pi\)
\(978\) 0.110449 + 0.768191i 0.00353178 + 0.0245640i
\(979\) −1.09945 + 0.706574i −0.0351386 + 0.0225822i
\(980\) 6.01340 6.93983i 0.192091 0.221685i
\(981\) −8.65065 + 18.9423i −0.276194 + 0.604780i
\(982\) 1.62521 + 1.04446i 0.0518627 + 0.0333301i
\(983\) 30.9104 9.07613i 0.985890 0.289483i 0.251236 0.967926i \(-0.419163\pi\)
0.734654 + 0.678442i \(0.237345\pi\)
\(984\) 1.39280 + 1.60738i 0.0444008 + 0.0512412i
\(985\) −0.251976 0.0739870i −0.00802864 0.00235742i
\(986\) 0.715594 + 1.56693i 0.0227892 + 0.0499013i
\(987\) 0.600344 4.17548i 0.0191092 0.132907i
\(988\) −31.6618 −1.00729
\(989\) −25.3916 4.96978i −0.807407 0.158030i
\(990\) −0.358697 −0.0114001
\(991\) −1.54572 + 10.7507i −0.0491013 + 0.341507i 0.950431 + 0.310935i \(0.100642\pi\)
−0.999533 + 0.0305723i \(0.990267\pi\)
\(992\) −0.396047 0.867221i −0.0125745 0.0275343i
\(993\) −15.7335 4.61978i −0.499288 0.146604i
\(994\) −0.995387 1.14874i −0.0315718 0.0364358i
\(995\) −4.15101 + 1.21885i −0.131596 + 0.0386400i
\(996\) −7.30834 4.69678i −0.231574 0.148823i
\(997\) −8.76152 + 19.1851i −0.277480 + 0.607597i −0.996141 0.0877636i \(-0.972028\pi\)
0.718661 + 0.695360i \(0.244755\pi\)
\(998\) −0.582455 + 0.672189i −0.0184373 + 0.0212778i
\(999\) −46.6687 + 29.9922i −1.47653 + 0.948910i
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 115.2.g.a.31.1 yes 10
5.2 odd 4 575.2.p.a.399.1 20
5.3 odd 4 575.2.p.a.399.2 20
5.4 even 2 575.2.k.a.376.1 10
23.3 even 11 inner 115.2.g.a.26.1 10
23.7 odd 22 2645.2.a.o.1.4 5
23.16 even 11 2645.2.a.n.1.4 5
115.3 odd 44 575.2.p.a.49.1 20
115.49 even 22 575.2.k.a.26.1 10
115.72 odd 44 575.2.p.a.49.2 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
115.2.g.a.26.1 10 23.3 even 11 inner
115.2.g.a.31.1 yes 10 1.1 even 1 trivial
575.2.k.a.26.1 10 115.49 even 22
575.2.k.a.376.1 10 5.4 even 2
575.2.p.a.49.1 20 115.3 odd 44
575.2.p.a.49.2 20 115.72 odd 44
575.2.p.a.399.1 20 5.2 odd 4
575.2.p.a.399.2 20 5.3 odd 4
2645.2.a.n.1.4 5 23.16 even 11
2645.2.a.o.1.4 5 23.7 odd 22